tag:blogger.com,1999:blog-39117927947936923662017-07-19T15:18:46.210+02:00Quantum OstinatoPilgrimage of a periphysicist looking for a trace of reality in a maze of quantum speculations staying tuned in to the spectral information provided by physics and noncommutative geometry / Pérégrination d'un périphysicien cherchant la trace du réel dans un dédale de spéculations quantiques, en restant accordé sur l'information spectrale fournie par la physique et la géométrie noncommutativeCédric Bardothttps://plus.google.com/104733107894701960711noreply@blogger.comBlogger228125tag:blogger.com,1999:blog-3911792794793692366.post-82658867244332573442017-07-04T17:17:00.003+02:002017-07-04T17:17:42.867+02:00Five years after the "fifth" boson discovery ...<div dir="ltr" style="text-align: left;" trbidi="on"><b>... a step further in building the quantum "naturalness" for the 125 GeV Higgs scalar?</b><br /><blockquote class="tr_bq"><div style="text-align: justify;"><i>The major appeal of the more traditional approaches to beyond the standard model building such as supersymmetry (as well as technicolor, extra dimensions, etc.) is that they address the hierarchy problem, and that they shed light on the apparent unification of couplings, both within the context of local effective field theory (EFT). However, this apparent theoretical appeal of supersymmetry does not exclude approaches that do not necessarily follow the local EFT paradigm. For example, in the Spectral Standard Model approach of Connes et al. [<a href="https://math.berkeley.edu/~lott/partmodels.pdf" target="_blank">147</a>, <a href="https://arxiv.org/abs/hep-th/9606056" target="_blank">148</a>, <a href="https://arxiv.org/abs/hep-th/9606001" target="_blank">149</a>, <a href="https://arxiv.org/abs/hep-th/0608226" target="_blank">152</a>–<a href="https://arxiv.org/abs/1304.8050" target="_blank">156</a>, <a href="http://www.alainconnes.org/docs/book94bigpdf.pdf" target="_blank">189</a>] the hierarchy problem can be addressed in a completely different fashion [154].<u> The crucial noncommutative geometric (and thus in some sense non-local) aspect of the SM is found in the Higgs sector, which in principle comes with an extra (second) scale, to be distinguished from the usual UV scale of local EFT. The hierarchy between the Higgs and the UV (Planck) scale can be associated (as shown by Chamseddine and Connes in Ref. [154]) with the natural exponential factor that comes from the dynamical discrete geometry of the Higgs sector. Similarly, the apparent gauge unification (in the guise of an effective SO(10) relation between the gauge couplings) is also incorporated into the Spectral SM. These aspects of the NCG approach to the SM are almost completely unknown in the particle physics community, and at the moment, almost completely undeveloped from a phenomenological viewpoint</u>. One of our aims in our upcoming review of the Spectral SM [162] is to clarify these interesting features of the NCG approach to the SM and make them palatable to the wider phenomenological community. We are also motivated by a deeper need to understand the limitations of the local EFT paradigm from the point of view of the physics of quantum gravity, which is usually, rather naively, ignored at the currently interesting particle physics scales, by invoking the concept of decoupling, which represents another central feature of the local EFT and which is also challenged by the NCG approach to the SM. Finally, as we discuss in the next concluding subsection of this paper, the usual RG analysis of the local EFT should be re-examined in the new light of the non-commutative/non-local structure of the SM, and the apparent existence of two natural (and naturally related) physics scales.</i></div><div style="text-align: justify;"><i><br /></i></div><div style="text-align: justify;"><i><u style="text-decoration-line: underline;">One of the most interesting aspects of the NCG of the SM and its Pati-Salam-like completion is the existence of the GUT scale which can be found in the close proximity to the Planck scale</u>, i.e., the scale of quantum gravity. Given this fact as well as the presence of a hidden fundamental noncommutative structure in this approach, <u style="text-decoration-line: underline;">this suggests that the hierarchy problem should get a quantum gravitational rather than an effective field theory treatment</u><u>. The more convincing physical meaning of this GUT scale also comes after one realizes that Connes’ approach also produces a gravity sector in parallel with the standard model (and its Pati-Salam completion) and thus the GUT scale should be viewed as being close to the natural scale of gravity</u>, i.e., the Planck scale, and indeed the two scales are not that far apart in the non-commutative approach...</i><span style="text-align: left;"> </span></div></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><i><u>The Higgs scale also naturally appears as a geometric scale in Connes’ non-commutative geometry approach, in complete analogy with the geometric meaning of the Planck and the Hubble scales</u>. Actually, because of the appearance of gravity and the standard model Lagrangians in the Connes’s spectral action, and because of the discrete nature of the Higgs dimension, <u>there is a natural Higgs-like degree of freedom on the gravity side – a Brans-Dicke-Jordan-like scalar – which can be argued to contribute to the geometric warping of the Higgs discrete dimension</u>. This is similar to the infinite extra dimensional scenarios, however, without infinite extra dimensions [152, 154]. <u>In our view, the approach based on NCG (and its related proposal based on the superconnection approach [<a href="https://arxiv.org/abs/1409.7574" target="_blank">159</a>, <a href="https://arxiv.org/abs/1304.6092" target="_blank">163</a>]) offers a new and, phenomenologically, almost completely unexplored view on the rationale for the SM and also for its natural completion</u>. This approach also offers a possibly exciting relation with the fundamental physics of quantum gravity, thus relating the infrared physics of the current exciting experimental searches conducted at the LHC to the hidden ultraviolet physics of quantum theory of space and time.</i></div></blockquote><blockquote><div style="text-align: right;"><i><a href="http://inspirehep.net/record/1605109" target="_blank">Constraining New Physics with Colliders and Neutrinos</a></i></div><div style="text-align: right;"><a href="http://inspirehep.net/author/profile/Sun%2C%20Chen?recid=1605109&ln=fr">Chen Sun</a> (<a href="http://inspirehep.net/search?cc=Institutions&p=institution:%22Virginia%20Tech.%22&ln=fr">Virginia Tech.</a>) </div><div style="text-align: right;">May 12, 2017</div><br /><div style="text-align: justify;"><i></i></div></blockquote><br /></div>Cédric Bardothttps://plus.google.com/104733107894701960711noreply@blogger.com0tag:blogger.com,1999:blog-3911792794793692366.post-73490717974841683232017-06-03T21:36:00.003+02:002017-06-21T18:45:44.369+02:00Higgs discovery at LHC was a giant step for experimenters (and possibly spacetime geometers) but a small one (up to now) for theoreticians<div dir="ltr" style="text-align: left;" trbidi="on"><h4 style="text-align: left;"><b>What elementary particle physics program following the 13 TeV scale probing?</b></h4><div style="text-align: justify;">A possibly naive answer to this important question can be found at the end of this post. But let us start with a more reliable view from a beloved high energy physics blogger currently silent on his <a href="http://resonaances.blogspot.fr/" target="_blank">website</a> but still <a href="https://twitter.com/resonaances?lang=fr" target="_blank">tweeting</a> when he doesn't whistle:</div><div style="text-align: justify;"><br /></div><blockquote class="tr_bq"><div style="text-align: justify;"><i><u>The possibility that the LHC will only further confirm the Standard Model is often referred to as the nightmare scenario. The puzzles that emerge are not the nightmare; physicists love difficult problems. On the contrary, it is the indefinite persistence of the current confusing situation that is considered nightmarish</u>.</i></div><div style="text-align: justify;"><i><br /></i></div><div style="text-align: justify;"><i>The most efficient method developed thus far for revealing the fundamental secrets of nature has been to increase beam energy to probe increasingly small distances. Larger and more powerful colliders are seen as the solution. The design and construction of the LHC was a gargantuan task that required decades of work and billions of dollars. Such an undertaking will only become more difficult in the future. Would a doubling of energy be sufficient for any new collider project? Is a factor-of-ten increase needed? <u>It may be the case that the answers we seek are to be found at energy levels that are simply unattainable for the foreseeable future. It is also unclear whether a bigger collider would resolve currently unanswered questions</u>... </i></div></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><i><u>As was the case with the space program following the moon landing, there is on the one hand a grandiose plan, and on the other, more modest proposals with clear goals</u>. There are two ways to investigate matter at very small scales. <u>The first is to channel vast energies into a small volume, so that it can be converted into the creation of new particles.</u> This is the most straightforward method and results can be interpreted with minimal ambiguity.</i> </div></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><i><u>The second approach involves taking advantage of the uncertainty principle in quantum mechanics. According to this principle, very heavy particles can be continuously created from a vacuum</u>. These particles exist for a short time, during which they may affect the behavior of known particles, such as electrons, muons, Higgs bosons, and so on. <u>By measuring the properties of known particles with great precision, and comparing the results to theoretical predictions, insights can be derived into physical laws at energies inaccessible to collider experiments.</u></i><u> </u></div></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><div style="text-align: justify;"><i>Many such experiments are currently being conducted. Examples include research into the magnetic and electric properties of elementary and composite particles, such as muons, tau leptons, protons, neutrons, and kaons. The MEG, Muon g-2, nEDM, NA62, and Qweak experiments, among others, indirectly probe physics at energies well above what can be reached at the LHC, or, for that matter, a future one-hundred-kilometer collider. In many cases, a modest budget can improve precision by orders of magnitude within just a few years. Precision experiments also touch upon many distinct areas of physics—atomic physics, laser physics, condensed matter physics, and nuclear physics—promoting collaboration between particle physics and other domains of science...</i></div></div></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><i><u>Which is it to be: a one-hundred-kilometer collider, or one hundred precision experiments at CERN? This is a serious question. Not only the future but possibly the survival of particle physics is at stake. Shifting the focus away from high-energy colliders toward precision experiments may be the most efficient way to continue exploration of fundamental interactions in the decades ahead</u>. It may even allow particle physics to emerge stronger from its current crisis.</i></div></blockquote><blockquote class="tr_bq"><div style="text-align: right;"><i><a href="http://inference-review.com/article/higgs-on-the-moon" target="_blank">Higgs on the Moon</a></i></div><div style="text-align: right;"><a href="http://inference-review.com/author/adam-falkowski/"></a><a href="http://inference-review.com/author/adam-falkowski/">Adam Falkowski</a>, </div></blockquote><br /><h4 style="text-align: left;"><b>Adding a usual advisory and this blog's obstinate reminder </b></h4><blockquote class="tr_bq"><div style="text-align: justify;"><i>The LHC experiment is not yet done—far from it. The collider is scheduled to operate for another fifteen years, accumulating something like one hundred times more data than it has to date. Physicists will be scrutinizing the data for any signs of new particles. The Higgs boson will be studied with an eye towards determining how well it conforms to the specific predictions of the Standard Model. A breakthrough may happen at any moment...</i></div><br /><div style="text-align: right;"><a href="http://inference-review.com/article/higgs-on-the-moon"><i>Id.</i></a></div></blockquote><br /><span style="color: #999999;">Reading the next quote, one may add to what Adam wrote:</span> a breakthrough has already happened <span style="color: #999999;">but it has yet to be granted as it did not occured at CERN but on the operator-algebraic-clad peaks of the quantum geometric models of spacetime, a place where "oxygen" (physics intuition) is naturally scarce. </span><br /><br /><blockquote class="tr_bq" style="text-align: justify;"><i><u>The noncommutative geometry dictated by physics is the product of the ordinary 4-dimensional continuum by a finite noncommutative geometry</u> which appears naturally from the classification of finite geometries of KO-dimension equal to 6 modulo 8 (cf. [<a href="https://arxiv.org/abs/0706.3688" target="_blank">8</a>, <a href="https://arxiv.org/abs/hep-th/0610241" target="_blank">11</a>]). <u>The compatibility of the model with the measured value of the Higgs mass was demonstrated in [<a href="https://www.blogger.com/"><span id="goog_2032314956"></span>13<span id="goog_2032314957"></span></a>] due to the role in the renormalization of {an ultra-heavy Higgs-like singlet} scalar field</u> already present in {our model before Higgs discovery}[<a href="https://arxiv.org/abs/1208.1030" target="_blank">12</a>]. In [<a href="https://arxiv.org/abs/1409.2471" target="_blank">14</a>, <a href="https://arxiv.org/abs/1411.0977" target="_blank">15</a>], with Chamseddine and Mukhanov, <u>we gave the conceptual explanation of the finite noncommutative geometry from Clifford algebras and obtained a higher form of the Heisenberg commutation relations between p and q, whose irreducible Hilbert space representations correspond to 4-dimensional spin geometries. </u>The role of p is played by the Dirac operator and the role of q by the Feynman slash of coordinates using Clifford algebras. <u>The proof that all spin geometries are obtained relies on deep results of immersion theory and ramified coverings of the sphere. The volume of the 4-dimensional geometry is automatically quantized by the index theorem</u>; <u>and the spectral model, taking into account the inner automorphisms due to the noncommutative nature of the Clifford algebras, gives Einstein gravity coupled with a slight extension of the standard model, which is a Pati-Salam model</u>. This model was shown in our joint work with A. Chamseddine and W. van Suijlekom [<a href="https://arxiv.org/abs/1304.8050" target="_blank">17</a>, <a href="https://arxiv.org/abs/1507.08161" target="_blank">18</a>] to yield unification of coupling constants.</i></blockquote><blockquote><div style="text-align: right;"><i><a href="https://arxiv.org/abs/1703.02470" target="_blank">Geometry and the Quantum</a></i></div><div style="text-align: right;"><a href="https://arxiv.org/find/hep-th/1/au:+Connes_A/0/1/0/all/0/1" target="_blank"></a><a href="https://arxiv.org/find/hep-th/1/au:+Connes_A/0/1/0/all/0/1">Alain Connes</a> (Submitted on 7 Mar 2017)</div><span style="text-align: justify;"></span></blockquote><br /><b><br /></b><br /><h4 style="text-align: justify;"><b>Building a new articulation of quantum matter and gauge interactions through an updated spacetime geometry to forge new experimental tools with the Higgs scalar boson ruler!</b></h4><div style="text-align: justify;">This is my "educated" guess, based on the spectral noncommutative geometric insight exposed above and also inspired from the epistemological hindsight <strike>developped</strike> <span style="color: #999999;">described</span> by the late french mathematician and philosopher Gilles Châtelet below:</div><blockquote class="tr_bq" style="text-align: justify;"><i>Toute physique mathématique est fondée par un protocole d'articulation du sens géométrique et du sens physique... Pourquoi donc préférer {la} certitude ... [que {je} peux refermer {mon} poing sur l'électron qui est là devant moi par la simple connaissance de sa position-vitesse] à la richesse de l'algèbre des observables qui en dit beaucoup plus sur le jeu expérimental : symétrie, compatibilité de certaines pratiques, règles de jeu de mesures... Les relations d'incertitudes ... sont à appréhender ... comme le simple refus du physique à se donner par saisie cartésienne {commutative}. Celle-ci est impuissante à comprendre les rôles, les places, les intrigues du théâtre ... quantique.</i></blockquote><blockquote class="tr_bq"><div style="text-align: right;"><i><a href="http://www.presses.ens.fr/454-hors-collection-enchantement-du-virtuel-l.html" target="_blank">L'enchantement du virtuel</a></i></div><div style="text-align: right;">Gilles Châtelet</div></blockquote><br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-D5q1868-S-I/WTVYKcqDNyI/AAAAAAAACSQ/njWk0_QQKWsC1KuARYwwsi1FqXiqbDK8gCEw/s1600/LHC3.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="799" data-original-width="789" height="640" src="https://1.bp.blogspot.com/-D5q1868-S-I/WTVYKcqDNyI/AAAAAAAACSQ/njWk0_QQKWsC1KuARYwwsi1FqXiqbDK8gCEw/s640/LHC3.png" width="628" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><div style="font-size: medium;"><div style="text-align: justify;"><span style="font-size: small;"><span style="color: #999999;">Will the LHC bring physicists "closer to the moon", namely to a grand unification of fundamental interactions, while <a href="http://inference-review.com/article/natural-physics" target="_blank">no sign of new "natural physics</a>" shows up aside the Higgs boson? A positive answer could rely on the building of a new natural spacetime model offering <a href="https://arxiv.org/abs/hep-ph/0503147" target="_blank">a proper geometric interpretation to the scalar particle</a> discovered by the LHC. The <a href="http://www.waltervansuijlekom.nl/wp-content/uploads/2014/12/naw5-2014-15-4-2401.pdf" target="_blank">spectral model of particle physics</a> is a quite successfull example of such a program that <a href="https://arxiv.org/abs/1208.1030" target="_blank">learnt the lesson from the 125 GeV mass</a> measured in 2012. It recently led to put in place <a href="https://arxiv.org/abs/1703.02470" target="_blank">a possible foundation stone to clarify the issue of quantising spacetime</a> and it is based on the formalism that made it possible to quantise radiation and matter. Last but not least it <a href="https://arxiv.org/abs/1702.08180" target="_blank">establishes a logical link</a> with <a href="https://arxiv.org/abs/1601.04941" target="_blank">mimetic dark matter and dark energy models</a>. </span></span><br /><span style="font-size: small;"><span style="color: #999999;">(Background picture from the <a href="https://cds.cern.ch/record/42370?ln=fr" target="_blank">CERN image library</a> shows the area under which the tunnel for LHC can be found near to Geneva and lac Leman. The French Alps with Mont Blanc provides a natural backdrop and a reminder for the past discovery of particles like positron, muon, meson, kaon...that occured in high altitude </span><span style="color: #999999;">cosmic ray laboratories. The drawing is the currently experimentally proven and conceptually understood version of the <a href="https://quantumostinato.blogspot.fr/2015/07/circumnavigating-great-loop-of-physics.html" target="_blank">grand loop of physics</a>)</span>.</span></div></div><div style="font-size: medium;"><br /><div style="text-align: justify;"><span style="color: #999999;">//last edit June <strike>5</strike> 6, 2017</span></div></div></td></tr></tbody></table></div>Cédric Bardothttps://plus.google.com/104733107894701960711noreply@blogger.com0tag:blogger.com,1999:blog-3911792794793692366.post-89850502488188081712017-05-11T10:38:00.003+02:002017-05-26T11:45:32.150+02:00"All results are consistent with the Standard Model (SM) and constrain New Physics..."<div dir="ltr" style="text-align: left;" trbidi="on"><h3 style="text-align: left;"><b>... but statistical fluctuations would not be unexpected</b></h3><blockquote class="tr_bq"><div style="text-align: justify;"><i><u>In the SM, Flavour Changing Neutral Currents (FCNCs) occur at loop level and are suppressed by the GIM mechanism, and sometimes helicity suppression. As New Physics (NP) is not necessarily suppressed, FCNCs probe physics at energies beyond the LHC centre-of-mass energy</u>. One such FCNC is the b → s</i><i><span style="text-align: left;">ℓ</span><span style="text-align: left;">ℓ</span></i><i> transition. <u>Several theory groups have performed global fits to b → s<span style="text-align: left;">ℓ</span><span style="text-align: left;">ℓ</span> observables in the Effective Field Theory (EFT) framework, and find that the data deviate by ∼ 4 standard deviations with respect to the SM</u>... </i><span style="text-align: left;"> </span></div></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><u><i>Here, the new LHCb analysis of </i><i>B⁰₍ₛ₎→µ⁺+µ⁻</i><i> observables is presented. It is based on data corresponding to an integrated luminosity of 1 fb</i><i>⁻¹ </i><i> of pp collisions at a centre-of-mass energy of √s = 7 TeV, 2 fb</i><i>⁻¹ </i></u><i><u> at √ s = 8 TeV and 1.4 fb⁻¹ at √s = 13 TeV</u>. The first two datasets are referred to as Run 1, the latter as Run 2...</i><span style="text-align: left;"> </span></div></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><i>The </i><i>B⁰ₛ→µ⁺+µ⁻</i><i> decay is observed with a significance of 7.8 standard deviations, and its branching fraction is measured to be B(B⁰ₛ→µ⁺+µ⁻) = (3.0±0.6+0.3 −0.2)×10⁻⁹, where the first uncertainty is statistical and the second systematic. In addition, the first measurement of the </i><i>B⁰ₛ→µ⁺+µ⁻</i><i> effective lifetime is performed: τ(</i><i>B⁰ₛ→µ⁺+µ⁻</i><i>) = 2.04± 0.44±0.05 ps. No significant excess of </i><i>B⁰→µ⁺+µ⁻</i><i> decays is observed, and a 95% confidence level upper limit is determined, B(</i><i>B⁰→µ⁺+µ⁻</i><i>)<3.4×10⁻¹⁰. <u>All results are consistent with the SM and constrain New Physics in b → s</u></i><u><i><span style="text-align: left;">ℓ</span><span style="text-align: left;">ℓ</span></i><i> processes.</i></u></div></blockquote><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-9qarrpBwN3s/WRQifPeAOwI/AAAAAAAACPw/i0Hio4K6o8syP5Are2B1KmzbER13SOAmACLcB/s1600/LHCb.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="209" src="https://3.bp.blogspot.com/-9qarrpBwN3s/WRQifPeAOwI/AAAAAAAACPw/i0Hio4K6o8syP5Are2B1KmzbER13SOAmACLcB/s640/LHCb.jpg" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">– (left) Mass distribution of selected <i style="font-size: medium; text-align: justify;">B⁰ₛ→µ⁺+µ⁻</i> candidates in the four most sensitive BDT bins. The result of the fit is overlaid. (right) The 2D confidence interval in <i style="font-size: medium; text-align: justify;">B⁰ₛ→µ⁺+µ⁻</i>, <i style="font-size: medium; text-align: justify;">B⁰→µ⁺+µ⁻</i> from this measurement.</td></tr></tbody></table><br /><blockquote class="tr_bq"><div style="text-align: right;"><a href="https://arxiv.org/abs/1705.03274" target="_blank"><i>The branching fraction and effective lifetime of B0(s)→μ+μ− at LHCb with Run 1 and Run 2 dat</i>a</a></div><div style="text-align: right;"><a href="https://arxiv.org/find/hep-ex/1/au:+Mulder_M/0/1/0/all/0/1">Mick Mulder</a>, for the <a href="https://arxiv.org/find/hep-ex/1/au:+Collaboration_LHCb/0/1/0/all/0/1">LHCb Collaboration</a></div><div style="text-align: right;">(Submitted on 9 May 2017)</div></blockquote><br /><h3 style="text-align: left;"><b>Just a reminder</b></h3><blockquote class="tr_bq" style="text-align: justify;"><i>Even though the CKM picture appears to be in excellent agreement with the data overall (Fig.2), new physics may still affect a subset of observables. Theoretically, there is no preference for the scale of fundamental flavor dynamics: it may be at the TeV scale, in which case it must be very special, or just as well at the Planck scale as is the case in string theory. Given that the flavor structures we see in the SM are special, one should keep an open mind and be prepared for surprises. Having said that, it is important to appreciate the sheer volume of B–physics data: the B+ meson already has close to 500 decay modes, such that statistical fluctuations would not be unexpected...</i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>The highlights and take–home lessons from Moriond QCD 2017 can be summarized by the following bullet points:</i> </blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>• remarkable progress in precision calculations. NNLO precision is now a commonplace allowing for unprecedented accuracy at a hadron machine.</i> </blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>• Higgs precision era. Higgs pT distributions, interference effects, etc. allow for accurate tests of the Higgs nature.</i> </blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>• intriguing B–physics anomalies. Several 2 − 3σ deviations in clean semi-leptonic observables leave ample room for new physics. [While ... anomaly </i>{in some observable} <i>is driven by the LHCb data,</i> {others} <i>show... deviations of varying significance in all three experiments: BaBar, Belle and LHCb... more statistics is needed to see if the current tendency persists] </i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>• data–driven theory: test “unmotivated” ideas. Given the absence of striking signatures of “traditional” forms of new physics, the theory approach should be more inclusive. May require painstaking analysis of difficult observables. </i></blockquote><blockquote class="tr_bq"><div style="text-align: right;"><a href="https://arxiv.org/abs/1704.08937v2" target="_blank"><i>Moriond QCD 2017: theoretical summary</i></a></div><div style="text-align: right;"><a href="https://arxiv.org/find/hep-ph/1/au:+Lebedev_O/0/1/0/all/0/1">Oleg Lebedev</a></div><div style="text-align: right;">(Submitted on 28 Apr 2017 (<a href="https://arxiv.org/abs/1704.08937v1">v1</a>), last revised 10 May 2017 (this version, v2))</div></blockquote><span style="text-align: justify;"><b><br /></b></span><span style="text-align: justify;"><b><br /></b></span><span style="text-align: justify;"><b>A last <strike>periphrase</strike>* personal comment </b></span><br /><div style="text-align: justify;">Amending the concluding point of O. Lebedev in his summary article, one could write the following. Given the absence of striking signatures of traditional forms of new particle physics, the theory approach may be more inclusive. It should require <a href="https://arxiv.org/abs/hep-th/0608226">challenging the traditional extensions of physical spacetime</a> studied up to now and considering some <a href="https://arxiv.org/abs/1703.02470">recent theoretical results</a> that make it possible to watch on the blind spot (understand more fundamentally the phenomenological aspect) of quantum non-abelian gauge theories with spontaneous symmetry breaking in the light of the <a href="https://arxiv.org/abs/hep-th/0111236">possible connection of Higgs mechanism with gravity</a>, possibly shedding <a href="https://arxiv.org/abs/1702.08180">new light on the dark sector(s) of astrophysics</a>.</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">*last edit : May 26 2017</div></div>Cédric Bardothttps://plus.google.com/104733107894701960711noreply@blogger.com0tag:blogger.com,1999:blog-3911792794793692366.post-62587647985063736222017-05-07T16:15:00.000+02:002017-05-10T00:29:12.572+02:00Following the Higgs and top quark trails through the "big desert", chasing a complex scalar singlet and right-handed neutrinos...<div dir="ltr" style="text-align: left;" trbidi="on"><h3 style="text-align: left;"><b> <span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">... riding two loop renormalisation group flow, guided by the spectral standard model</span></b></h3><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><br /></span><br /><blockquote class="tr_bq" style="text-align: justify;"><i><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><u>The Lagrangian of the spectral standard model comes from the most general form of the Dirac operator consistent with axioms of noncommutative geometry plus an additional constrain called the first order condition. This Lagrangian possesses three important features distinguishing it from the minimal standard model. First, the couplings of the model are not totally arbitrary and there are relations between them at the unification scale</u>. These relations are consistent with grand unified theories such as SU(5) unified theory. <u>Second, there is a singlet scalar field present in the spectral action. It is shown that this field can help the situation with low Higgs mass which is not otherwise consistent with the unification of spectral action in high energies</u> [<a href="https://arxiv.org/abs/1208.1030" target="_blank">6</a>]. We will see in this letter that the results improve if the scalar field is taken to be complex. It is also seen that such an extra scalar field can be responsible for dark matter particle [<a href="https://arxiv.org/abs/hep-ph/0011335" target="_blank">1</a>, <a href="https://arxiv.org/abs/1411.4048" target="_blank">14</a>]. <u>Finally, right-handed neutrino appears into the picture automatically as well as its Yukawa interaction</u>. These terms are needed to give a small mass to the left-handed neutrino by see-saw mechanism and usually are added to the standard model by hand...</span></i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><u>In [<a href="https://arxiv.org/abs/1208.1030" target="_blank">6</a>], the singlet scalar field was assumed to be real... In fact, the reality condition on the singlet field is not necessary and we assume the singlet to be a complex field in this work</u>. Our consideration shows the model in its most general form is consistent with the current experimental values of the Higgs and top quark masses. Furthermore, <u>we use 2-loop </u></span></i><i><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><u>renormalisation group (RG) </u></span></i><i><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><u>equations to compare the following cases: when the added singlet is a complex field, when it is real, and the pure standard model with neutrino mixing. We show that while running RG equations from unification scale toward current experimental energies, the model with added complex singlet behaves slightly better than the other two cases. Yet, like the standard model itself, one can only attain the experimentally observed gauge couplings at low energies within some percent of accuracy</u>. This agrees with the separations of the standard model gauge at the unification scale when we start from experimental values and run them upward...</span></i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">We ... show ... that... <u>a few extra terms are added to the RG equations due to the complex singlet field</u>, ... <u>their effect on the negativity of the Higgs self-coupling at high energies can be substantial. The reason we cannot predict what exactly happens for the coupling is that the experimentally unknown right-handed neutrino Yukawa coupling contributes in the RG equations as well. This coupling also plays a role in determining the Higgs and top quark masses at low energies. What we can do is to follow its effect by following RG equations down and looking at the particle masses. The proper value of right-handed neutrino Yukawa coupling - turns out to be between 0.411 and 0.455 at unification scale</u> ... The resulting value for this coupling at Z boson mass region is also between 0.517 and 0.530, while Yukawa coupling of the top quark is about 0.995. Besides, the values of scalar sector couplings are derivable in this scale from RG equations. <u>We argue that in this acceptable range of the couplings, although vacuum instability is not cured, but the situation is improved by the presence of the complex scalar field</u>. We use two-loop equations and near to the leading order three-loop equations to assess the loop correction effects in presence of a complex or real singlet field.</span></i></blockquote><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-Ha08t8KK-RQ/WQ8oL_9efRI/AAAAAAAACPU/U1xr5h_98BEuXvGpDBkhW6cGFyoftfaeACEw/s1600/SpecSMHiggs.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><img border="0" src="https://2.bp.blogspot.com/-Ha08t8KK-RQ/WQ8oL_9efRI/AAAAAAAACPU/U1xr5h_98BEuXvGpDBkhW6cGFyoftfaeACEw/s1600/SpecSMHiggs.jpg" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: justify;"><blockquote class="tr_bq"><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif; font-size: small;"><i>Each line shows the suitable values of unification scale U (logarithmic scale normalized by Z boson mass) and the squared ratio between the Yukawa couplings of tau-neutrino and top quark labelled n, in order to retrieve the experimental values of Higgs (dotted lines) or top quark (solid lines) masses at low energies from two-loop renormalisation group running down. Each set of three lines is for a specific unification gauge coupling value g</i> <i>and is illustrated with a particular thickness</i><i>. It can be inferred from this figure that within a reasonable range of g, the lines associated with top quark and Higgs always have a collision point. Therefore suitable n and U can always be found to fit the low energy values for the Higgs and top quark masses. This is true for both real and complex cases which are distinguished by blue and green lines.</i></span></blockquote></td></tr></tbody></table><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><br /></span><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><br /></span><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-69EJMA_ewpE/WQ78fh8rY7I/AAAAAAAACO8/jJBKDNOTrmQcqahFrNyS32EPoylLd7ExwCLcB/s1600/SpecSMHiggsSelfCoupling.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><img border="0" src="https://1.bp.blogspot.com/-69EJMA_ewpE/WQ78fh8rY7I/AAAAAAAACO8/jJBKDNOTrmQcqahFrNyS32EPoylLd7ExwCLcB/s1600/SpecSMHiggsSelfCoupling.jpg" /></span></a></td></tr><tr><td class="tr-caption" style="text-align: justify;"><blockquote class="tr_bq"><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif; font-size: small;"><i>Comparison of the Higgs self-coupling running from unification scale down to the electroweak scale for the standard model with neutrino mixing and for the spectral standard model containing a real or complex singlet scalar. The figure shows that the addition of new fields could improve the stability problem of the Higgs vacuum. (Warning : the unified gauge coupling value used here to show the effect of the scalar singlet on the eletroweak vacuum stability does not lead to the correct gauge couplings at low energy. This is a generic feature of spectral standard model which can be overcome abandoning the "big desert" hypothesis with a Pati Salam type scalar extension [<a href="https://arxiv.org/abs/1304.8050" target="_blank">10</a>] not studied here)</i></span></blockquote></td></tr></tbody></table><blockquote class="tr_bq" style="text-align: justify;"><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><i><br /><u> We stress that {these} results are not merely derivable from the standard model plus a complex singlet</u>. The reason is that in our considerations, we use the initial conditions predicted by the spectral action approach [<a href="https://arxiv.org/abs/hep-th/0610241" target="_blank">8</a>]. Moreover <u>here a neutrino coupling is present in RG equations and contributes to the values of particle masses. The form of potential is also restricted and is different from extended standard model cases with complex singlet described in the literature</u>. In our case, the results for stability are slightly better (e.g. compare with [</i><i><a href="https://arxiv.org/abs/1202.5717" target="_blank">11</a>, </i><i><a href="https://arxiv.org/abs/1411.4048" target="_blank">14</a>, </i><i><a href="https://arxiv.org/abs/1203.0237" target="_blank">17</a>, </i><i><a href="https://arxiv.org/abs/1202.1316" target="_blank">20</a>]).</i></span></blockquote><blockquote class="tr_bq"><div style="text-align: right;"><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">{slightly adapted from} <a href="https://arxiv.org/abs/1705.01605"><i>Implications of the complex Singlet field for Noncommutative Geometry model</i></a></span></div><div style="text-align: right;"><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><a href="https://arxiv.org/find/hep-ph/1/au:+Khozani_H/0/1/0/all/0/1"></a><a href="https://arxiv.org/find/hep-ph/1/au:+Khozani_H/0/1/0/all/0/1">Hosein Karimi Khozani</a> (Submitted on 3 May 2017)</span></div></blockquote><b><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><br /></span></b><b><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><br /></span></b><br /><h3 style="text-align: left;"><b><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">Next time at the Pati-Salam caravanserai</span></b></h3><b><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><br /></span></b><br /><blockquote class="tr_bq" style="text-align: justify;"><i><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">... <u>in the simple version that we considered here ... one could not fully {retrieve} the gauge couplings at low energies. Yet, the... better results {presented here} with this minimal change in the settings of the standard model might urge us to investigate {extended} models derived from noncommutative geometry principles </u>{without the order one condition for example)... Further investigations showed in 2014 that <u>imposing a generalized version of Heisenberg uncertainty relations leads to Pati-Salam models as the most general possible outcome of this approach </u>[<a href="https://arxiv.org/abs/1304.8050" target="_blank">10</a>]. <u>The model we considered here is the simplest special case of that general theory</u>. The Pati-Salam model has a rich content of beyond SM fields that might help the situation and will be the subject of our further investigations.</span></i></blockquote><blockquote class="tr_bq" style="text-align: right;"><i><a href="https://arxiv.org/abs/1705.01605" target="_blank"><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"> Id.</span></a></i></blockquote><br /><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">A personal comment (updated on May 9)</span><br /><br /><div style="text-align: justify;"><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">The article quoted here was written in all likelihood by a Ph D. student of Ali Chamseddine, one of the father of the spectral standard model. It does a nice job in adding a piece to the fascinating picture puzzle of unification of fundamental forces and also to the spectral unification model I was dreaming about in the <a href="https://quantumostinato.blogspot.fr/2017/04/solving-7-problems-of-particle-physics.html" target="_blank">last post.</a></span></div><div style="text-align: justify;"><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><br /></span></div><div style="text-align: justify;"><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">I regret nevertheless there is no mention of the <a href="https://inspirehep.net/record/1419192/files/Farnsworth_Shane.pdf" target="_blank">doctoral work </a>of Shane Farnsworth who has proposed an original motivation for considering as complex the scalar singlet derived from the spectral action principle by Chamseddine and Connes in their 2010 article (see <a href="http://www.connes70.fudan.edu.cn/Assets/userfiles/sys_eb538c1c-65ff-4e82-8e6a-a1ef01127fed/files/slides/workshop1/Chamseddine.pdf" target="_blank">here</a> for a vivid description of their collaboration). </span></div><div style="text-align: justify;"><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><br /></span></div><div style="text-align: justify;"><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">In light of the promissing evidence already uncovered, it will be a tremendous achievement to compute the </span><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">renormalisation group equations from </span><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">the specific Pati-Salam extension of the spectral standard model and a fantastic piece of information to find out </span><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">proper initial conditions</span><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"> </span><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">able to recover all known low energy data after running down from </span><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">the </span><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">spectral unification scale</span><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">. </span><br /><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"><br /></span><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">Even more exciting would be exploring</span><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"> the quite constrained scalar spectrum</span><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"> in </span><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">spectral Pati-Salam models and </span><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">testing in parallel the vanilla leptogenesis scenario. It has been already tested </span><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">successfully </span><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">in </span><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">nonsupersymmetric SO(10) models based on </span><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">a </span><a href="https://arxiv.org/pdf/1705.01935.pdf" style="font-family: "helvetica neue", arial, helvetica, sans-serif;" target="_blank">hierarchical</a><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"> or a </span><a href="https://arxiv.org/abs/1412.4776" style="font-family: "helvetica neue", arial, helvetica, sans-serif;" target="_blank">compact</a><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;"> right-handed neutrino spectrum with normal ordered masses. This kind of test was shown - under the last hypothesis </span><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">at least - to be able to fix a</span><span style="font-family: "helvetica neue" , "arial" , "helvetica" , sans-serif;">ll the parameters of the model thanks to neutrino mixing data and the amount of baryon asymmetry in the visible universe!</span></div></div>Cédric Bardothttps://plus.google.com/104733107894701960711noreply@blogger.com0tag:blogger.com,1999:blog-3911792794793692366.post-16851031555611492632017-04-02T22:55:00.000+02:002017-05-27T22:32:32.326+02:00Solving 7 problems of particle physics and cosmology at one blow?<div dir="ltr" style="text-align: left;" trbidi="on"><div><h3 style="text-align: left;"><b>The SUM of all fears and hopes</b></h3><br /><div style="text-align: right;"><i><a href="https://en.wikiquote.org/wiki/Talk:Albert_Einstein" target="_blank">"Any fool can know. The point is to understand"</a></i><br /><br /><i>“You can't always get what you want … but if you try … you might find … you get what you need”</i><br /><i><a href="https://indico.in2p3.fr/event/13763/session/17/contribution/117/material/slides/1.pdf" target="_blank">So let's keep trying.</a></i><br /><br /></div><b><br /></b></div><div style="text-align: justify;">As an echo from the last post I indulge myself wearing Seven-League Boots stolen to some Giants (those who tailored the Standard Model of particle physics and the current cosmological concordance model and some others who have extracted the essential marrow from both). My point is to attempt to browse the <a href="https://quantumostinato.blogspot.fr/2015/07/circumnavigating-great-loop-of-physics.html" target="_blank">Glashow's Grand Loop</a> of physics, writing a fake "article" for fun but making it informative as well. </div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Physicist advisory: several articles reporting on contemporary or vintage models have been copycatted in the making of the following mashup...<br /><br /><h2 style="text-align: center;"><b>Report on progress in Spectral Unification Model building </b></h2><h3 style="text-align: center;"><b>Solving 7 problems of particle physics and cosmology at one blow and </b><b>consolidating a bridge to span 14 orders of magnitudes in energy </b><b>from 125 GeV to O(10) YeV</b></h3></div><div style="text-align: justify;"><div><h4 style="text-align: center;"></h4><h4 style="text-align: center;">Tom Thumb and the Brave Model Tailors</h4></div><div style="text-align: center;"><img src="https://1.bp.blogspot.com/-RNPRvh0QqbI/WOFlfqSj4xI/AAAAAAAACHI/DclNQqSI-PMoW8vd6jggl9mfFiC_EcwZQCLcB/s200/Sept.jpg" /></div><div><br /><br /></div><div style="text-align: center;"><i>(Submitted on 1 Apr 2017, last revised </i><i><i>7 Apr 2017</i>)</i></div></div><div style="text-align: justify;"><br />ABSTRACT: We present minimalist matched extensions of both the Standard Model (SM) of elementary-particle forces and General Relativity (GR) in the form of an effective quantum field theory valid up to an order of magnitude of 10 YeV coupled to gravity with an extended scalar mimetic sector. This so called Spectral Unification Model (SUM) relies on two hypotheses: i) the space-time-matter-radiation structure of the physical universe is the solution of a generalized Heisenberg commutation relation (abbreviated in C<i style="text-align: justify;"><sup>2</sup></i>M for <a href="https://arxiv.org/abs/1703.02470">Chamseddine-Connes-Mukhanov)</a> expressed as an index-like formula in noncommutative geometry and its dynamics is computed from ii) <a href="https://arxiv.org/abs/hep-th/9606001">the spectral action principle</a> which is basically <a href="https://arxiv.org/abs/hep-th/0111236">a stronger hypothesis than the usual diffeomorphism invariance of the action of general relativity</a>. The C<i style="text-align: justify;"><sup>2</sup></i>M commutation relation in dimension four is essentially a quantization condition that <a href="https://arxiv.org/abs/1606.01189">determines in a unique way the noncommutative space defining our space-time </a>as a tensor product of continuous and discrete spaces. It <a href="https://arxiv.org/abs/1606.01189">implies that the volume of the continuous part is quantized</a> and provides a noncommutative space predicting with the help of its spectral action the existence of a <a href="https://arxiv.org/abs/1304.8050">unified model of all particle interactions based on a Pati-Salam (PS) symmetry and as a special case the SM</a> while the <a href="https://arxiv.org/abs/1409.2471">volume quantization gives a modified version of Einstein gravity with a mimetic sector.</a> Thus the SUM provides <a href="https://arxiv.org/abs/1507.08161">a consistent picture of particle physics from the electroweak scale to the PS gauge couplings unification (1) scale</a> and of cosmology <a href="https://arxiv.org/abs/1403.3961">from inflation (2) until today accelerating expansion (3)</a> with <a href="https://arxiv.org/abs/1412.4776">baryogenesis (4) occurring through leptogenesis</a> during reheating. <a href="https://arxiv.org/abs/1304.8050">The new matter content consists essentially in three ultra-heavy right-handed neutrinos and a SM-singlet scalar whose vacuum expectation value around </a><a href="https://arxiv.org/abs/1304.8050">10<span style="text-align: justify;"><sup>11</sup></span> GeV breaks the PS symmetry</a> and gives a Majorana mass to the right-handed neutrinos. At low energies, the model reduces to the SM, augmented by seesaw generated neutrino masses and mixing (5). The Einstein's equations are modified such that the cosmological constant (6) is now an integration constant and is not present in the action. The volume quantization condition expressed in space-times with Lorentzian signature generates a scalar field modifying only the longitudinal part of the graviton which plays the role of mimetic dark matter (7). In conclusion, seven fundamental problems of particle physics and cosmology can be solved at one blow in the SUM which is very economical in new hypotheses beyond the SM spectrum and spacetime dimensions and is compatible with experiments and observations from zeptometer scale to the enneameter one.<br /><br /><br /><br />DISCUSSION: At the time being, it is difficult to envision a direct probe for the SUM but any upcoming experimental evidence for supersymmetric particles at the TeV scale, any kind of wimp or a proton disintegration signal would probably falsify it. We emphasize that the SUM is computed from a mathematically quite rigid noncommutative geometric framework based on few axioms which number has decreased since its inception as the experimental validation of the standard model has been completed. On the other hand, once the SUM spectrum posited, all its phenomenological consequences discussed up to now have been derived thanks to well established quantum field theories, renormalisation methods and Einstein general relativity. Last but not least all the conditions required to fulfil low energy experiments and cosmological observations are so restrictive that the SUM is quite unique. The reason why it has escaped examination up to now by high energy physics community must probably be attributed to its lack in new particle phenomenology at accessible energies. After all until the construction of the LHC and its 2012 discovery there were clever people who did not believe in the existence of the Higgs boson despite the confirmation of the Glashow-Weinberg-Salam model at LEP. The thorough study of <a href="https://arxiv.org/abs/1412.4776">minimal non-supersymmetric SO(10) GUTs which shares some important feature</a>s with SUM (up to the seesaw scale) was also left aside for many years due to <a href="https://inspirehep.net/record/363861?ln=fr">problems with tachyonic instabilities proven to be absent in the full quantum theory</a> (perhaps even more probably due to its non-SUSY nature). The situation for the SUM may change in a foreseeable future particularly if conventional dark matter and TeV scale particles search stay unsuccessful. On a more cheerful tone the fact that we can envision on a pretty firm basis, in lieu of the string landscape, one specific bridge from our electroweak precision data set to the fuzzy PS gauge couplings unification extrapolation (spanning fourteen orders of magnitudes in energy from the 125 GeV Higgs mass to the ≈10<span style="text-align: justify;"><sup>16</sup></span> GeV natural scale of spectral action) is a significant progress providing incentives to address for instance the important hierarchy problem not dealt with here. <a href="https://arxiv.org/abs/hep-th/0512169">It is indeed worth reminding that the spectral action includes naturally a dilaton field which guarantees the scale invariance of the standard model interactions, and provides a mechanism to generate mass hierarchies.</a> Moreover considerations of scale invariance require including new terms in the spectral action that makes it possible to avoid <a href="https://arxiv.org/abs/1612.05860">cosmological</a> and <a href="https://arxiv.org/abs/1612.05861">black hole</a> singularities in GR.<br /><br /></div><div style="text-align: justify;"><div class="separator" style="clear: both; text-align: center;"></div><div style="text-align: center;"><div class="separator" style="clear: both; text-align: center;"></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-2TZqROx2Sz0/WSl8HAGvPZI/AAAAAAAACRk/sziIug9IwoYkveYT7kWAFRjweiNG71TaQCLcB/s1600/SUM2.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="927" data-original-width="1007" height="588" src="https://1.bp.blogspot.com/-2TZqROx2Sz0/WSl8HAGvPZI/AAAAAAAACRk/sziIug9IwoYkveYT7kWAFRjweiNG71TaQCLcB/s640/SUM2.png" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><div style="font-size: 12.8px;"><div style="text-align: center;"><span style="font-size: small;"><span style="font-size: xx-small;">The place of the <b>S</b>pectral <b>U</b>nification <b>M</b>odel in </span>the Grand Loop of Physics. </span></div><div style="text-align: center;"><span style="font-size: small;"><br /></span></div><div style="text-align: justify;"><span style="font-size: small;">This picture is a possible update of the 1980s <a href="https://scalometer.wikispaces.com/Glashow,+Sheldon+Lee" style="font-size: medium;" target="_blank">Glashow</a><a href="https://scalometer.wikispaces.com/Glashow,+Sheldon+Lee" style="font-size: medium;" target="_blank">'</a><span style="font-size: xx-small;">s</span><span style="font-size: xx-small;"> </span><a href="http://physics.ucsc.edu/cosmo/primack_abrams/COSMO.HTM" style="font-size: medium;" target="_blank">cosmic Uroboros</a> in light of the current (2017) available data, emphasizing the Higgs boson scalar discovery (as well as the lack of Dark Matter or SUSY particle detection) and its potential significance for other scales in a<a href="https://arxiv.org/abs/1008.0985" target="_blank"> spectral </a></span><span style="font-size: small;"><a href="https://arxiv.org/abs/1008.0985" target="_blank">noncommutative geometric perspective</a> epitomized by the <a href="https://arxiv.org/abs/1703.02470" target="_blank">Chamseddine-Connes-Mukhanov (</a></span><span style="font-size: small;">C²M</span><span style="font-size: small;"><a href="https://arxiv.org/abs/1702.08180" target="_blank">) </a></span><span style="font-size: small;">commutation relation shown below </span><span style="font-size: small;">Tom Thumb wearing seven-league boots (as a replacement to the classic snake devouring its tail).</span><span style="font-size: small; text-align: center;"> In this framework the recently discovered Higgs boson mass value fixes a new small scale picture for the quantum matter-radiation dynamics arena consisting in </span><span style="font-size: small; text-align: center;"><a href="http://www.waltervansuijlekom.nl/wp-content/uploads/2014/12/naw5-2014-15-4-2401.pdf" target="_blank">two layers of 4D spacetime</a></span><span style="font-size: small; text-align: center;"> </span><span style="font-size: small; text-align: center;">separated by a distance of 10⁻²⁰ cm and</span><span style="font-size: small;"> </span><span style="font-size: small; text-align: center;">connected thanks to the Higgs field. For such a noncommutative space structure to be a consistent solution of the </span><span style="font-size: small;">C²M equation </span><span style="font-size: small; text-align: center;">requires a third layer at 10⁻²⁹ cm associated with a hypothetical sigma scalar that triggers the seesaw mechanism. This new scalar would explain </span><span style="font-size: small; text-align: center;">on the one side </span><span style="font-size: small; text-align: center;">the weak mass of left-handed neutrinos and on the other side a<a href="https://arxiv.org/abs/1412.4776" target="_blank"> baryogenesis through leptogenesis scenario</a> implying three superheavy right-handed neutrinos also naturally derived from spectral noncommutative first principles. <a href="https://arxiv.org/abs/hep-th/0111236" target="_blank">S</a></span><span style="font-size: small; text-align: center;"><a href="https://arxiv.org/abs/hep-th/0111236" target="_blank">trong, weak and electromagnetic interactions are seen as manifestation of gravity on the former extended spacetime</a> and all merge at some unification scale <a href="https://arxiv.org/abs/1507.08161" target="_blank">in a Pati-Salam model</a>.</span><span style="font-size: small; text-align: center;"> Last but not least, the C²M commutation relation implies also volume quantization which <a href="https://arxiv.org/abs/1702.08180" target="_blank">can lead to mimetic dark matter and dark energy phenomenology at very large scales.</a></span></div></div></td></tr></tbody></table><br /></div><div style="text-align: center;"><br /><div style="text-align: justify;"><br /></div><br /><div style="text-align: justify;"><br /></div></div></div><div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"></div><br /></div></div>Cédric Bardothttps://plus.google.com/104733107894701960711noreply@blogger.com0tag:blogger.com,1999:blog-3911792794793692366.post-57581054223176658022017-04-01T00:14:00.000+02:002017-04-05T17:13:29.114+02:00SUSY has already been uncovered thanks to STRING ;-)<div dir="ltr" style="text-align: left;" trbidi="on"><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-yK5Y70TqNVw/WOUJi1Z26RI/AAAAAAAACLk/9nWRqA7q7YAJjQ_uoAoSeCerqyOeDfWaACLcB/s1600/AprilFool2017b.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://4.bp.blogspot.com/-yK5Y70TqNVw/WOUJi1Z26RI/AAAAAAAACLk/9nWRqA7q7YAJjQ_uoAoSeCerqyOeDfWaACLcB/s640/AprilFool2017b.png" width="570" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">The cat's <a href="https://arxiv.org/abs/1702.08180" target="_blank">seven-league boots</a> to travel <a href="https://www.theguardian.com/science/life-and-physics/2017/mar/24/from-gravity-to-the-higgs-were-still-waiting-for-new-physics" target="_blank">from Higgs to gravity</a> (in two strides from Fermi to the seesaw then unification scales)</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-owe_b095ahQ/WN7PAsLbXJI/AAAAAAAACFQ/UcGdFbhQkXkc87csiKGejsL1hU2H7ok7QCEw/s1600/CalvinApril2017.JPG" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="216" src="https://2.bp.blogspot.com/-owe_b095ahQ/WN7PAsLbXJI/AAAAAAAACFQ/UcGdFbhQkXkc87csiKGejsL1hU2H7ok7QCEw/s640/CalvinApril2017.JPG" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: right;"><span style="font-size: small;">adapted from <a href="http://www.gocomics.com/calvinandhobbes/2015/03/03" target="_blank">Watterson</a></span></td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://arxiv.org/abs/1004.0464" target="_blank"><b>S</b>pectral noncommutative <b>U</b>nification of fundamental interactions based on gauge <b>S</b>ymmetries and <b>Y</b>ukawa mixing</a> is a proved <a href="https://quantumostinato.blogspot.fr/search?q=maldacena+string" target="_blank"><b>S</b>erious <b>T</b>heoretical <b>R</b>esearch <b>I</b>n <b>N</b>atural <b>G</b>eometries</a> leading to the<a href="https://arxiv.org/abs/1208.1030" target="_blank"> only experimentally tested model in town </a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="pw-hidden-cp" style="text-align: center;">Merry April Fools' Day everybody </div><div class="pw-hidden-cp" style="text-align: center;"><br />and happy christmas to Alain Connes!</div></div>Cédric Bardothttps://plus.google.com/104733107894701960711noreply@blogger.com0tag:blogger.com,1999:blog-3911792794793692366.post-58891637199258716562017-03-16T20:35:00.001+01:002017-04-03T17:25:48.494+02:00La cℏorégraphie d'Alice et BoB sur l'horizon d'un trou noir<div dir="ltr" style="text-align: left;" trbidi="on"><b><span style="color: blue;">En attendant l'hypothétique rendez-vous des quanta d'espacetemps avec les paires intriquées de particules de Hawkings ...</span></b><br /><div><br /></div><div><blockquote class="tr_bq" style="text-align: right;">Physiciens écoutez cette phrase est pour vous<br />Le trou noir est un astre à la taille volage<br />Qui ne se laisse pas quantifier par vous<br />Ses quanta se cachent sur l'horizon face à nous<br />Quand on le croit plein son coeur vide pour nous<br />vibre, vibre tandis que voyagent<br /> et dansent appariés ses quanta en un ballet flou<br />Cherchez-les ils sont un peu partout...</blockquote></div><div><blockquote class="tr_bq" style="text-align: right;">sur un air célèbre du <i><a href="http://www.charles-trenet.net/chansons/soleil-lune.html" target="_blank">fou chantant</a> </i></blockquote><br /><br /><div style="text-align: justify;"><span style="color: blue;">Comme le Soleil a rendez-vous avec la Lune d'après la chanson française fameuse de Charles Trenet, la relativité générale et la mécanique quantique doivent bien se rencontrer quelque part, par exemple sur l'horizon des trous noirs. Les modalités de cette réunion n'ont pas encore été observées ni même probablement complètement comprises malgré la théorie "thermodynamique" initiée dans les années 70 puis popularisées dans les années 90 entre autre par Stephen Hawking. Certes elle apporte des éléments d'informations qui convainquent la majorité des physiciens en postulant l'existence d'un processus d'émission de particules qui émergent du trou noir via des fluctuations du vide quantique et conduisent à une lente évaporation de l'astre sombre à cause de son couplage gravitationnel au reste de l'univers ... Or il existe une théorie sinon dissidente du moins nettement moins vulgarisée, développée avec patience et obstination par Gerard 't Hooft, théoricien hollandais et héros quantique reconnu de ses pairs mais méconnu du grand public, qui ne renonce pas à une description quantique unitaire de l'évolution des trous noirs. Ses réflexions <a href="http://www.staff.science.uu.nl/~hooft101/gthpub/Black_Hole_Q_Structure_1985.pdf" target="_blank">initiées dans les années quatre-vingt</a> se sont enrichies de nouvelles idées et d'une hypothèse sinon originale du moins presque oubliée et <a href="http://www.readcube.com/articles/10.1007/s10701-016-0014-y?author_access_token=QkaVx_kMNTqKOFBcX6Zqfve4RwlQNchNByi7wbcMAY7yx4zihl-jZL3XXjBuFqQnhe4FwIgQN1C5a-fIz77asB3I2jW4-pUm5CblHGg5Su3X3hePgfCHIwi28iJ7NRTfO4LnxcfpHa-ujLsYh1ngMA%3D%3D" target="_blank">récemment remise en avant</a> permettant une avancée significative déjà discutée dans ce blog <a href="https://quantumostinato.blogspot.fr/2016/08/how-not-to-be-afraid-by-octopussy-and.html" target="_blank">ici</a> et <a href="https://quantumostinato.blogspot.fr/2017/01/sil-vous-plait-m-t-hooft-chante-nous-un.html" target="_blank">là</a>. </span></div><span style="color: blue;"><br /></span><br /><div style="text-align: justify;"><span style="color: blue;">Le billet d'aujourd'hui se penche <span style="text-align: justify;">sur le travail d'un trio de jeunes physicien-ne-s éduqué-e-s comme l'immense majorité de leurs contemporain-e-s au sein généreux de la théorie des cordes et qui explorent la voie ouverte par leur illustre aîné avec leurs propres outils conceptuels, ce qui permet d'apprécier sous un angle différent le travail de 't Hooft et nous offrent l'occasion de présenter un tableau imagé assez clair du ballet chorégraphié par la mécanique quantique et l'interaction gravitationnelle entre Alice et BoB ou plus explicitement entre un paquet d'onde de matière "</span>traversant" l'horizon d'un trou noir et une paire de particules de Hawking quantiquement intriquées de façon antipodale sur l'horizon en question :</span></div><br /><blockquote><div style="text-align: justify;"><i><u>We revisit the old black hole S-Matrix construction and its new partial wave expansion of ’t Hooft. Inspired by old ideas from non-critical string theory & Matrix Quantum Mechanics, we reformulate the scattering in terms of a quantum mechanical model—of waves scattering off inverted harmonic oscillator potentials—that exactly reproduces the unitary black hole S-Matrix for all spherical harmonics</u>; each partial wave corresponds to an inverted harmonic oscillator with ground state energy that is shifted relative to the s-wave oscillator. Identifying a connection to 2d string theory allows us to show that there is an exponential degeneracy in how a given total initial energy may be distributed among many partial waves of the 4d black hole...</i></div><div style="text-align: justify;"><i><br /></i></div><div style="text-align: justify;"><i><b>Antipodal entanglement</b></i> </div></blockquote><blockquote><div style="text-align: justify;"><i><u>Unitarity of the S-Matrix demands that both the left and right exteriors in the two-sided Penrose diagram need to be accounted for; they capture the transmitted and reflected pieces of the wave-function, respectively</u>. In the quantum mechanics model, there appears to be an ambiguity of how to associate the two regions I and II of the scattering diagram in Fig. 1 to the two exteriors of the Penrose diagram. We saw, in the previous section, that <u>the quantum mechanical model appears to support the creation of physical black holes by exciting appropriate oscillators. Therefore, in this picture there is necessarily only one physical exterior. To resolve the issue of two exteriors, it was proposed that one must make an antipodal identification on the Penrose diagram </u>[19]; see figure 3. <b>Unitarity is arguably a better physical consistency condition than a demand of the maximal analytic extension.</b> The precise identification is given by x → Jx with </i> </div></blockquote><blockquote><div style="text-align: center;"><i>J : (u +, u−, θ, φ) ←→ (−u +, −u −, π − θ, π + φ). (5.1)</i></div></blockquote><blockquote><div style="text-align: justify;"><i>[... the simpler mapping of identifying points in I, II via (u</i><i style="text-align: justify;"><b><sup style="text-align: center;">+</sup></b></i><i>, u</i><i style="text-align: justify;"><span style="text-align: left; vertical-align: super;">−</span></i><i>, θ, φ)↔(−u</i><i style="text-align: justify;"><b><sup style="text-align: center;">+</sup></b></i><i>,−u</i><i style="text-align: justify;"><span style="text-align: left; vertical-align: super;">−</span></i><i>,θ,φ) is singular on the axis u</i><i style="text-align: justify;"><b><sup style="text-align: center;">+</sup></b></i><i>, u</i><i style="text-align: justify;"><span style="text-align: left; vertical-align: super;">−</span></i><i>=0]. Note that J has no fixed points and is also an involution, in that J</i><sup style="text-align: left;">2</sup><i>=1. Such an identification implies that spheres on antipodal points in the Penrose diagram are identified with each other. In particular, this means</i> </div></blockquote><blockquote><div style="text-align: center;"><i>u</i><sup style="text-align: left;">±</sup><i>(θ, φ) = − u</i><sup style="text-align: left;">±</sup><i>(π − θ, π + φ) and </i><i>p</i><sup style="text-align: left;">±</sup><i>(θ, φ) = − p</i><sup style="text-align: left;">±</sup><i>(π − θ, π + φ). (5.2)</i> </div></blockquote><blockquote><div style="text-align: justify;"><i>Therefore, noting that the spherical harmonics then obey Y<sub>l,m</sub>(π-θ,π+φ)= (−1)<sup>l</sup> </i><i>Y<sub>l,m</sub></i><i>(θ,φ), we see that only those modes with an l that is odd contribute. However, <u>owing to the validity of the S-Matrix only in the region of space-time that is near the horizon, this identification is presumably valid only in this region.</u></i><span style="text-align: left;"><u> </u></span></div></blockquote><blockquote><div style="text-align: justify;"><i>Global identifications of the two exteriors have been considered in the past [56–58]. <u>The physics of the scattering, with this identification is now clear</u>. <b>In-going wave-packets move towards the horizon where gravitational back-reaction is strongest according to an asymptotic observer. Most of the information then passes through the antipodal region and a small fraction is reflected back</b>. <b>Turning on quantum mechanics implies that ingoing position is imprinted on outgoing momenta and consequently, an highly localised ingoing wave-packet transforms into two outgoing pieces—transmitted and reflected ones—but both having highly localised momenta</b>. <b>Their positions, however, are highly delocalised. This is how large wavelength Hawking particles are produced out of short wavelength wave-packets and an IR-UV connection seems to be at play</b>. Interestingly, the maximal entanglement between the antipodal out-going modes suggests a wormhole connecting each pair [59]; the geometric wormhole connects the reflected and transmitted Hilbert spaces. Furthermore, as the study of the Wigner time-delay showed, the reflected and transmitted pieces arrive with a time-delay that scales logarithmically in the energy of the in-going wave. This behaviour appears to be very closely related to scrambling time (not the lifetime of the black hole) and we leave a more detailed investigation of this feature to the future. One may also wonder why transmitted pieces dominate the reflected ones. It may be that the attractive nature of gravity is the actor behind the scene.</i><span style="text-align: left;"> </span></div></blockquote><blockquote><div style="text-align: justify;"><i><b>Approximate thermality</b></i></div><div style="text-align: justify;"><i>We now turn to the issue of thermality of the radiated spectrum. Given a number density, say Nin(k) as a function of the energy k, we know that there is a unitary matrix that relates it to radiated spectrum. This unitary matrix is precisely the S-Matrix of the theory...</i></div><div style="text-align: justify;"><i>In our context, since <b>we do not yet have a first principles construction of the appropriate second quantised theory</b>, this in-state may be chosen. For instance, a simple pulse with a wide-rectangular shape would suffice. <u>One may hope to create such a pulse microscopically, by going to the second quantised description and creating a coherent state. Alternatively, one may hope to realize a matrix quantum mechanics model that realizes a field theory in the limit of large number of particles.</u> After all, we know that each oscillator in our model really corresponds to a partial wave and not a single particle in the four dimensional black hole picture.</i></div><b></b><br /><div style="text-align: justify;"><b><b><i>Second Quantization v/s Matrix Quantum Mechanics</i></b></b></div><b></b><br /><div style="text-align: justify;"><i>Given the quantum mechanical model we have studied in this article, we may naively promote the wave-functions ψlm into fields to obtain a second quantized Lagrangian: ...</i></div><div style="text-align: justify;"><i>The form of the Lagrangian being first order in derivatives indicates that the Rindler fields are naturally fermionic. In this description we have a collection of different species of fermionic fields labelled by the {l, m} indices. And the interaction between different harmonics would correspond to interacting fermions of the kind above. <u>The conceptual trouble with this approach is that each “particle” to be promoted to a field is in reality a partial wave as can be seen from the four-dimensional picture. Therefore, second quantizing this model may not be straight-forward</u> [20]. It appears to be <u>more appealing to think of each partial wave as actually arising from an N-particle matrix quantum mechanics model which in the large-N limit yields a second quantized description</u>. Since N counts the number of degrees of freedom, it is naturally related to c via</i><span style="text-align: left;"> </span></div></blockquote><blockquote><div style="text-align: justify;"><div style="text-align: center;"><i>1/N</i><i style="background-color: rgba(255, 255, 255, 0);"><i style="text-align: justify;"><span style="text-align: center;"><span style="text-align: justify;"><sup>2</sup></span></span></i></i><i>∼ c = 8πG R</i><i style="background-color: rgba(255, 255, 255, 0);"><i style="text-align: justify;"><span style="text-align: center;"><span style="text-align: justify;"><sup>2</sup></span></span></i></i><i>∼ l</i><i style="background-color: rgba(255, 255, 255, 0);"><i style="text-align: justify;"><span style="text-align: center;"><span style="text-align: justify;"><sup>2</sup></span></span></i></i><i style="text-align: justify;"><sub>P</sub></i><i> /R</i><i style="background-color: rgba(255, 255, 255, 0);"><i style="text-align: justify;"><span style="text-align: center;"><span style="text-align: justify;"><sup>2</sup></span></span></i></i><i>. (5.8)</i><span style="text-align: left;"> </span></div></div></blockquote><blockquote><div style="text-align: justify;"><i>Therefore, N appears to count the truly microscopic Planckian degrees of freedom that the black hole is composed of. The collection of partial waves describing the Schwarzschild black hole would then be a collection of such N-particle matrix quantum mechanics models. Another possibility is to describe the total system in terms of a single matrix model but including higher representations/non-singlet states to describe the higher l modes. This seems promising because if one fixes the ground state energy of the lowest l=0 (or l=1 after antipodal) oscillator, the higher l oscillators have missing poles in their density of states compared to the l=0, much similar to what was found for the adjoint and higher representations in [60]...</i></div><div style="text-align: justify;"><i>To sharpen any microscopic statements about the S-matrix, one might first need to derive an MQM model that regulates Planckian effects.</i></div></blockquote><br /><blockquote class="tr_bq"><div style="text-align: right;"><i><a href="https://arxiv.org/abs/1607.07885" target="_blank">The Black Hole S-Matrix from Quantum Mechanics</a></i></div><div style="text-align: right;"><a href="https://arxiv.org/find/hep-th/1/au:+Betzios_P/0/1/0/all/0/1">Panagiotis Betzios</a>, <a href="https://arxiv.org/find/hep-th/1/au:+Gaddam_N/0/1/0/all/0/1">Nava Gaddam</a>, <a href="https://arxiv.org/find/hep-th/1/au:+Papadoulaki_O/0/1/0/all/0/1">Olga Papadoulaki</a></div><div style="text-align: right;">(Submitted on 26 Jul 2016 (<a href="https://arxiv.org/abs/1607.07885v1">v1</a>), last revised 23 Nov 2016 (this version, v2))</div></blockquote><br /><div style="text-align: justify;"><br /><span style="color: blue;">Puissent d'autres physiciennes et physiciens à l'oreille cette fois familière au hiératique chant spectral noncommutatif suivre l'exemple précédent et enrichir à leur tour de leur répertoir propre la mystérieuse musique du cℏoeur quantique des trous noirs révélé par G. 't Hooft en trouvant comment accorder ses paires de particules antipodales intriquées sur l'horizon du trou noir avec l<a href="https://arxiv.org/abs/1702.08180">es deux types de quanta de volume à la base des solutions d'espacetemps spinoriels à quatre dimensions</a> pour l'<a href="https://arxiv.org/abs/1703.02470">équation de Chamseddine-Connes-Mukhanov</a>.</span><br /><span style="color: blue;"><br /></span><span style="color: blue;"><br /></span><span style="color: blue;">//Modification du titre du billet et du corps du texte en français le 25 Mars 2017</span><br /><span style="color: blue;"><br /></span><span style="color: blue;"><br /></span><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-fP3mMFTGaD4/WN_XVbDe5EI/AAAAAAAACGg/OhElyCAbpNogHpJnRdtDpga6UHLLUut0QCLcB/s1600/AliceBob.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="180" src="https://1.bp.blogspot.com/-fP3mMFTGaD4/WN_XVbDe5EI/AAAAAAAACGg/OhElyCAbpNogHpJnRdtDpga6UHLLUut0QCLcB/s320/AliceBob.JPG" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;">Alice and Bob in Wonderland (Video <a href="https://insidetheperimeter.ca/alice-bob-in-wonderland-can-we-travel-through-time/" target="_blank">here</a>)</div><span style="color: blue;"><br /></span></div></div></div>Cédric Bardothttps://plus.google.com/104733107894701960711noreply@blogger.com0tag:blogger.com,1999:blog-3911792794793692366.post-14874982377218582312017-03-08T17:33:00.001+01:002017-03-08T19:16:48.558+01:00The birth of (an intuition about) at(t)oms of spacetime<div dir="ltr" style="text-align: left;" trbidi="on"><div style="text-align: justify;">Thinking for some time now on how to conceptually grasp and empirically catch <a href="https://quantumostinato.blogspot.fr/2015/07/a-tale-of-two-tt-oms-new-hypotheses.html"><i>attoms of spacetime</i> </a> I could not fail to share this interesting and accessible lecture, taking the opportunity to prove today the progress made by physics community to put women contributions in the forefront!</div><div style="text-align: justify;"><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/VhHE86d-Th8/0.jpg" frameborder="0" height="266" src="https://www.youtube.com/embed/VhHE86d-Th8?feature=player_embedded" width="320"></iframe></div><blockquote class="tr_bq" style="text-align: justify;"><div style="text-align: center;"><a href="https://arxiv.org/abs/1405.3492" target="_blank">Fay Dowker</a> Public Lecture - </div><div style="text-align: center;"><i style="font-style: italic;">Spacetime Atoms and the Unity of Physics </i>(Perimeter Public Lecture)</div></blockquote><br /><br />One will find below a reading proposal to experience again the very pedagogical quality of Fay Dowker (I am not competent to emit judgment on her research) talking about the dynamics of spacetime in general relativity:<br /><br /><blockquote class="tr_bq" style="text-align: justify;"><i>... <u>I wish to suggest, our inability to reach consensus on the passage of time could be a consequence of our not yet having made the necessary scientific progress. We do not have a successful theory of spacetime that coherently incorporates the quantum nature of the physical world, so we do not yet know the nature of the deep structure of spacetime.</u> Some of the observational facts on which the new theory will be built may, therefore, now be only roughly communicable and our sense-experience of the passage of time may be an example of such a fact. <u>In the last decades, however, progress on one approach to finding a theory of quantum spacetime – or quantum gravity as it is usually called – affords us a forward look at how the passage of time may eventually find a place in science. The approach, causal set theory, is based on the hypothesis that spacetime is fundamentally granular or atomic at the Planck scale and this atomicity opens the door to new dynamical possibilities for spacetime and, hence, to a new perspective on the dichotomy of Being and Becoming</u>. In this article I will describe this progress and will expand upon R. D. Sorkin’s claim that it gives us scientific purchase on the concept of passage [2].</i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i> <u>Spacetime is a continuous, smooth, four-dimensional material that bends, warps and ripples according to dynamical law as specified by the Einstein equations. Even when there is no matter present, “empty” spacetime itself can carry energy in the form of gravitational waves. Indeed this is the explanation for the variation in the rotation rate of the Hulse-Taylor binary pulsar system, which can be accurately modelled as a system losing energy via this gravitational radiation. The spacetime material is, however, very different from those substances that populated pre-relativistic physical theory in that it is intrinsically four-dimensional.</u> It cannot be understood as a three-dimensional entity – “space” – evolving in time because that would imply a global time in which the evolution occurs and there is no such global, physical time in General Relativity (GR). <u>The notion that at one moment of time there is space, a 3-d geometry, and at the next moment space has evolved to another 3-d geometry is wrong in GR. There is no such physically meaningful entity as 3-d space, no physically meaningful slicing of spacetime into space-changing-in-time.</u></i> </blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>Having focussed on what spacetime in GR is not, we can ask what it is. <u>The structure of spacetime that takes centre stage in understanding the physics of GR is its causal structure. This causal structure is a partial order on the points of spacetime.1 Given two points of spacetime, call them A and B, they will either be ordered or unordered. If they are ordered then one, let’s say A without loss of generality, precedes – or, is to the past of – the other, B. This ordering is transitive: if A precedes B and B precedes C then A precedes C. The order is partial because there are pairs of spacetime points such that there is no physical sense in which one of the pair precedes the other, they are simply unordered.</u> This lack of ordering does not mean the points of the pair are simultaneous because that would imply they occur at the same “time” and require the existence of a global time for them to be simultaneous in. Again: global time does not exist in GR.</i> </blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><u>This partial ordering of the points of spacetime is referred to as the causal structure of spacetime because it coincides with the potential for physical effects to propagate. Physical effects can propagate from A to B in spacetime if and only if A precedes B in the causal structure. If two spacetime points are unordered then no physical effect can propagate from one to the other because to do so would require something physical to travel faster than light.</u>Causal structure plays a central role in GR and indeed the epitome of the theory, a black hole, is defined in terms of the causal structure: it is a region of spacetime such that nothing that happens in that region can affect anything outside the region. <u>It is only by thinking of a black hole in terms of causal structure that its physics can be understood</u>. [As an example of this, it is very difficult to answer the question, “Does someone falling feet first into a black hole lose sight of their feet as their feet cross the horizon?” without drawing the conformal “Penrose” diagram that depicts the causal structure.]</i> </blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><u>If there is no global, universal time, where do we find within GR the concept of physical time at all? Physical time in GR is associated, locally and “personally,” with every localised physical system, in a manner that more closely reflects our intimate experience of time than the global time of pre-relativistic Newtonian mechanics</u>. Each person or object traces out a trajectory or worldline through spacetime, a continuous line in spacetime that is totally ordered by the causal order: for any 2 points on the worldline, one precedes the other. <u>GR also provides a quantitatively precise concept of proper time that elapses along each timelike worldline. A clock carried by a person following a worldline through spacetime will measure this proper time as it elapses, locally along the worldline. Viewed from this perspective, the famous “twin paradox” is no longer a paradox: two people who meet once, then follow different worldlines in spacetime and meet a second time in the future will in general have experienced different amounts of proper time – real, physical time – elapsing along their different worldlines between the meetings. Clocks are “odometers for time” along worldlines through spacetime</u>. The remarkable thing, from this perspective, is that we get by in everyday life quite well under the assumption that there is a global Now, a universal global time, and that we can synchronise our watches when we meet, then do different things and when we meet again our watches will still be synchronised. <u>GR</u> explains this because it <u>predicts that as long as the radius of curvature of spacetime is large compared to the physical scale of the system and the relative velocities of the subsystems involved are small compared with the speed of light, the differences in proper time that elapse along our different worldlines will be negligible. We can behave as if there is a global time, a global moment of Now, because for practical everyday purposes our clocks will remain synchronised to very high precision</u>. </i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><u>In addition to being the key to understanding GR, the causal structure of spacetime is a unifying concept. Theorems by Kronheimer and Penrose [4], Hawking [5] and Malament [6] establish that the causal order unifies within itself topology, including dimension, differentiable structure (smoothness) and almost all the spacetime geometry.</u> <b>The only geometrical information that the causal structure lacks is local physical scale.</b>[Technically, the result states that if two distinguishing spacetimes are causally isomorphic then they are conformally isometric. In 4 dimensions this implies that the causal structure provides 9/10 of the metrical information as the metric is given by a symmetric 4 × 4 matrix field of 10 spacetime functions, 9 of which can be fixed in terms of the 10th.</i><i>] <b>This local scale information can be furnished by providing the spacetime volume of every region of spacetime or, alternatively, the amount of proper time that elapses – the duration – along every timelike worldline. In the continuum, the causal structure and local scale information complement each other to give the full geometry of spacetime, the complete spacetime fabric</b>... </i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>There are strong, physical arguments that the smooth manifold structure of spacetime must break down at the Planck scale where quantum fluctuations in the structure of spacetime cannot be ignored. <u>The most convincing evidence that spacetime cannot remain smooth and continuous at arbitrarily small scales and that the scale at which the continuum breaks down is the Planck scale is the finite value of the entropy of a Black Hole [7]. Fundamental spacetime discreteness is a simple proposal that realises the widely held expectation that there must be a physical, Planck scale cutoff in nature. According to this proposal, spacetime is comprised of discrete “spacetime atoms” at the Planck scale.</u>The causal set programme for quantum gravity [8, 9, 10] is based on the observation that such atomicity is exactly what is needed in order to conceive of spacetime as pure causal order since in a discrete spacetime, physical scale – missing in the continuum – can be provided by counting. <u>For example, a worldline in a discrete spacetime would consist of a chain of ordered spacetime atoms and its proper time duration, in fundamental Planckian scale units of time of roughly 10 </u></i><i style="text-align: justify;"><sup>-43</sup></i><i><u> seconds, would be simply the number of spacetime atoms that comprise the worldline.</u></i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>Causal set theory thus postulates that underlying our seemingly smooth continuous spacetime there is an atomic spacetime taking the form of a discrete, partially ordered set or causal set, whose elements are the spacetime atoms. <u>The order relation on the set gives rise to the spacetime causal order in the approximating continuum spacetime and the number of causal set elements comprising a region gives the spacetime volume of that region in fundamental units.</u> The Planckian scale of the atomicity means that there would be roughly 10</i><i style="text-align: justify;"><sup>240</sup></i><i>spacetime atoms comprising our observable universe.</i> </blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>According to causal set theory, spacetime is a material comprised of spacetime atoms which are, in themselves, featureless, with no internal structure and are therefore identical. Each atom acquires individuality as an element of a discrete spacetime, a causal set, in view of its order relations with the other elements of the set. Let me stress here a crucial point: the elements of the causal set, the discrete spacetime, are atoms of 4-d spacetime, not atoms of 3-d space. An atomic theory of space would run counter to the physics of GR in which 3-d space is not a physically meaningful concept. An atom of spacetime is an idealisation of a click of the fingers, an explosion of a firecracker, a here-and-now.</i></blockquote><blockquote class="tr_bq"><div style="text-align: right;"><i><a href="https://arxiv.org/abs/1405.3492" target="_blank">The birth of spacetime atoms as the passage of time</a></i></div><div style="text-align: right;"><a href="https://arxiv.org/find/gr-qc/1/au:+Dowker_F/0/1/0/all/0/1">Fay Dowker</a></div><div style="text-align: right;">(Submitted on 14 May 2014)</div></blockquote><br />More about causal set theory and quantum gravity in the former post...<br /><br /><div style="text-align: justify;">I remind the reader that my choice of the words <i>attoms of spacetime </i>has many motives, the most important one conceptually can be formulated now in the following way:</div><blockquote class="tr_bq" style="text-align: justify;"><b>the Higgs boson discovery which is a new fundamental piece of local information at the <i>atto</i>meter scale, <a href="https://arxiv.org/abs/1304.8050" target="_blank">if it is understood in a spectral noncommutative geometric perspective</a>, confirms the global piece of information provided by dark matter and possibly dark energy interpreted as mimetic gravity aspects of the quantisation of spacetime as described by a <a href="https://arxiv.org/abs/1703.02470" target="_blank">higher Heisenberg equation proposed by Chamseddine, Connes and Mukhanov that fixes the volume form of 4 dimensional spacetime</a>s.</b></blockquote><br /><br /></div>Cédric Bardothttps://plus.google.com/104733107894701960711noreply@blogger.com0tag:blogger.com,1999:blog-3911792794793692366.post-986310759918885162017-03-08T16:30:00.003+01:002017-03-08T17:43:21.366+01:00Next station : naturalness, terminus cosmos<div dir="ltr" style="text-align: left;" trbidi="on"><div style="text-align: justify;"><b>What if the cosmological constant was a nonlocal quantum residue of discreteness of spacetime </b>... just like mimetic dark matter is a nonlocal noncommutative consequence of the quantisation of space-time volume?</div><div style="text-align: justify;"><br /></div><div><div style="text-align: justify;"><br /></div><blockquote class="tr_bq"><div style="text-align: right;"><i>Lieber Ehrenfest! </i><span style="text-align: left;"> </span></div></blockquote><blockquote class="tr_bq"><i></i><br /><div style="text-align: right;"><i><i>... Ich habe auch wieder <a href="http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/echo/einstein/sitzungsberichte/S250UZ0K/index.meta" target="_blank">etwas verbrochen in der Gravitationstheorie</a>, was mich ein wenig in Gefahr setzt, in einem Tollhaus interniert zu werde.</i></i></div><i></i></blockquote><div class="tr_bq"><blockquote class="tr_bq" style="text-align: right;"><a href="http://einsteinpapers.press.princeton.edu/vol8a-doc/458?ajax" target="_blank">Einstein's letter February 4th 1917</a></blockquote><br /><br /><div class="tr_bq"><br /></div><div style="text-align: justify;">The former post provides an(other) opportunity to the readers of this blog to watch a presentation of the new conceptual framework envisioned by the geometer Alain Connes and his closest physicist collaborator Ali Chamseddine with the help of cosmologist Sacha Mukhanov in order to show how the standard model of quantum matter-radiation interactions emerges from the discreteness of spacetime formulated with a spectral noncommutative geometric equation. If the physical consequences of this breakthrough that leads to understanding dark matter as some mimetic gravity is analysed in detail by Chamseddine in a very recent review article, the impact on <a href="https://arxiv.org/abs/1701.07261" target="_blank">cosmological constant </a>is more elusive not to speak about the quantisation of spacetime dynamics.<br /><br />Looking for more insight about what could be a heuristic hypothesis toward the discreteness of spacetime volume I could not afford to talk about, or rather quote, causal set approach to quantum gravity:</div><div style="text-align: justify;"><br /></div></div><blockquote><div style="text-align: justify;"><u><i>The evidence ... points to a cosmological constant of magnitude, Λ≈10</i><i><span style="text-align: justify;"><span style="text-align: justify;"><span style="text-align: center;"><span style="text-align: justify;"><sup>-120</sup></span></span></span></span></i><i>κ</i><i><span style="text-align: justify;"><span style="text-align: justify;"><span style="text-align: center;"><span style="text-align: justify;"><sup>-2</sup></span></span></span></span></i></u><i><u> , and this raises two puzzles:</u> [I prefer the word puzzle or riddle to the word problem, which suggests an inconsistency, rather than merely an unexplained feature of our theoretical picture.] <u>Why is Λ so small without vanishing entirely, and Why is it so near to the critical density ρ<sub style="text-align: justify;">critical</sub> = 3H<span style="text-align: justify;"><span style="text-align: justify;"><span style="text-align: center;"><span style="text-align: justify;"><sup>2</sup></span></span></span></span></u>...</i> </div></blockquote><blockquote><div style="text-align: justify;"><u><i>Is the latter just a momentary occurrence in the history of the universe (which we are lucky enough to witness), or has it a deeper meaning? Clearly both puzzles would be resolved if we had reason to believe that Λ ≈ H</i><i><span style="text-align: justify;"><span style="text-align: justify;"><span style="text-align: center;"><span style="text-align: justify;"><sup>2</sup></span></span></span></span></i></u><i><u> always. In that case, the smallness of Λ today would merely reflect the large age of the cosmos. But such a Λ would conflict with our present understanding of nucleosynthesis in the early universe and of “structure formation” more recently</u>. (In the first case, the problem is that the cosmic expansion rate influences the speed with which the temperature falls through the “window” for synthesizing the light nuclei, and thereby affects their abundances. According to </i>{the Friedmann equations}<i> a positive Λ at that time would have increased the expansion rate, which however is already somewhat too big to match the observed abundances. In the second case, the problem is that a more rapid expansion during the time of structure formation would tend to oppose the enhancement of density perturbations due to gravitational attraction, making it difficult for galaxies to form.) <u>But neither of these reasons excludes a <b>fluctuating Λ with typical magnitude |Λ|∼H</b></u></i><u><i><span style="text-align: justify;"><span style="text-align: justify;"><span style="text-align: center;"><span style="text-align: justify;"><sup><b>2</b></sup></span></span></span></span></i><i> but mean value <Λ>=0. The point now is that such fluctuations <b>can arise as a residual, nonlocal quantum effect of discreteness</b>, and specifically of the type of discreteness embodied in the causal set...</i> </u></div></blockquote><blockquote style="text-align: justify;"><i>In order to explain this claim, I will need to review some basic aspects of causet theory. [<a href="https://arxiv.org/abs/gr-qc/0508109" target="_blank">5</a>] <u>According to the causal set hypothesis, the smooth manifold of general relativity dissolves, near the Planck scale, into a discrete structure whose elements can be thought of as the “atoms of spacetime”</u>. These atoms can in turn be thought of as representing “births”, and as such, they carry a relation of ancestry that mathematically defines a partial order, x ≺ y. Moreover, in our best dynamical models [<a href="https://arxiv.org/abs/gr-qc/9904062" target="_blank">6</a>], the births happen sequentially in such a way that the number n of elements plays the role of an auxiliary time-parameter. (In symbols, n ∼ t.)[It is an important constraint on the theory that this auxiliary time-label n should be “pure gauge” to the extent that it fails to be determined by the physical order-relation ≺. That is, it must not influence the dynamics, this being the discrete analog of general covariance] <u>Two basic assumptions complete the kinematic part of the story by letting us connect up a causet with a continuum spacetime. One posits first, that the underlying microscopic order ≺ corresponds to the macroscopic relation of before and after, and second, that the number of elements N comprising a region of spacetime equals the volume of that region in fundamental (i.e. Planckian) units</u>. (In slogan form: geometry = order + number.) <u>The equality between number N and volume V is not precise however, but subject to Poisson fluctuations, whence instead of N=V, we can write only</u></i> </blockquote><blockquote style="text-align: center;"><i><u>N∼V±√V</u>. (5)</i> </blockquote><blockquote style="text-align: justify;"><i><u>(These fluctuations express a “kinematical randomness” that seems to be forced on the theory by the noncompact character of the Lorentz group.)</u>To complete the causet story, one must provide a “dynamical law” governing the birth process by which the causet “grows” (the discrete counterpart of {the Einstein} equation...). This we still lack in its quantum form, but for heuristic purposes we can be guided by the classical sequential growth (CSG) models referred to above; and this is what I have done in identifying n as a kind of time-parameter... </i> </blockquote><blockquote style="text-align: justify;"><i><u>We can now appreciate why one might expect a theory of quantum gravity based on causal sets to lead to a fluctuating cosmological constant. Let us assume that at sufficiently large scales the effective theory of spacetime structure is governed by a gravitational path-integral, which at a deeper level will of course be a sum over causets. That n plays the role of time in this sum suggests that it must be held fixed, which according to (5) corresponds to holding V fixed in the integral over 4-geometries.</u> If we were to fix V exactly, we’d be doing “unimodular gravity”, in which setting it is easy to see that V and Λ are conjugate to each other in the same sense as energy and time are conjugate in nonrelativistic quantum mechanics. [This conjugacy shows up most obviously in the Λ-term in the gravitational action-integral, which is simply </i></blockquote><blockquote style="text-align: center;"><i>−Λ <span style="text-align: left;">∫</span>√−g d</i><i style="text-align: justify;"><span style="text-align: justify;"><span style="text-align: justify;"><span style="text-align: center;"><span style="text-align: justify;"><sup>2</sup></span></span></span></span></i><i>x = −ΛV . (6) </i></blockquote><blockquote style="text-align: justify;"><i>It can also be recognized in canonical formulations of unimodular gravity [<a href="http://inspirehep.net/record/283907/?ln=fr" target="_blank">7</a>], and in the fact that (owing to (6)) the “wave function” Ψ(<span style="text-align: justify;"><span style="text-align: justify;"><span style="text-align: center;"><span style="text-align: justify;"><sup>3</sup></span></span></span></span>g; Λ) produced by the unrestricted path-integral with parameter Λ is just the Fourier transform of the wave function Ψ(<span style="text-align: justify;"><span style="text-align: justify;"><span style="text-align: center;"><span style="text-align: justify;"><sup>3</sup></span></span></span></span>g; Λ)n produced at fixed V.] <u>In analogy to the ∆E∆t uncertainty relation, we thus expect in quantum gravity to obtain</u> </i></blockquote><blockquote style="text-align: center;"><i>∆Λ ∆V ∼ <span style="background-color: white; font-family: "times new roman"; text-align: left;">ℏ </span> (7) </i></blockquote><blockquote style="text-align: justify;"><i><u>Remember now, that even with N held exactly constant, V still fluctuates, following (5), between N + √ N and N − √ N</u>; that is, we have N ∼ V ± √N ⇒ V ∼ N ± √V , or ∆V∼√V . <u>In combination with (7), this yields for the fluctuations in Λ the central result </u></i></blockquote><blockquote style="text-align: center;"><i>∆Λ ∼ V <span style="text-align: justify;"><span style="text-align: justify;"><span style="text-align: justify;"><span style="text-align: center;"><span style="text-align: justify;"><sup>-1/2</sup></span></span></span></span></span> (8) </i></blockquote><blockquote style="text-align: justify;"><i>Finally, let us assume that, for reasons still to be discovered, the value about which Λ fluctuates is strictly zero: <Λ>=0. (This is the part of the Λ puzzle we are not trying to solve...) A rough and ready estimate identifying spacetime volume with the Hubble scale H <span style="text-align: justify;"><span style="text-align: justify;"><span style="text-align: center;"><span style="text-align: justify;"><sup>-1</sup></span></span></span></span> then yields V∼(H <span style="text-align: justify;"><span style="text-align: justify;"><span style="text-align: center;"><span style="text-align: justify;"><sup>-1</sup></span></span></span></span>)<span style="text-align: justify;"><span style="text-align: justify;"><span style="text-align: center;"><span style="text-align: justify;"><sup>4</sup></span></span></span></span>⇒ Λ∼<span style="text-align: center;">V </span><span style="text-align: justify;"><span style="text-align: justify;"><span style="text-align: center;"><span style="text-align: justify;"><sup>-1/2</sup></span></span></span></span>∼H<span style="text-align: justify;"><span style="text-align: justify;"><span style="text-align: center;"><span style="text-align: justify;"><sup>2</sup></span></span></span></span>∼ρ</i><i><sub style="text-align: justify;">critical</sub></i><i> (where I’ve used that Λ=Λ−<Λ> since <Λ>=0). In other words, Λ would be “ever-present” (at least in 3+1 dimensions)...</i> </blockquote><blockquote style="text-align: justify;"><i>In trying to develop (8) into a more comprehensive model, we not only have to decide exactly which spacetime volume ‘V’ refers to, we also need to interpret the idea of a varying Λ itself. <u>Ultimately the phenomenological significance of V and Λ would have to be deduced from a fully developed theory of quantum causets, but until such a theory is available, the best we can hope for is a reasonably plausible scheme which realizes (8) in some recognizable form. </u></i></blockquote><blockquote style="text-align: justify;"><i><u>As far as V is concerned, it pretty clearly wants to be the volume to the past of some hypersurface, but which one</u>? If the local notion of “effective Λ at x” makes sense, and if we can identify it with the Λ that occurs in (8), then<u> it seems natural to interpret V as the volume of the past of x, or equivalently (up to Poisson fluctuations) as the number of causet elements which are ancestors of x: </u></i></blockquote><blockquote style="text-align: center;"><i>V = volume(past(x)).</i></blockquote><blockquote style="text-align: justify;"><i>One could imagine other interpretations... but this seems as simple and direct as any... </i></blockquote><blockquote style="text-align: justify;"><i>A<u>s far as Λ is concerned, the problems begin with Einstein's equation itself</u>, whose divergence implies (at least naively... ) that Λ = constant. The model of [<a href="https://arxiv.org/abs/astro-ph/0209274" target="_blank">2</a>] and [</i><i><u><a href="https://arxiv.org/abs/1210.2589" target="_blank">3</a></u></i><i>] addresses this difficulty... <u>we are forced to modify the Friedmann equations... The most straightforward way of doing so is to retain only one of them, or possibly some other linear combination</u>... Then <u>our dynamical scheme is just </u></i></blockquote><blockquote style="text-align: center;"><i>3(<span style="text-align: left;">ȧ</span>/a)<span style="text-align: justify;"><span style="text-align: justify;"><span style="text-align: justify;"><span style="text-align: center;"><span style="text-align: justify;"><sup>2</sup></span></span></span></span></span> = ρ + ρΛ (9a)</i></blockquote><blockquote style="text-align: center;"><i> 2 <span style="text-align: left;">ä</span>/a + (<span style="text-align: left;">ȧ</span>/a)<span style="text-align: justify;"><span style="text-align: justify;"><span style="text-align: justify;"><span style="text-align: center;"><span style="text-align: justify;"><sup>2</sup></span></span></span></span></span> = −(p + p<sub>Λ</sub>) (9b) </i></blockquote><blockquote style="text-align: justify;"><i>with ρ<sub style="text-align: center;">Λ</sub>=Λ and p<sub style="text-align: center;">Λ</sub>= −Λ − ̇Λ/3H. Finally, <u>to complete our model and obtain a closed system of equations, we need to specify Λ as a (stochastic) function of V , and we need to choose it so that ∆Λ∼<span style="text-align: center;">V <span style="text-align: justify;"><span style="text-align: justify;"><span style="text-align: justify;"><span style="text-align: center;"><span style="text-align: justify;"><sup>-1/2</sup></span></span></span></span></span></span>. But this is actually easy to accomplish</u>, if we begin by <u>observing that (with κ = <span style="text-align: center;"><span style="background-color: white; font-family: "times new roman"; text-align: left;">ℏ</span></span> = 1) Λ = S/V ≈ S/N can be interpreted as the action per causet element that is present even when the spacetime curvature vanishes</u>. (As one might say, it is the action that an element contributes just by virtue of its existence.† ) <u>Now imagine that each element contributes (say) ±<span style="text-align: center;"><span style="background-color: white; font-family: "times new roman"; text-align: left;">ℏ</span></span> to S, with a random sign. Then S is just the sum of N independent random variables, and we have S/<span style="text-align: center;"><span style="background-color: white; font-family: "times new roman"; text-align: left;">ℏ</span></span> ∼ ±√ N ∼ ±√(V /ℓ<span style="text-align: center;"><span style="text-align: justify;"><span style="text-align: justify;"><span style="text-align: justify;"><span style="text-align: center;"><span style="text-align: justify;"><sup>4</sup></span></span></span></span></span></span>), where ℓ∼√(<span style="text-align: center;"><span style="background-color: white; font-family: "times new roman"; text-align: left;">ℏ</span></span>κ) is the fundamental time/length of the underlying theory, which thereby enters our model as a free phenomenological parameter.</u> This in turn implies, as desired, that<span style="text-align: left;"> </span></i></blockquote><blockquote style="text-align: justify;"><div style="text-align: center;"><i>Λ = S/V ∼ ± (<span style="text-align: center;"><span style="background-color: white; font-family: "times new roman"; text-align: left;">ℏ</span></span>/ℓ<span style="text-align: center;"><span style="text-align: justify;"><span style="text-align: justify;"><span style="text-align: justify;"><span style="text-align: center;"><span style="text-align: justify;"><sup>2</sup></span></span></span></span></span></span>)/√V (10)<span style="text-align: left;"> </span></i></div></blockquote><blockquote style="text-align: justify;"><i>We have thus arrived at an ansatz that, while it might not be unique, succeeds in producing the kind of fluctuations we were seeking. Moreover, it lends itself nicely to simulation by computer... <span style="text-align: left;"> </span><span style="text-align: left;"> </span></i></blockquote><blockquote style="text-align: justify;"><i><u>An extensive discussion of the simulations can be found in [<a href="https://arxiv.org/abs/1210.2589" target="_blank">3</a>] and [<a href="https://arxiv.org/abs/astro-ph/0209274" target="_blank">2</a>]. The most important finding was that... the absolute value of Λ follows ρradiation very closely during the era of radiation dominance, and then follows ρmatter when the latter dominates. Secondly, the simulations confirmed that Λ fluctuates with a “coherence time” which is O(1) relative to the Hubble scale</u>. Thirdly, a range of present-day values of Ω<sub style="text-align: center;">Λ</sub> is produced, and these are O(1) when ℓ<span style="text-align: center;"><span style="text-align: justify;"><span style="text-align: justify;"><span style="text-align: justify;"><span style="text-align: center;"><span style="text-align: justify;"><sup>2</sup></span></span></span></span></span></span>= O(κ). (Notice in this connection that <u>the variable Λ of our model cannot simply be equated to the observational parameter Λ</u></i><i style="text-align: center;"><sub><u>obs </u></sub></i><i><u>that gets reported on the basis of supernova observations, for example, because Λobs results from a fit to the data that presupposes a constant Λ, or if not constant then a deterministically evolving Λ with a simple “equation of state”. It turns out that correcting for this tends to make large values of Ω<sub style="text-align: center;">Λ</sub> more likely</u> [</i><i><u><a href="https://arxiv.org/abs/1210.2589" target="_blank">3</a></u></i><i>].) Fourthly, the Λ-fluctuations affect the age of the cosmos (and the horizon size), but not too dramatically. In fact they tend to increase it more often than not. Finally, <u>the choice of (9a) for our specific model seems to be “structurally stable“ in the sense that the results remain qualitatively unchanged if one replaces (9a) by some linear combination thereof with (9b)</u>, as discussed above...</i></blockquote><blockquote style="text-align: justify;"><i><u>Heuristic reasoning rooted in the basic hypotheses of causal set theory predicted Λ∼±1/√V , in agreement with current data</u>. But a fuller understanding of this prediction awaits the ... new ... quantum causet dynamics”... Meanwhile, <u>a reasonably coherent phenomenological model exists</u>, based on simple general arguments.<u> It is broadly consistent with observations but a fuller comparison is needed. It solves the “why now” problem: Λ is “ever-present”</u>. It predicts further that pΛ </i><span style="text-align: left;">≠</span><i> −ρΛ (w </i><span style="text-align: left;">≠</span><i> −1) and that Λ has probably changed its sign many times in the past.[ It also tends to favor the existence of something, say a “sterile neutrino”, to supplement the energy density at nucleosynthesis time. Otherwise, we might have to assume that Ω<sub style="text-align: center;">Λ </sub>had fluctuated to an unusually small value at that time. It also carries the implication that “large extra dimensions” will not be observed at the LHC...] <u>The model contains a single free parameter of order unity that must be neither too big nor too small.</u>[unless we want to try to make sense of imaginary time (= quantum tunneling?) or to introduce new effects to keep the right hand side of (9) positive (production of gravitational waves? onset of large-scale spatial curvature or “buckling”?).] <u>In principle the value of this parameter is calculable, but for now it can only be set by hand. </u> <span style="text-align: left;"> </span></i></blockquote><blockquote style="text-align: justify;"><i>In this connection, it’s intriguing that there exists an analog condensed matter system the “fluid membrane”, whose analogous parameter is not only calculable in principle from known physics, but might also be measurable in the laboratory! [<a href="https://arxiv.org/abs/cond-mat/0603804" target="_blank">9</a>]...</i></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><i></i></div><div style="text-align: justify;"><i><u>In itself the smallness of Λ is a riddle and not a problem</u>. But <b>in a fundamentally discrete theory, recovery of the continuum is a problem, and I think that the solution of this problem will also explain the smallness of Λ</b>. (The reason is that <u>if Λ were to take its “natural”, Planckian value, the radius of curvature of spacetime would also be Planckian, but in a discrete theory such a spacetime could no more make sense than a sound wave with a wavelength smaller than the size of an atom. Therefore the only kind of spacetime that can emerge from a causet or other discrete structure is one with Λ≪1</u>.) One can also give good reasons why the emergence of a manifold from a causet must rely on some form of nonlocality. The size of Λ should also be determined nonlocally then, and this is precisely the kind of idea realized in the above model.</i><span style="text-align: left;"> </span></div></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><i><u>One pretty consequence of this kind of nonlocality is a certain restoration of symmetry between the very small and the very big. Normally, we think of G (gravity) as important on large scales, with h (quantum) important on small ones.</u><b> But we also expect that on still smaller scales G regains its importance once again and shares it with </b></i><b><span style="background-color: white; font-family: "times new roman"; text-align: left;">ℏ </span><i> (quantum gravity). If the concept of an ever-present Λ is correct then symmetry is restored, because </i><span style="background-color: white; font-family: "times new roman"; text-align: left;">ℏ </span></b><b><i>rejoins G on the largest scales in connection with the cosmological constant.</i><span style="text-align: left;"> </span></b></div></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><i>Finally, let me mention a “fine tuning” that our model has not done away with, namely the tuning of the spacetime dimension to d=4. <u>In any other dimension but 4, Λ could not be “ever-present”, or rather it could not remain in balance with matter. Instead, the same crude estimates that above led us to expect Λ∼H</u></i><i style="text-align: justify;"><i><i style="text-align: justify;"><span style="text-align: center;"><span style="text-align: justify;"><sup><u>2</u></sup></span></span></i></i></i><i><u> , lead us in other dimensions to expect either matter dominance (d>4) or Λ-dominance (d<4). Could this be a dynamical reason favoring 3+1 as the number of noncompact dimensions</u>?...[<a href="https://arxiv.org/abs//gr-qc/0612128" target="_blank">10</a>]...</i><span style="text-align: left;"> </span> </div></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><span style="text-align: left;"><i>A last word</i></span></div></blockquote><blockquote class="tr_bq" style="text-align: right;"><i>The cosmological constant is just as constant as Hubble’s constant.</i></blockquote><br /><blockquote class="tr_bq"><div style="text-align: right;"><i><a href="https://arxiv.org/abs/0710.1675" target="_blank">Is the cosmological "constant" a nonlocal quantum residue of discreteness of the causal set type?</a></i></div><div style="text-align: right;"><a href="https://arxiv.org/find/gr-qc/1/au:+Sorkin_R/0/1/0/all/0/1">Rafael D. Sorkin</a> (Perimeter Institute and Syracuse University)</div><div style="text-align: right;">(Submitted on 9 Oct 2007)</div></blockquote><br /></div></div>Cédric Bardothttps://plus.google.com/104733107894701960711noreply@blogger.com0tag:blogger.com,1999:blog-3911792794793692366.post-18801246384781521592017-03-08T15:28:00.004+01:002017-04-01T15:32:21.025+02:00The spring is coming...<div dir="ltr" style="text-align: left;" trbidi="on"><div class="separator" style="clear: both; text-align: justify;"><b>... as a possible relevant quantum geometry of space-time-matter-radiation blossoms ...</b></div><div class="separator" style="clear: both; text-align: justify;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-G4wszQs2Otg/WL2-03NAFII/AAAAAAAACDg/nZmIWewA2kw8TmFliydqkWhWlhaokSKNwCLcB/s1600/NCGDico01.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://3.bp.blogspot.com/-G4wszQs2Otg/WL2-03NAFII/AAAAAAAACDg/nZmIWewA2kw8TmFliydqkWhWlhaokSKNwCLcB/s640/NCGDico01.JPG" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-Gp9zvi_zBv8/WL2-0yoG4hI/AAAAAAAACDc/y73K4b5qby0KPLQwWl16IBeOmAikJ47MgCLcB/s1600/NCGDico1.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="396" src="https://3.bp.blogspot.com/-Gp9zvi_zBv8/WL2-0yoG4hI/AAAAAAAACDc/y73K4b5qby0KPLQwWl16IBeOmAikJ47MgCLcB/s640/NCGDico1.JPG" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-tQPDSmDzt50/WL2-1dbJs3I/AAAAAAAACDk/QebrHuiKWc4pPthzA5ngv_TEcKQG-vZrwCLcB/s1600/NCGDico2.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="374" src="https://4.bp.blogspot.com/-tQPDSmDzt50/WL2-1dbJs3I/AAAAAAAACDk/QebrHuiKWc4pPthzA5ngv_TEcKQG-vZrwCLcB/s640/NCGDico2.JPG" width="640" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: justify;"><b>... out of the Heisenberg-like Connes-Chamseddine-Mukhanov equation and the spectral action principle</b></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-S0DHuXdR_2c/WL2-Zb31qvI/AAAAAAAACDU/imd6HDj3JP8dr6B3HNNQ0TTGU8PDMiKPgCLcB/s1600/NCGDico0.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="409" src="https://3.bp.blogspot.com/-S0DHuXdR_2c/WL2-Zb31qvI/AAAAAAAACDU/imd6HDj3JP8dr6B3HNNQ0TTGU8PDMiKPgCLcB/s640/NCGDico0.JPG" width="640" /></a></div><br /><b>....expressed in Noncommutative Geometry as a Framework for Unification of all Fundamental Interactions including Gravity. </b><br /><br /><a href="https://3.bp.blogspot.com/-ychNBlywKDA/WL2-0wlmVAI/AAAAAAAACDY/k2al-exokvosHVzwARwSssr9RkxYGxkmwCLcB/s1600/NCGDico02.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" height="406" src="https://3.bp.blogspot.com/-ychNBlywKDA/WL2-0wlmVAI/AAAAAAAACDY/k2al-exokvosHVzwARwSssr9RkxYGxkmwCLcB/s640/NCGDico02.JPG" width="640" /></a><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><b style="text-align: left;"><br /></b></div><div class="separator" style="clear: both; text-align: center;"><b style="text-align: left;">Here is the part II video follow-up of <a href="https://arxiv.org/abs/1004.0464" target="_blank">Part I</a> article </b></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/UZ9MVkoR38Y/0.jpg" frameborder="0" height="266" src="https://www.youtube.com/embed/UZ9MVkoR38Y?feature=player_embedded" width="320"></iframe></div><br /></div>Cédric Bardothttps://plus.google.com/104733107894701960711noreply@blogger.com0tag:blogger.com,1999:blog-3911792794793692366.post-5142687938679447592017-03-01T21:25:00.001+01:002017-03-08T19:12:47.481+01:00Consequences of volume quantisation of space-time<div dir="ltr" style="text-align: left;" trbidi="on"><span style="color: blue;">Here is the fourth (and last fragment for a while) of my <i>Lover's Dictionary of Spectral Physics</i>:</span><br /><div><span style="color: blue;"><br /></span></div><div><span style="color: blue;"><br /></span><span style="color: blue;"><b>Quantisation of space-time </b>(and a<b> </b></span><span style="color: blue;">heuristic point of view towards a spectral unification of fundamental interactions based on the noncommutative Heisenberg-like Chamseddine-Connes-Mukhanov equation to develop*...)</span></div><div><b><br /></b><br /><blockquote class="tr_bq"><div style="text-align: right;"><i><span style="color: blue;">... when the intellectual despotism of the Church, which had been maintained through the Middle Ages, had crumbled, and a wave of scepticism threatened to sweep away all that had seemed most fixed, those who believed in Truth clung to Geometry as to a rock, and it was the highest ideal of every scientist to carry on his science "more geometrico".</span></i></div></blockquote><blockquote class="tr_bq"><div style="text-align: right;"><a href="https://archive.org/details/spacetimematter00weyluoft" target="_blank"><i>Space-time-matter</i></a><span style="color: blue;">, </span></div><span style="color: blue;"></span><br /><div style="text-align: right;"><span style="color: blue;">Hermann Weyl, 1917</span></div><span style="color: blue;"></span></blockquote><br /><div><blockquote class="tr_bq" style="text-align: right;"><span style="color: blue;"><i>La nature est localement quantique et globalement noncommutative</i></span></blockquote><blockquote class="tr_bq" style="text-align: right;"><span style="color: blue;">Folklore </span></blockquote><br /><b><br /></b><br /><div style="text-align: justify;"><span style="color: blue;">As the last echo to the <a href="http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Planck%20(1900),%20Improvement%20of%20Wien's.pdf" target="_blank">quantisation of matter-radiation interaction</a> started with Planck in 1900</span>, the recent completion of the standard model of unification of the strong and electroweak interactions has advanced our ideas of the subatomic world a step further. It is even not unreasonable to conceive that the next scale of particle physics lies beyond 10<span style="text-align: justify;"><sup style="text-align: center;">10</sup></span> GeV! Now <i>wider expanses and greater depths are thus exposed to the searching eye of knowledge</i><span style="color: blue;"> (to quote</span><i> </i><span style="color: blue;">Hermann Weyl in a <a href="https://archive.org/details/spacetimematter00weyluoft" target="_blank">100 year-old reflexive text</a> about <a href="https://tel.archives-ouvertes.fr/tel-00651772/document" target="_blank">the foundation of differential geometry and general relativity</a>). </span>The more so as tremendous progress in astrophysics have seen the emergence of a testable cosmological standard model that offers a window on energy scales of which we had hardly a hope to probe a decade ago. Both standard models have already <i>brought us much nearer to grasping the plan that underlies all physical happening.</i><br /><span style="color: blue;">May be it is time now to repeat the saga initiated by Planck and Einstein (from the experimental data collected by an army of spectroscopists raised by Newton) to envision a quantisation of space-time. </span>This is what <strike>I want to</strike><span style="color: blue;"> is</span> report<span style="color: blue;">ed</span> below through a spectral ride on the loop where the micro and macro worlds meet to uncover <i>regions of which we had not even a presentiment</i><i>. </i><span style="color: blue;">To say shortly <b>the consequence of the</b></span><span style="text-align: start;"><b><span style="color: blue;"> quantisation of space-time heuristic hypothesis</span> <span style="color: blue;">based on a Heisenberg-like equation found by Chamseddine, Connes and Mukhanov might be</span> a pretty unique, spectrally unified and global noncommutative </b></span><b style="text-align: start;">framework for </b><b style="text-align: start;">space-time-matter-radiation as we know it here (13 TeV) and now (2,7 K).</b></div><div style="text-align: justify;"><br /></div><blockquote class="tr_bq" style="text-align: justify;"><div style="text-align: justify;"><i>... <u><b>by starting from a quantization condition on the volume of the noncommutative space, all fields and their interactions are predicted and given by a Pati-Salam model which has three special cases one of which is the Standard Model with neutrino masses and a singlet field. The spectral Standard Model predicts unification of gauge couplings and the correct mass for the top quark and is consistent with a low Higgs mass of 125 Gev</b>. </u>The unification model is assumed to hold at the unification scale and when the gauge, Yukawa and Higgs couplings relations are taken as initial conditions on the RGE, one finds complete agreement with experiment, except for the meeting of the gauge couplings which are off by 4%. <u>This suggests that a Pati-Salam model defines the physics beyond the Standard Model, and where we have shown [<a href="https://arxiv.org/abs/1507.08161" target="_blank">16</a>] that it allows for unification of gauge couplings, consistent with experimental data. </u></i></div></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><b><u>The assumption of volume quantization has consequences on the structure of General Relativity</u>.</b> Equations of motion agree with Einstein equations except for the trace condition, which now determines the Lagrange multiplier enforcing volume quantization. <b>The cosmological constant, although not included in the action, is now an integration constant</b>... <u><b>To have a physical picture of time we have also considered a four-manifold formed with the topology of R × Σ3, where Σ3 is a three dimensional hypersurface, to allow for space-times with Lorentzian signature. The quantization condition</b> is modified to have two mappings from Σ3 → S 3 and a mapping X : R → R. The resulting algebra of the noncommutative space is unchanged, and the three dimensional volume is quantized provided that the mapping field X is constrained to have unit gradient. This field X <b>modifies only the longitudinal part of the graviton and plays the role of mimetic dust. It thus solves, without extra cost, the dark matter problem [<a href="https://arxiv.org/abs/1308.5410" target="_blank">33</a>]</b></u>. Recently, we have shown that this field X can be used to build realistic cosmological models [<a href="https://arxiv.org/abs/1403.3961" target="_blank">34</a>]. In addition, and under certain conditions, could be used to avoid singularities in General relativity for Friedmann, Kasner [<a href="http://a.%20h.%20chamseddine%20and%20v.%20mukhanov%2C%20mimetic%20dark%20matter/" target="_blank">35</a>] and Black hole solutions [<a href="http://arxiv.org/abs/1612.05861" target="_blank">36</a>]. This is possible because this scalar field modifies the longitudinal sector in GR... </i><span style="text-align: left;"> </span><span style="text-align: left;"> </span></blockquote><blockquote class="tr_bq" style="text-align: justify;"><span style="color: blue; text-align: left;"><i>We have presented enough evidence that a framework where space-time assumed to be governed by noncommutative geometry results in a unified picture of all particles and their interactions. The axioms could be minimized by starting with a volume quantization condition, which is the Chern character formula of the noncommutative space and a special case of the orientability condition. This condition determines uniquely the structure of the noncommutative space. Remarkably, the same structure was also derived, in slightly less unique way, by classifying all finite noncommutative spaces [<a href="https://arxiv.org/abs/1411.0977" target="_blank">10</a>].</i></span></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>The picture is very compelling, in contrast to other constructions, such as grand unification, supersymmetry or string theory, where there is no limit on the number of possible models that could be constructed. <u>The picture, however, is ... incomplete as there are still many unanswered questions and we now list few of them. Further studies are needed to determine the structure and hierarchy of the Yukawa couplings, the number of generations, the form of the spectral function and the physics at unification scale, quantizing the fields appearing in the spectral action and in particular the gravitational field</u>. To conclude, noncommutative geometry as a basis for unification, is a predictive and exciting field with very appealing features and many promising new directions for research.</i></blockquote><blockquote class="tr_bq"><div style="text-align: right;"><i><a href="https://arxiv.org/abs/1702.08180" target="_blank">Quanta of Space-Time and Axiomatization of Physics</a></i></div><div style="text-align: right;"><a href="https://arxiv.org/find/hep-th/1/au:+Chamseddine_A/0/1/0/all/0/1">Ali H. Chamseddine</a> </div><div style="text-align: right;">Contribution to the special issue of IJGMMP celebrating the one century anniversary of the program announced in 1916 by Hilbert entitled " Foundations of Mathematics and Physics", (Submitted on 27 Feb 2017)</div></blockquote><br /><br /><div style="text-align: justify;"><span style="color: blue;">Remark: the reader is warmly invited to have a careful look at the above article particularly on the twenty pages starting from section 9 <i>Consequences of volume quantization </i>(for astrophysics and cosmology)<i> </i>where the technical details are thoroughly discussed by Ali Chamseddine in the perfectly classical differential geometric language used for general relativity but with a new conformal nondynamical so called <i>mimetic</i> degree of freedom.</span><br /><br /><br /><span style="color: blue;">*A</span><span style="color: blue;"><span style="color: blue;"><b> </b></span><span style="color: blue;">heuristic point of view</span>... in progress (?)</span><!--[if gte mso 9]><xml> <w:WordDocument> <w:View>Normal</w:View> <w:Zoom>0</w:Zoom> <w:HyphenationZone>21</w:HyphenationZone> <w:DoNotOptimizeForBrowser/> </w:WordDocument></xml><![endif]--> <br /><blockquote><i><br /><span style="color: blue;">An accidental conceptual distinction exists between the theoretical concepts which physicists have forged building the quantum gauged interactions between fundamental spinor fermions and vector bosons on a flat space-time and the Einstein theory of gravitational processes on a curved space-time. While we can consider the energetic state of matter-radiation in the universe to be completely determined by a very large, yet finite, number of quanta, we make use of continuous spatial functions to describe the geometrodynamical state of a given volume of spacetime, and a finite number of parameters cannot be regarded as sufficient for the complete determination of such a state. <br /><br />Classical differential geometry, which operates with commutative algebra of coordinates, has worked quite well up to now as the handmaiden of general relativity to induce the matter content of our local universe from the matching between the radiation observations and general relativity predictions and will continue to provide invaluable services to scrutinize dark compact objects with the advent of gravitational waves detectors. It should be kept in mind, however, that the current astrophysical inferences from galactic to cosmological scales suffer huge discrepancies when one confronts </span></i><i><span style="color: blue;">the global matter-radiation content of the universe </span><span style="color: blue;">with its local spectrum observed on Earth (</span></i><i><span style="color: blue;">thanks to telescopes, particle accelerators/detectors and both Standard and </span><span style="text-align: left;"><span style="color: blue;">ΛCDM m</span></span><span style="color: blue;">odels) </span></i></blockquote><blockquote><i><span style="color: blue;"> In spite of the complete experimental confirmations of Einstein's general relativity based on two degrees of freedom (inferred from commutative geometric insight) as applied to the dynamics of the dilute solar system, denser pairs of neutron stars not to mention more compact black holes, it is now conceivable that the standard cosmological model may lead to contradictions with experience when its dark matter phenomenology parameterisation and the current cosmological acceleration are confronted with the particle spectrum inferred from sub-attoscale experiments and our understanding of quantum vacuum.</span></i><br /><i><br />It seems to me that the observations associated with dark matter and possibly dark energy both connected with correlations of matter-radiation in spectral data collected on very large and very small scales are more readily understood if one assumes a spacetime volume quantization provided by the spectral noncommutative geometric foresight supported by the 125 GeV Higgs boson hindsight.</i></blockquote><div style="text-align: right;"><blockquote class="tr_bq"><span style="color: blue;">Walking in the footsteps of <a href="http://www.esfm2005.ipn.mx/ESFM_Images/paper1.pdf" target="_blank">a giant</a></span></blockquote></div></div><br /><div><span style="color: blue;">//<strike>last </strike>edit March 2, 2017</span><br /><span style="color: blue;">//new edit only in the <i>heuristic point of view</i> part on March <strike>4</strike> 8</span></div></div></div></div>Cédric Bardothttps://plus.google.com/104733107894701960711noreply@blogger.com0tag:blogger.com,1999:blog-3911792794793692366.post-53593155211491660392017-03-01T12:01:00.002+01:002017-03-01T21:29:51.779+01:00Les physiciens : à table ! (invitation à un banquet spectral)<div dir="ltr" style="text-align: left;" trbidi="on"><br /><blockquote class="tr_bq" style="text-align: justify;">Vous trouvez la géométrie noncommutative un peu grosse à avaler pour un spécialiste de physique des particules et vous restez sur votre faim en contemplant le menu du jour du LHC ? PAS DE PANIQUE, faites confiance au guide du boson de Higgs et du voyageur spectral et suivez l'exemple des bosons de jauge qui mangent des bosons de Goldstone au festin dont le Soleil nous régale quotidiennement* ;-)</blockquote><div><br /></div><div><br /></div>The last issue (draft version) of the Spectral-hiker's Guide to noncommutative geometry for particle physics is:<br /><div><br /></div><blockquote class="tr_bq"><div style="text-align: right;"><i><a href="http://www.waltervansuijlekom.nl/wp-content/uploads/2017/02/ncgphysics.pdf" target="_blank">Noncommutative Geometry and Particle Physics</a> by </i>Walter D. van Suijlekom (2015)</div><div style="text-align: right;">(published version <a href="http://www.springer.com/gb/book/9789401791618" target="_blank">here</a>)</div></blockquote><br /><br /><div style="text-align: justify;">For gourmets only, looking for <i>The Restaurant at the Planck Scale</i>, I recommend the great <i>Per </i><i>Non Commutativa </i><i>Prisma</i><i>, Quantum Ratio Quoris</i> <i>Encyclopædia </i>one can find in a nice hypertext version below:</div><br /><blockquote class="tr_bq"><div style="text-align: right;"><a href="https://ncatlab.org/nlab/show/Noncommutative+Geometry,+Quantum+Fields+and+Motives" target="_blank"><i>Noncommutative Geometry, Quantum Fields and Motives</i></a></div><div style="text-align: right;">by Alain Connes and Matilde Marcolli (2008)</div></blockquote><br /><div style="text-align: justify;">*grâce à la survie du photon qui ne s'est pas fait croqué en se fondant dans le décor quantique <strike>relativiste</strike> local pour prendre la tangente dans l'espace-temps relativiste...</div><div class="MsoNormal"><span style="background: white; color: #252525; font-family: "arial" , sans-serif; font-size: 10.5pt; line-height: 107%;"><i><o:p></o:p></i></span></div></div>Cédric Bardothttps://plus.google.com/104733107894701960711noreply@blogger.com0tag:blogger.com,1999:blog-3911792794793692366.post-55719497445705617952017-02-27T20:48:00.001+01:002017-03-01T10:07:29.442+01:00(Celebrating fifty years of) electroweak symmetry breaking theory <div dir="ltr" style="text-align: left;" trbidi="on"><div class="tr_bq">This is the third fragment of my<i> Lover's dictionary of Spectral Physics,</i> for the new entry:</div><br /><b><br /></b><b>Electroweak symmetry <i>breaking</i> theory </b><br /><br /><blockquote class="tr_bq" style="text-align: right;"><i>The Standard Model wins all the battles </i></blockquote><blockquote class="tr_bq"><div style="text-align: right;">Jean Iliopoulos in <i><a href="https://cds.cern.ch/record/2217096/files/9789814733519_0002.pdf" target="_blank">The Making of the Standard Theory</a></i></div></blockquote><br /><blockquote class="tr_bq" style="text-align: right;"><i>Yes but only those requiring a limited weapon finesse ;-)</i></blockquote><blockquote class="tr_bq" style="text-align: right;">a grand unified theory build<span style="color: blue;">ing gam</span>er troll</blockquote><br /><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br />This important part of the Standard Model is fifty years old this year 2017 and it is still undefeated experimentally by LHC Run 2. Yet it is far from having been thoroughly tested in its full Standard Model version as you will read it below:</div><br /><blockquote class="tr_bq" style="text-align: justify;"><i><span style="text-align: left;"><u>Spontaneous symmetry breaking occurs when the ground state or vacuum, or equilibrium state of a system does not share the underlying symmetries of the theory. It is ubiquitous in condensed matter physics, associated with phase transitions</u>. Often, there is a high-temperature symmetric phase and a critical temperature below which the symmetry breaks spontaneously. A simple example is crystallization. If we place a round bowl of water on a table, it looks the same from every direction, but when it freezes the ice crystals form in specific orientations, breaking the full rotational symmetry. The breaking is spontaneous in the sense that, unless we have extra information, we cannot predict in which directions the crystals will line up... <u>In 1960, Nambu [12] pointed out that gauge symmetry is broken in a superconductor when it goes through the transition from normal to superconducting, and that this gives a mass to the plasmon, although this view was still quite controversial in the superconductivity community (see also Anderson [13]). Nambu suggested that a similar mechanism might give masses to elementary particles</u>... </span><span style="text-align: left;">The next year, with Jona-Lasinio [14], he proposed a specific model, though not a gauge theory...</span><span style="text-align: left;"> </span></i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><span style="text-align: left;"><u>The model had a significant feature, a massless pseudoscalar particle</u>, which Nambu and Jona-Lasinio tentatively identified with the pion. To account for the non-zero (though small) pion mass, they suggested that the chiral symmetry was not quite exact even before the spontaneous symmetry breaking. <u>Attempts to apply this idea to symmetry breaking of fundamental gauge theories however ran into a severe obstacle, the Goldstone theorem</u>... </span><span style="text-align: left;">the spontaneous breaking of a continuous symmetry often leads to the appearance of massless spin-0 particles. The simplest model that illustrates this is the Goldstone model [15]... </span></i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><span style="text-align: left;"><u>The appearance of the... massless spin-zero Nambu–Goldstone bosons was believed to be an inevitable consequence of spontaneous symmetry breaking in a relativistic theory</u>; this is the content of the Goldstone theorem. That is a problem because such massless particles, if they had any reasonable interaction strength, should have been easy to see, but none had been seen... </span><span style="text-align: left;"> </span></i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><span style="text-align: left;"><u>This problem was obviously of great concern to all those who were trying to build a viable gauge theory of weak interactions</u>. </span><span style="text-align: left;">When Steven Weinberg came to spend a sabbatical at Imperial College in 1961, he and Salam spent a great deal of time discussing the obstacles. They developed a proof of the Goldstone theorem, published jointly with Goldstone [16]...</span></i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><span style="text-align: left;"><i><u>Spontaneous symmetry breaking implied massless spin-zero bosons, which should have been easy to see but had not been seen. On the other hand adding explicit symmetry-breaking terms led to non-renormalizable theories predicting infinite results</u>. Weinberg commented ‘Nothing will come of nothing; speak again’, a quotation from King Lear. Fortunately, however, our community was able to speak again...</i></span></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><span style="text-align: left;"><u>The {</u></span></i><i><span style="text-align: left;"><u>Goldstone theorem}</u> </span></i><i><span style="text-align: left;">argument fails in the case of a gauge theory, for quite subtle reasons ... {its} <u>proof is valid, but there is a hidden assumption which, though seemingly natural, is violated by gauge theories. This was discovered independently by three groups</u>, first Englert and Brout from Brussels [19], then Higgs from Edinburgh [20, 21] and finally Guralnik, Hagen and myself from Imperial College [22]. <u>All three groups published papers in Physical Review Letters during the summer and autumn of 1964</u>...</span><span style="text-align: left;"> </span></i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><span style="text-align: left;"><u>The 1964 papers from the three groups attracted very little attention at the time. Talks on the subject were often greeted with scepticism</u>. By the end of that year, the mechanism was known, and Glashow’s (and Salam and Ward’s) SU(2) × U(1) model was known. But, <u>surprisingly perhaps, it still took three more years for anyone to put the two together. This may have been in part at least because many of us were still thinking primarily of a gauge theory of strong interactions, not weak</u>. </span> </i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><span style="text-align: left;"><u>In early 1967, I did some further work on the detailed application of the mechanism to models with larger symmetries than U(1), in particular on how the symmetry breaking pattern determines the numbers of massive and massless particles </u>[<a href="http://symmetry%20breaking%20in%20nonabelian%20gauge%20theories%20t.w.b.%20kibble%20%28imperial%20coll.%2C%20london%29/" target="_blank">23</a>]. I had some lengthy discussions with Salam on this subject, which I believed helped to renew his interest in the subject. <u>A unified gauge theory of weak and electromagnetic interactions of leptons was first proposed by Weinberg later that year</u> [<a href="http://www.hep.uiuc.edu/LC/pdf_docs/weinberg.pdf" target="_blank">24</a>].<u> Essentially the same model was presented independently by Salam in lectures he gave at Imperial College in the autumn of 1967 — he called it the electroweak theory</u>. (I was not present because I was in the United States, but I have had accounts from others who were.) <u>Salam did not publish his ideas until the following year, when he spoke at a Nobel Symposium</u> [<a href="http://inspirehep.net/record/53083" target="_blank">25</a>], largely perhaps because his attention was concentrated on the development in its crucial early years of his International Centre for Theoretical Physics in Trieste. <u>Weinberg and Salam both speculated that their theory was renormalizable, but they could not prove it. An important step was the working out by Faddeev and Popov of a technique for applying Feynman diagrams to gauge theories [26]. Renormalizability was finally proved by a young student, Gerard ’t Hooft [27], in 1971, a real tour de force</u> using methods developed by his supervisor, Martinus Veltman, especially the computer algebra programme Schoonship.</span> </i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><span style="text-align: left;"><u>In 1973, the key prediction of the electroweak theory, the existence of the neutral current interactions — those mediated by Z0 — was confirmed at CERN [28]...</u></span><span style="text-align: left;"><u>The next major step was the discovery of the W and Z particles at CERN in 1983</u> [29, 30]...</span> </i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>In 1964, or 1967, the existence of a massive scalar boson had been a rather minor and unimportant feature. The important thing was the mechanism for giving masses to gauge bosons and avoiding the appearance of massless Nambu–Goldstone bosons. But <u>after 1983, the Higgs boson began to assume a key importance as the only remaining undiscovered piece of the standard-model jigsaw — apart that is from the last of the six quarks, the top quark. The standard model worked so well that the Higgs boson, or something else doing the same job, more or less had to be present</u>. Finding the boson was one of the main motivations for building the Large Hadron Collider (LHC) at CERN. <u>Over a period of more than twenty years, the two great collaborations, ATLAS and CMS, have designed, built and operated their two huge and massively impressive detectors. As is by now well known, their efforts were rewarded in 2012 by the unambiguous discovery of the Higgs boson by each of the two detectors</u> [31, 32].</i></blockquote><blockquote class="tr_bq" style="text-align: right;"><a href="https://arxiv.org/abs/1502.06276"><i>History of electroweak symmetry breaking</i></a> <a href="https://arxiv.org/find/physics/1/au:+Kibble_T/0/1/0/all/0/1">T.W.B. Kibbl</a>e<br />2015</blockquote><div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">I think it is fair to complete the previous experimental success story of the electroweak symmetry breaking theory by the following facts:</div><blockquote class="tr_bq"><div style="text-align: justify;"><i>... in computing the theoretical predictions [of the Standard Model], one should include also the strong interactions, so the model is really the gauge theory of the group U(1)×SU(2)×SU(3). Here <u>we shall present only a list of the most spectacular successes in the electroweak sector</u>:</i></div><div style="text-align: justify;"><i>...</i></div><div style="text-align: justify;"><i>• <u>The discovery of charmed particles at SLAC in 1974–1976</u>. Their characteristic property is to decay predominantly in strange particles. </i></div><div style="text-align: justify;"><i>• A necessary condition for the consistency of the Model is that ∑<span style="text-align: justify;"><sub>i</sub></span> Q<span style="text-align: justify;"><sub>i</sub></span> =0 inside each family. <u>When the τ lepton was discovered the b and t quarks were predicted with the right electric charges</u>.</i></div><div style="text-align: justify;"><i>...</i></div><div style="text-align: justify;"><i>• <u>The t-quark was seen at LEP through its effects in radiative corrections before its actual discovery at Fermilab</u>.</i></div><div style="text-align: justify;"><i>• An impressive series of experiments have tested the Model at a level such that the weak interaction radiative corrections are important.</i></div></blockquote><blockquote class="tr_bq"><div style="text-align: right;"><i><a href="https://cds.cern.ch/record/2217096/files/9789814733519_0002.pdf" target="_blank">The Making of the Standard Theory </a></i></div><div style="text-align: right;">John Iliopoulos, 2016</div></blockquote><i><br /></i><br /><br /><div style="text-align: justify;">And now for a nice outlook of the 125 GeV Higgs boson discovery let us read an eminent superviser of the TeV scale physics exploration using hadron colliders:</div><br /><blockquote class="tr_bq" style="text-align: justify;"><i>The most succinct summary we can give is that <u>the data from the ATLAS and CMS experiments are developing as if electroweak symmetry is broken spontaneously through the work of elementary scalars, and that the emblem of that mechanism is the standard-model Higgs boson</u>...</i> </blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>As one measure of the progress the discovery of the Higgs boson represents, let us consider some of the questions I posed before the LHC experiments ...</i> </blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>1. What is the agent that hides the electroweak symmetry? Specifically, is there a Higgs boson? Might there be several? </i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><u>To the best of our knowledge, H(125) displays the characteristics of a standard model Higgs boson, an elementary scalar. Searches will continue for other particles that may play a role in electroweak symmetry breaking. </u></i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>2. Is the “Higgs boson” elementary or composite? How does the Higgs boson interact with itself? What triggers electroweak symmetry breaking? </i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><u>We have not yet seen any evidence that H(125) is other than an elementary scalar. Searches for a composite component will continue. The Higgs-boson self-interaction is almost certainly out of the reach of the LHC; it is a very challenging target for future, very-high-energy, accelerators. We don’t yet know what triggers electroweak symmetry breaking. </u></i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>3. Does the Higgs boson give mass to fermions, or only to the weak bosons? What sets the masses and mixings of the quarks and leptons? </i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><u>The experimental evidence suggests that H(125) couples to t</u></i><span style="text-align: left; text-decoration: overline;"><u><i>t</i></u></span><i><u>, b</u></i><span style="text-align: left; text-decoration: overline;"><u><i>b</i></u></span><i><u>, and τ+τ−</u>, so the answer is probably yes. <u>All these are third-generation fermions, so even if the evidence for these couplings becomes increasingly robust, we will want to see evidence that H couples to lighter fermions. The most likely candidate, perhaps in High-Luminosity LHC running, is for the Hµµ coupling, which would already show that the third generation is not unique in its relation to H. Ultimately, to show that spontaneous symmetry breaking accounts for electron mass, and thus enables compact atoms, we will want to establish the He</u></i><span style="text-align: left; text-decoration: overline;"><i><u>e</u></i></span><i><u> coupling. That is extraordinarily challenging because of the minute branching fraction</u>. </i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>10. What lessons does electroweak symmetry breaking hold for unified theories of the strong, weak, and electromagnetic interactions? </i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><u>Establishing that scalar fields drive electroweak symmetry breaking will encourage the already standard practice of using auxiliary scalars to hide the symmetries that underlie unified theories. </u></i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>To close, I offer a revised list of questions to build on what our first look at the Higgs boson has taught us. Issues Sharpened by the Discovery of H (125) </i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>1. How closely does H(125) hew to the expectations for a standard-model Higgs boson? Does H have any partners that contribute appreciably to electroweak symmetry breaking? </i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>2. Do the HZZ and HWW couplings indicate that H(125) is solely responsible for electroweak symmetry breaking, or is it only part of the story? </i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>3. Does the Higgs field give mass to fermions beyond the third generation? Does H(125) account quantitatively for the quark and lepton masses? What sets the masses and mixings of the quarks and leptons? </i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>4. What stabilizes the Higgs-boson mass below 1 TeV? </i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>5. Does the Higgs boson decay to new particles, or via new forces? </i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>6. What will be the next symmetry recognized in Nature? Is Nature supersymmetric? Is the electroweak theory part of some larger edifice? </i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>7. Are all the production mechanisms as expected? </i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>8. Is there any role for strong dynamics? Is electroweak symmetry breaking related to gravity through extra spacetime dimensions? </i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>9. What lessons does electroweak symmetry breaking hold for unified theories of the strong, weak, and electromagnetic interactions? </i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>10. What implications does the value of the H(125) mass have for speculations that go beyond the standard model?...for the range of applicability of the electroweak theory? </i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>In the realms of refined measurements, searches, and theoretical analysis and imagination, great opportunities lie before us! </i></blockquote><blockquote class="tr_bq" style="text-align: right;"><a href="https://arxiv.org/abs/1503.01756"><i>Electroweak Symmetry Breaking in Historical Perspective</i></a> <a href="https://arxiv.org/find/hep-ph/1/au:+Quigg_C/0/1/0/all/0/1">Chris Quigg</a> 2015</blockquote><br /><br /><div style="text-align: justify;">Now what about the role geometry plays in the game? It may be relevant to go once more to the historical review by Iliopoulos:</div><br /><blockquote class="tr_bq" style="text-align: justify;"><i><b>The construction of the Standard Model</b>, which became gradually the Standard Theory of elementary particle physics, is, probably, the most remarkable achievement of modern theoretical physics.... as we intend to show, the <b>initial motivation was not really phenomenological. It is one of these rare cases in which a revolution in physics came from theorists trying to go beyond a simple phenomenological model, not from an experimental result which forced them to do so. </b><b>This search led to the introduction of novel symmetry concepts which brought geometry into physics</b>...</i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><span style="text-align: left;"><u>At the beginning of the twentieth century the development of the General Theory of Relativity offered a new paradigm for a gauge theory</u>. The fact that it can be written as the theory invariant under local translations was certainly known to Hilbert, hence the name of Einstein–Hilbert action. <u>The two fundamental forces known at that time, namely electromagnetism and gravitation, were thus found to obey a gauge principle. It was, therefore, tempting to look for a unified theory.</u>..</span><span style="text-align: left;"> </span></i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><span style="text-align: left;"><u>The transformations of the vector potential in classical electrodynamics are the first example of an internal symmetry transformation, namely one which does not change the space–time point x. However, the concept, as we know it today, belongs really to quantum mechanics. It is the phase of the wave function, or that of the quantum fields, which is not an observable quantity and produces the internal symmetry transformations</u>. The local version of these symmetries are the gauge theories we study here. The first person who realised that the invariance under local transformations of the phase of the wave function in the Schrödinger theory implies the introduction of an electromagnetic field was Vladimir Aleksandrovich Fock in 1926, just after Schrödinger wrote his equation...</span><span style="text-align: left;"> </span></i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><span style="text-align: left;"><i><u>In 1929 Hermann Klaus Hugo Weyl extended this work to the Dirac equation.</u> In this work he introduced many concepts which have become classic, such as the Weyl two-component spinors and the vierbein and spin-connection formalism. Although the theory is no more scale invariant, he still used the term gauge invariance, a term which has survived ever since.</i></span></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><span style="text-align: left;">Naturally, </span><span style="text-align: left;">one would expect non-Abelian gauge theories to be constructed following the same principle immediately after Heisenberg introduced the concept of isospin in 1932. But here history took a totally unexpected route. </span><span style="text-align: left;"> </span></i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><span style="text-align: left;"><u>The first person who tried to construct the gauge theory for SU(2) is Oskar Klein</u> who, in an obscure conference in 1938, he presented a paper with the title: On the theory of charged fields. The most amazing part of this work is that he follows an incredibly circuitous road: He considers general relativity in a five-dimensional space and compactifies à la Kaluza–Klein. Then he takes the limit in which gravitation is decoupled. In spite of some confused notation, he finds the correct expression for the field strength tensor of SU(2). <u>He wanted to apply this theory to nuclear forces</u> by identifying the gauge bosons with the new particles which had just been discovered, (in fact the muons), misinterpreted as the Yukawa mesons in the old Yukawa theory in which the mesons were assumed to be vector particles. He considered massive vector bosons and it is not clear whether he worried about the resulting breaking of gauge invariance.</span><span style="text-align: left;"> </span></i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><span style="text-align: left;"><u>The second work in the same spirit is due to Wolfgang Pauli who, in 1953, in a letter to Abraham Pais, developed precisely this approach: the construction of the SU(2) gauge theory as the flat space limit of a compactified higher-dimensional theory of general relativity</u>... </span><span style="text-align: left;"> </span></i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><span style="text-align: left;"><u>It seems that the fascination </u></span><span style="text-align: left;"><u>which general relativity had exerted on this generation of physicists was such that, for many years, local transformations could not be conceived independently of general coordinate transformations. </u><b>Yang and Mills were the first to understand that the gauge theory of an internal symmetry takes place in a fixed background space which can be chosen to be flat, in which case general relativity plays no role</b><b>...</b></span></i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><span style="text-align: left;"><u>In particle physics we put the birth of non-Abelian gauge theories in 1954, with the fundamental paper of Chen Ning Yang and Robert Laurence Mills</u>. It is the paper which introduced the SU(2) gauge theory and, although it took some years before interesting physical theories could be built, <u>it is since that date that non-Abelian gauge theories became part of high energy physics</u>. It is not surprising that they were immediately named Yang–Mills theories. <u>Although the initial motivation was a theory of the strong interactions, the first semi-realistic models aimed at describing the weak and electromagnetic interactions</u>. In fact, following the line of thought initiated by Fermi, the theory of electromagnetism has always been the guide to describe the weak interactions...</span><span style="text-align: left;"> </span></i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><span style="text-align: left;"><u>Gauge invariance requires the conservation of the corresponding currents and a zero masse for the Yang–Mills vector bosons. None of these properties seemed to be satisfied for the weak interactions. People were aware of the difficulty, but had no means to bypass it. The mechanism of spontaneous symmetry breaking was invented a few years later</u> in 1964... </span><span style="text-align: left;">The synthesis of Glashow’s 1961 model with the mechanism of spontaneous symmetry breaking was made in 1967 by Steven Weinberg, followed a year later by Abdus Salam... </span><span style="text-align: left;">Many novel ideas have been introduced in this paper, mostly connected with <u>the use of the spontaneous symmetry breaking</u> which <u>became the central point of the theory.</u></span></i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><u>Gauge theories contain three independent worlds. The world of radiation with the gauge bosons, the world of matter with the fermions and the world of BEH scalars. In the framework of gauge theories these worlds are essentially unrelated to each other</u>. Given a group G the world of radiation is completely determined, but we have no way to know a priori which and how many fermion representations should be introduced; the world of matter is, to a great extent, arbitrary. </i> </blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><u>This arbitrariness is even more disturbing if one considers the world of BEH scalars. Not only their number and their representations are undetermined, but their mere presence introduces a large number of arbitrary parameters into the theory</u>. Notice that this is independent of our computational ability, since these are parameters which appear in our fundamental Lagrangian. What makes things worse, is that these arbitrary parameters appear with a wild range of values. <u>From the theoretical point of view, an attractive possibility would be to connect the three worlds with some sort of symmetry principle. Then the knowledge of the vector bosons will determine the fermions and the scalars and the absence of quadratically divergent counterterms in the fermion masses will forbid their appearance in the scalar masses. We shall call such transformations supersymmetry transformations and we see that a given irreducible representation will contain both fermions and bosons</u>. It is not a priori obvious that such supersymmetries can be implemented consistently, but in fact they can. </i> </blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><i>... <u>supersymmetric field theories have remarkable renormalisation properties [<a href="http://cds.cern.ch/record/415096/files/CM-P00060544.pdf" target="_blank">57</a>] which make them unique. In particular, they offer the only field theory solution of the hierarchy problem. Another attractive feature refers to grand unification. The presence of the supersymmetric particles modifies the renormalisation group equations and the effective coupling constants meet at high scales</u>... </i><span style="text-align: left;"> </span><span style="text-align: left;"> </span></div></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>An interesting extension consists of considering gauge supersymmetry transformations, i.e. transformations whose infinitesimal parameters — which are anticommuting spinors — are also functions of the space–time point x... </i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><u>The miraculous cancellation of divergences we find in supersymmetry theories raises the hope that the supersymmetric extension of general relativity will give a consistent quantum field theory. In fact local supersymmetry, or “supergravity”, is the only field theoretic extension of the Standard Model which addresses the issue of quantum gravity</u>...</i></blockquote><blockquote class="tr_bq"><i></i><br /><div style="text-align: justify;"><i><i><u>N=8 supergravity promised to give us a truly unified theory of all interactions, including gravitation and a description of the world in terms of a single fundamental multiplet</u>. The main question is whether it defines a consistent field theory. At the moment we have no clear answer to this question, although it sounds rather unlikely. In some sense N = 8 supergravity can be viewed as the end of a road, the road of local quantum field theory. The usual response of physicists whenever faced with a new problem was to seek the solution in an increase of the symmetry. <u>This quest for larger and larger symmetry led us to the standard model, to grand unified theories and then to supersymmetry, to supergravity and, finally, to the largest possible supergravity, that with N=8.</u> <b>In the traditional framework we are working, that of local quantum field theory, there exists no known larger symmetry scheme</b>. </i></i></div><i></i></blockquote><blockquote class="tr_bq" style="text-align: right;"><i><a href="https://cds.cern.ch/record/2217096/files/9789814733519_0002.pdf" target="_blank">Id.</a></i></blockquote><div style="text-align: justify;"><br />I let the reader compare the above last Iliopoulos claims about supergravity with the following Connes' statement about the potential bonus offered by his geometric perspective in order to appreciate who sticks the most to the two guide lines of i) phenomenological approach in which the introduction of every new concept is motivated by the search of a consistent theory which agrees with experiment and ii) mathematical consistency which both helped in making the Standard Theory.</div><div style="text-align: justify;"><blockquote class="tr_bq"><i>... <u>the point of view adopted in this essay is to try to understand from a mathematical perspective, how the perplexing combination of the Einstein-Hilbert action coupled with matter, with all the subtleties such as the Brout-Englert-Higgs sector, the V-A and the see-saw mechanisms etc.. can emerge from a simple geometric model</u>. The new tool is the spectral paradigm and the new outcome is that geometry does emerge from purely Hilbert space and operator considerations, i.e. on the stage where Quantum Mechanics happens. The idea that group representations as operators in Hilbert space are relevant to physics is of course very familiar to every particle theorist since the work of Wigner and Bargmann. That the formalism of operators in Hilbert space encompasses the variable geometries which underly gravity is the leitmotiv of our approach. <u>In order to estimate the potential relevance of this approach to Quantum Gravity, one first needs to understand the physics underlying the problem of Quantum Gravity...</u>. Quoting from [<a href="https://arxiv.org/abs/0907.4238" target="_blank">40</a>]: “<u>Quantization of gravity is inevitable because part of the metric depends upon the other fields whose quantum nature has been well established”. Two main points are that the presence of the other fields forces one, due to renormalization, to add higher derivative terms of the metric to the Lagrangian and this in turns introduces at the quantum level an inherent instability that would make the universe blow up. This instability is instantly fatal to an interacting quantum field theory. Moreover primordial inflation prevents one from fixing the problem by discretizing space at a very small length scale. What our approach permits is to develop a “particle picture” for geometry and a careful reading of this paper should hopefully convince the reader that this particle picture stays very close to the inner workings of the Standard Model coupled to gravity</u>. For now the picture is limited to the “one-particle” description and there are deep purely mathematical reasons to develop the many particles picture.</i></blockquote></div><blockquote class="tr_bq"><div style="text-align: right;"><a href="https://www.dropbox.com/s/gzrqzjvilvgwfk9/J-Kouneiher.pdf?dl=0"><i>Geometry and the Quantum</i></a></div><div style="text-align: right;">Alain Connes</div><div style="text-align: right;">(still draft version February 21, 2017)</div></blockquote></div><div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Beyond the somewhat vein comparative on the respective merits of both approaches to unify the standard model interactions with gravitation at the Planck scale, one can't help to notice how far their geometrical premises are different. On the one side, there is supergravity as the boldest symmetric extension of local quantum field gauge theories on traditional but higher dimensional spacetimes with the hope to quantize gravity. On the other side one contemplates an original reformulation and slight but radical extension of spacetime in a framework derived from quantum mechanics with the full Standard Model theory emerging from an action principle inspired by general relativity.<br /><br />As a consequence, the grand unification scheme present in both approaches borrows nevertheless quite distinct paths. In the evocative words of some bold pioneers of the spectral noncommutative phenomenology:<br /><br /><blockquote class="tr_bq"><span style="text-align: left;"><i>... <u>at the higher [unification scale </u></i></span><i style="text-align: left;"><u>Λ</u></i><i style="text-align: left;"><u>]... it is not the particle spectrum that changes, but the geometry of spacetime itself.</u> We shall assume that the (commutative) Riemannian geometry of spacetime is only a low energy approximation of a – not yet known – noncommutative geometry. <u>Being noncommutative, this geometry has radically different short distance properties and is expected to produce quite a different renormalisation flow... At energies below Λ, this noncommutativity manifests itself only in its mild, almost commutative version through the gauge- and Higgs-fields of the standard model, which are magnetic-like fields accompanying the gravitational field</u>. </i></blockquote></div></div><blockquote class="tr_bq" style="text-align: right;"><i><a href="https://arxiv.org/abs/hep-ph/0605166" target="_blank">Spectral action and big desert</a> </i><a href="https://arxiv.org/find/hep-ph/1/au:+Knecht_M/0/1/0/all/0/1">Marc Knecht</a>, <a href="https://arxiv.org/find/hep-ph/1/au:+Schucker_T/0/1/0/all/0/1">Thomas Schucker</a> (2006)</blockquote><div style="text-align: right;"><br /></div><div><div style="text-align: justify;">To insist now on the foresights, one has also two very different landscapes. Roughly writing:<br /><br /><blockquote class="tr_bq"><b>- focussing on a solution to the naturalness problem of the Brout-Englert-Higgs scalar boson, supersymmetry predicts a new superparticle spectrum. From the knowledge of the vector bosons it will determine the fermions and the scalars and the absence of quadratically divergent counterterms in the fermion masses forbidding their appearance in the scalar masses. Then one can envision hopefully a supergravity theory amenable to quantize gravitation. </b></blockquote><blockquote class="tr_bq"><b>- Looking for a geometric understanding of the electroweak symmetry breaking, the spectral noncommutative framework distills from the knowledge of the spin one-half fermion particle spectrum of the current Standard Model completed minimally with three right-handed Majorana neutrinos (required to explain neutrino oscillations with a type I seesaw mechanism) the full scalar and vector boson spectra. Its operator theoretic formalism develops a “particle picture” for geometry that stays very close to the inner workings of the Standard Model coupled to gravity and it makes it already possible to describe a volume quantized 4D spacetime with a Euclidean signature translating phenomenologically in mimetic dark energy and dark matter models.</b></blockquote><br /><br />Considering the fact that no experimental evidence for supersymmetric particles has been found yet, one may appreciate then from a heuristic point of view the potential relevance of the spectral noncommutative geometrization of the Standard Model leading to a minimal Pati-Salam extension. The latter provides indeed a unification of electroweak and strong gauge interactions pretty close in its particle spectrum to the non-supersymmetric minimal SO(10) models currently consistent with current neutrino oscillations data that goes beyond the Standard Model (thus not under the scope of Iliopoulos review) and also with a leptogenesis scenario able to explain the asymmetry between matter and antimatter.<br /><br /></div><div style="text-align: justify;">At last, one may add the following from a more <i>consistent*</i> effective field theory perspective.<br /><blockquote class="tr_bq"><div style="text-align: justify;"><b>The <a href="http://www.waltervansuijlekom.nl/wp-content/uploads/2017/02/ncgphysics.pdf" target="_blank">spectral standard model post-diction for the 125 GeV mass of the Higgs boson that breaks the electroweak symmetry</a> requires its very small mixing with a "big" Higgs brother responsible in a Pati-Salam symmetry </b><b>breaking at around 10</b><sup style="text-align: justify;"><b>12</b> </sup><b>GeV consistent with a </b><b>see-saw mechanism amenable to explain the known data on left-handed neutrinos. Even if the naturalness problem is not settled here it is phenomenologically encouraging that the Higgs boson already discovered may talk with a very high seesaw scale </b><b>well motivated as a natural</b><b> effective field theory to explain the very low mass of active neutrinos. The ultra heavy singlet scalar could also help to unitarise the theory in the sub-Planckian regime where inflation happens. Last but not least one may be reminded that provided the arbitrary mass scale in the spectral action is made dynamical by introducing a dilaton field, the resulting action is <a href="https://arxiv.org/abs/hep-th/0512169" target="_blank">almost identical</a> to the one proposed for making the standard model scale invariant and has the same low-energy limit as the Randall-Sundrum model and remarkably, all desirable features with correct signs for the relevant terms are obtained uniquely and without any fine tuning.</b></div></blockquote><br /><div style="text-align: justify;">Whatever the path chosen by space-time-matter-radiation to cool down to nowadays cosmological background temperature one may conclude that the spectrum of particles required for an electroweak symmetry breaking theory consistent with energies beyond the TeV scale has not been fully probed yet. To know if this search will bring a novel symmetry concept to tame the Higgs scalar feared quantum instabilities and require noncommutative geometry into physics to do so, only future will tell but may be the past laying in the dark sky already knows...</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">* about the role of consistency in theory choice I would like to offer the following thoughts that seems to me particularly relevant at the present time for obvious reasons:</div><div style="text-align: justify;"><br /></div><blockquote class="tr_bq" style="text-align: justify;"><i><u>One of the most interesting questions in philosophy of science is how to determine the quality of a theory. Given the data, how can we infer a “best explanation” for the data. This often goes by the name “Inference to Best Explanation</u>” (IBE) [1, 2, 3]. The wide variety of claims for important criteria are a measure of how difficult it is to come up with a clear and general algorithm for choosing between theories. Some claim even that it is intrinsically not possible to come up with a methodology of deciding.<br /><br />... <u>in our discussion of IBE criteria... we must first ask ourselves what is non-negotiable. Falsifiability is clearly something that can be haggled over. Simplicity is subject to definitional uncertainty, and furthermore has no universally accepted claim to preeminence. Naturalness, calculability, unifying ability, predictivity, etc. are also subject to preeminence doubts</u>. <u><br /></u><u><br /></u><u>What is non-negotiable is consistency. A theory shown definitively to be inconsistent does not live another day</u>. It might have its utility, such as Newton’s theory of gravity for crude approximate calculations, but nobody would ever say it is a better theory than Einstein’s theory of General Relativity.<br /><br /><u>Consistency has two key parts to it. The first is that what can and has been computed must be consistent with all known observational facts. As Murray Gell-Mann said about his early graduate student years, “Suddenly, I understood the main function of the theoretician: not to impress the professors in the front row but to agree with observation [10].” Experimentalists of course would not disagree with this non-negotiable requirement of observational consistency</u>. If you cannot match the data what are you doing, they would say?<br /><br /><br /><u>However, theorists have a more nuanced approach to establishing observational consistency</u>. They often do not spend the time to investigate all the consequences of their theories. Others do not want to “mop up” someone else’s theory, so they are not going to investigate it either. <u>We often get into a situation of a new theory being proposed that solves one problem, but looks like it might create dozens of other incompatibilities with the data but nobody wants to be bothered to compute it. Furthermore, the implications might be extremely difficult to compute</u>.<br /><br /><u>Sometimes there must be suspended judgment in the competition between excellent theories and observational consequences. Lord Kelvin claimed Darwin’s evolution ideas could not be right because the sun could not burn long enough to enable long-term evolution over millions of years that Darwin knew was needed. Darwin rightly ignored such arguments, deciding to stay on the side of geologists who said the earth appeared to be millions of years old [11]. Of course we know now that Kelvin made a bad inference</u> because he did not know about the fusion source of burning within the sun that could sustain its heat output for billions of years.<br /><br /><u>A second part to consistency is mathematical consistency. There are numerous examples in the literature of subtle mathematical consistency issues that need to be understood in a theory. Massive gauge theories looked inconsistent for years until the Higgs mechanism was understood</u>. Some gauge theories you can dream up are “anomalous” and inconsistent. <u>Some forms of string theory are inconsistent unless there are extra spatial dimensions. Extra time dimensions appear to violate causality, even when one tries to demand it from the outset, thereby rendering the theory inconsistent. Theories with ghosts, which may not be obvious upon first inspection, give negative probabilities of scattering</u>. </i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><u>Mathematical consistency is subtle and hard at times</u>, and like observational consistency there is no theorem that says that it can be established to comfortable levels by theorists on time scales convenient to humans. <u>Sometimes the inconsistency is too subtle for the scientists to see right off. Other times the calculability of the mathematical consistency question is too difficult to give definitive answer and it is a “coin flip” whether the theory is ultimately consistent or not. For example, pseudomoduli potentials that could cause a runaway problem are incalculable in some interesting dynamically broken supersymmetric theories</u> [<a href="https://arxiv.org/abs/0809.3981" target="_blank">12</a>].<br /><br /><b>It is not controversial that observational consistency and mathematical consistency are non-negotiable; however, the due diligence given to them in theory choice is often lacking.</b> The establishment of observational consistency or mathematical consistency can remain in an embryonic state for years while research dollars flow and other IBE criteria become more motivational factors in research and inquiry, and the consistency issues become taken for granted.<br /><br />This is one of the themes of Gerard ‘t Hooft’s essay “<a href="http://www.staff.science.uu.nl/~hooft101/lectures/klein99.pdf" target="_blank">Can there be physicist without experiments?</a>”. He reminds the reader that <b>some of the grandest theories are investigations of the nature of spacetime at the Planck scale, which is many orders of magnitude beyond where we currently have direct experimental probes. If this is to continue as a physics enterprise it “may imply that we should insist on much higher demands of logical and mathematical rigour than before</b>.” Despite the weakness of verb tense employed, it is an incontestable point. It is in these Planckian theories, such as string theory and loop quantum gravity, where the lack of consistency rigor is so plainly unacceptable. However, <b>the cancer of lax attention to consistency can spread fast in an environment where theories and theorists are feted before vetted.</b></i></blockquote><blockquote><div style="text-align: right;"><br /></div><div style="text-align: right;"><i><a href="https://arxiv.org/abs/1211.0634" target="_blank">Effective Field Theories and the Role of Consistency in Theory Choice</a></i></div><div style="text-align: right;"><a href="https://arxiv.org/find/physics/1/au:+Wells_J/0/1/0/all/0/1">James D. Wells</a></div><div style="text-align: right;">(2012)</div></blockquote><div style="text-align: justify;"><span style="color: blue;">Added on February 28</span></div><span style="color: blue;"><br /></span><br /><div style="text-align: justify;"><span style="color: blue;">This long retroactive analysis of the already 50 years old story of electroweak symmetry breaking mechanism has been carried out in the light of experimental discovery of the 125 GeV resonance at LHC Run1 and through the prism of its geometrization with a tentative noncommutative biais to uncover a new spectrum of bright colours entangled in the pale glow of beyond the Standard Model physics.</span></div><div style="text-align: justify;"><span style="color: blue;"><br /></span></div><div style="text-align: justify;"><span style="color: blue;">As reported above, Iliopoulos explains nicely in his review how Yang and Mills succeeded in providing the first geometric setting to describe quantum non abelian gauge fields focusing on the interpretation of the latter as internal symmetries in a fixed background space where general relativity plays no role (even if it inspired them). It’s hard to miss the reversal and more extensive move operated by the spectral noncommutative paradigm of Connes and Chamseddine that have patiently build and polish a new mathematically and experimentally coherent geometric spectral standard model where the internal symmetries appear in a natural manner as a slight refinement of the algebraic rules of coordinates (different from supersymmetry).</span></div><div style="text-align: justify;"><span style="color: blue;"><br /></span></div><div style="text-align: justify;"><span style="color: blue;">Yang-Mills theories where first criticized by Pauli, as their quanta had to be massless in order to maintain gauge invariance. Thus this theory was set aside for a while before the concept of particles acquiring mass through symmetry breaking in massless theories was discovered triggering a significant restart of Yang–Mills theory studies.</span></div><div style="text-align: justify;"><span style="color: blue;"><br /></span></div><div style="text-align: justify;"><span style="color: blue;">As far as spectral geometric models are concerned there are at best marginally quoted in reviews but rarely considered seriously. What major advance will prompt a significant interest in the physics community is hard to anticipate. One can hope the already established connection of some mimetic gravity models with a possible quantization of the volume of spacetime will light the fire for a new kind of investigations on the cosmological standard model dark sector…</span></div><div style="text-align: justify;"><span style="color: blue;"><br /></span></div><div style="text-align: justify;"><span style="color: blue;">To come back to ground, one other obstacle for a more extensive study of spectral models is the emptiness of their expected spectrum of new fundamental particles to discover with man-made accelerators, but well, this is also a perspective sketched by the study of minimal but realistic grand unified SO(10) or recent SMASH models all accommodating the full spectrum of low energy phenomenology (with the exception of a very low axion particle).</span></div><div style="text-align: justify;"><span style="color: blue;"><br /></span></div><div style="text-align: justify;"><span style="color: blue;">Hopefully there is more to search for with nuclear reactors and hadron or lepton colliders than new elementary particles! A lot of physicists are involved in flavor mixing for instance. It could be that noncommutative geometry<a href="http://www.noncommutativegeometry.nl/lorentz-center-2013/study-groups/ncg-and-flavour-mixing/" target="_blank"> gives a fresh look here too</a>.</span></div><div style="text-align: justify;"><span style="color: blue;"><br /></span></div><div style="text-align: justify;"><span style="color: blue;">For the theorist, a critical of spectral noncommutative geometry might come from the prejudice against models that do not provide a solution to naturalness problem. May be this requirement might be suspended for a while waiting for a more extensive study of the fine tuning "parameters" (coming from new degrees of freedom like a singlet scalar and right-handed neutrinos) computable from the spectral action principle or required to make it mathematically coherent. Indeed these parameters involved in the renormalisation flow would have values constrained on the full energy spectrum : from low energy scale to the unification one in order to tame the quantum mass corrections to the Higgs boson and also on the intermediate seesaw scale to accommodate left-handed neutrino masses and leptogenesis cosmological scenario. If such a scenario were miraculously possible it could help to uncover some new hidden symmetry from possible <a href="https://arxiv.org/abs/1608.00087" target="_blank">accidental corrections</a> in the quadratic divergence of <strike>in some extended versions of</strike> the Standard model</span><span style="color: blue;"> </span><span style="color: blue;">Higgs sector</span><span style="color: blue;"> </span><span style="color: blue;">...</span><br /><span style="color: blue;"><br /></span><br /><span style="color: blue;"><br /></span></div></div></div></div>Cédric Bardothttps://plus.google.com/104733107894701960711noreply@blogger.com0tag:blogger.com,1999:blog-3911792794793692366.post-74558137523298344622017-02-24T21:58:00.002+01:002017-02-26T20:10:59.012+01:00(The inception of spectral) noncommutative geometry, its calculus and functional action principle (to model spacetime ?)<div dir="ltr" style="text-align: left;" trbidi="on"><div class="tr_bq">This is the second fragment of my<i> Lover's dictionary of Spectral Physics,</i> the entry is of course: <i><br /></i><br /><br /><b>Noncommutative Geometry</b></div><br /><blockquote class="tr_bq"><div style="text-align: justify;"><div style="text-align: right;"><i>Plato derives the knowledge of ideas from body by abstraction and cutting away, leading us by various steps in mathematical discipline from arithmetic to geometry, thence to astronomy, and setting harmony above them all. For things become geometrical by the accession of magnitude to quantity; solid, by the accession of profundity to magnitude; astronomical, by the accession of motion to solidity; harmonical, by the accession of sound to motion.</i><span style="text-align: left;"> </span></div></div></blockquote><blockquote class="tr_bq"><div style="text-align: right;"><i><a href="http://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:2008.01.0384:chapter=3&highlight=god%2Cgeometry" target="_blank">Platonicae quaestiones</a>,</i> Plutarch</div></blockquote><div style="text-align: right;"><br /></div><blockquote class="tr_bq" style="text-align: justify;"><div style="text-align: right;"><i><a href="https://books.google.fr/books?id=kQtYL7pUWSwC&pg=PA383&dq=Plutarch,+quaest+plat.+platon+geometrizes&hl=fr&sa=X&ved=0ahUKEwiJpcuCvKTSAhXEJcAKHVXoCdcQ6AEIHjAA#v=onepage&q=Plutarch%2C%20quaest%20plat.%20platon%20geometrizes&f=false" target="_blank">Plato alleges that God forever geometrizes</a>... meanwhile </i><i>Connes and </i><i>Chamseddine are computing what other children's of Archimedes have not finished to measure.</i></div></blockquote><blockquote class="tr_bq" style="text-align: right;"> Folklore</blockquote><br /><br /><blockquote class="tr_bq" style="text-align: justify;"><i><u>The geometric concepts have first been formulated and exploited in the Framework of Euclidean geometry. This framework is best described using Euclid’s axioms</u> (in their modern form by Hilbert’). These axioms involve the set X of points p</i><span style="text-align: left;">∈</span><i>X of the geometric space as well as families of subsets: the lines and the planes for 3-dimensional geometry. Besides incidence and order axioms one assumes that an equivalence relation (called congruence) is given between segments, i.e., pairs of points (p,q),p,q </i><span style="text-align: left;">∈</span><i>X and also between angles, i.e., triples of points (a,O,b);a,O,b </i><span style="text-align: left;">∈</span><i>X. These relations eventually allow us to define the length |(p.q)| of a segment and the size </i><span style="text-align: left;">∢</span><i>(a,O,b) of an angle. The geometry is uniquely specified once these two congruence relations are given. They of course have to satisfy a compatibility axiom: up to congruence a triangle with vertices a,O,b </i><span style="text-align: left;">∈</span><i>X is uniquely specified by the angle </i><span style="text-align: left;">∢</span><i>(a,O,b) and the lengths of (a,O) and (0,b) ... <u>Besides the completeness or continuity axiom, the crucial one is the axiom of unique parallel. The efforts of many mathematicians trying to deduce this last axiom from the others led to the discovery of non-Euclidean geometry</u>... </i><span style="text-align: left;"> </span></blockquote><blockquote class="tr_bq" style="text-align: justify;"><span style="text-align: left;"><u style="font-style: italic;">The introduction by Descartes of coordinates in geometry was at first an act of violence (cf. Ref. 2). In the hands of Gauss and Riemann it allowed one to extend considerably the domain of validity of geometric ideas</u><i>. In Riemannian geometry the space X</i></span><span style="text-align: justify;"><sup style="text-align: center;"><i>n</i></sup></span><i><span style="text-align: left;"> is an n-dimensional manifold. Locally in X a point p is uniquely specified by giving n real numbers x</span></i><span style="text-align: justify;"><sup style="text-align: center;"><i>1</i></sup></span><i><span style="text-align: left;">,...,x</span></i><span style="text-align: justify;"><sup style="text-align: center;"><i>n</i></sup></span><i><span style="text-align: left;"> which are the coordinates of p. The various coordinate patches are related by diffeomorphisms. The geometric structure on X is prescribed by a (positive definite) quadratic form, </span><span style="text-align: justify;"><span style="text-align: justify;">g</span><sub style="text-align: justify;">µν </sub>d</span><span style="text-align: justify;">x</span><span style="text-align: justify;"><sup>µ</sup>d</span><span style="text-align: justify;">x</span><span style="text-align: justify;"><sup>ν</sup></span><span style="text-align: left;">, (1.4) which specifies the length of tangent vectors... This allows, using integration, to define the length of a path</span><span style="text-align: left;"> </span><span style="text-align: left;">γ</span><span style="text-align: left;">... <u>The analog of the lines of Euclidean or non-Euclidean geometry are the geodesics</u>. The analog of the distance between two points p,q </span><span style="text-align: left;">∈</span><span style="text-align: left;">X is given by the formula, d(p,q)=Inf Length(</span><span style="text-align: left;">γ</span><span style="text-align: left;">)... where </span><span style="text-align: left;">γ</span><span style="text-align: left;"> varies among all paths with </span><span style="text-align: left;">γ(0</span><span style="text-align: left;">)=p, </span><span style="text-align: left;">γ(</span><span style="text-align: left;">l)=q ... <u>The obtained notion of “Riemannian space” has been so successful that it has become the paradigm of geometric space</u>. </span><span style="text-align: left;">There are </span><span style="text-align: left;">two main reasons behind this success. <u>On the one hand this notion of Riemannian space is general enough to cover the above examples of Euclidean and non-Euclidean geometries and also the fundamental example given by space-time in general relativity (relaxing the positivity condition Of (1.4</u>)). <u>On the other hand it is special enough to still deserve the name of geometry, the point being that through the use of local coordinates all the tools of the differential and integral calculus can be brought to bear </u>... </span><span style="text-align: left;"> </span></i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><span style="text-align: left;">Besides its success in physics as a model of space-time, Riemannian geometry plays a key role in the understanding of the topology of manifolds, starting with the Gauss Bonnet theorem, the theory of characteristic classes, index theory, and the Yang Mills theory.</span><span style="text-align: left;"> </span></i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><span style="text-align: left;"><u>Thanks to the recent experimental confirmations of general relativity from the data given by binary pulsars there is little doubt that Riemannian geometry provides the right framework to understand the large scale structure of space-time</u>.</span><span style="text-align: left;"> </span></i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><span style="text-align: left;"><u>The situation is quite different if one wants to consider the short scale structure of space-time</u>. We refer to Refs. <a href="https://cds.cern.ch/record/275631/files/SCAN-9501320.pdf" target="_blank">5</a> and <a href="https://arxiv.org/abs/hep-th/0303037" target="_blank">6 </a>for an analysis of the problem of the coordinates of an event when the scale is below the Planck length. <u>In particular there is no good reason to presume that the texture of space-time will still be the 4-dimensional continuum at such scales. </u></span><span style="text-align: left;"><u> </u></span></i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><span style="text-align: left;"><u>In this paper we shall propose a new paradigm of geometric space which allows us to incorporate completely different small scale structures. It will be clear from the start that our framework is general enough. It will of course include ordinary Riemannian spaces but it will treat the discrete spaces on the same footing as the continuum, thus allowing for a mixture of the two. It also will allow for the possibility of noncommuting coordinates</u>. Finally it is quite different from the geometry arising in string theory but is not incompatible with the latter since supersymmetric conformal field theory gives a geometric structure in our sense whose low energy part can be defined in our framework and compared to the target space geometry.</span><span style="text-align: left;"> </span></i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><span style="text-align: left;"><i><u>It will require the most work to show that our new paradigm still deserves the name of geometry. We shall need for that purpose to adapt the tools of the differential and integral calculus to our new framework</u>. This will be done by building a long dictionary which relates the usual calculus (done with local differentiation of functions) with the new calculus which will be done with operators in Hilbert space and spectral analysis, commutators.... The first two lines of the dictionary give the usual interpretation of variable quantities in quantum mechanics as operators in Hilbert space. For this reason and many others (which include integrality results) <u>the new calculus can be called the quantized calculus’ but the reader who has seen the word “quantized” overused so many times may as well drop it and use “spectral calculus” instead.</u> </i></span></blockquote><blockquote class="tr_bq"><div style="text-align: right;"><i><a href="http://www.alainconnes.org/docs/reality.pdf" target="_blank">Noncommutative geometry and reality</a></i> </div><div style="text-align: right;">Alain Connes </div><div style="text-align: right;">Received 4 April 1995; accepted for publication 7 June 1995</div></blockquote><blockquote class="tr_bq" style="text-align: justify;"></blockquote><br /><blockquote class="tr_bq" style="text-align: justify;"><span style="text-align: left;"><i>... <u>we shall build our notion of geometry, in a very similar but somehow dual manner [</u></i><u>to<i> the Riemann's concept]</i></u></span><span style="font-style: italic; text-align: left;"><u>, on the pair (A, ds) of the algebra A of coordinates and the infinitesimal length element ds. For the start we only consider ds as a symbol, which together with A generates an algebra (A, ds). The length element ds does not commute with the coordinates, i.e. with the functions f on our space, f ∈ A</u>. But it does satisfy non trivial relations.</span><span style="font-style: italic; text-align: left;"> </span></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>... <u>we shall write down the axioms of geometry as the presentation of the algebraic relations between A and ds and the representation of those relations in Hilbert space. In order to compare different geometries, i.e. different representations of the algebra (A, ds) generated by A and ds, we shall use the following action functional,</u></i> </blockquote><div style="text-align: center;"><blockquote class="tr_bq" style="text-align: justify;"><i><u>(14) Trace(ϕ(ds/</u></i><i>ℓ</i><i style="text-align: justify;"><sub style="text-align: justify;">p</sub></i><i><u>))</u></i> </blockquote></div><blockquote class="tr_bq" style="text-align: justify;"><i><u>where </u></i><i>ℓ</i><i style="text-align: justify;"><sub style="text-align: justify;">p </sub></i><i><u>is the Planck length and ϕ is a suitable cutoff function which will cut off all eigenvalues of ds larger than </u></i><i>ℓ</i><i style="text-align: justify;"><sub style="text-align: justify;">p</sub></i><i>. We shall show in [<a href="https://arxiv.org/abs/hep-th/9606056" target="_blank">CC</a>] that <u>for a suitable choice of the algebra A, the above action will give Einstein gravity coupled with the Lagrangian of the standard U(1)×SU(2)×SU(3) model of Glashow Weinberg Salam</u>. The algebra will not be C<sup>∞</sup>(M) with M a (compact) 4-manifold but a non commutative refinement of it which has to do with the quantum group refinement of the Spin covering of SO(4).</i><span style="text-align: left;"> </span></blockquote><blockquote class="tr_bq" style="text-align: center;"><span style="text-align: left;">1 → Z/2 → Spin(4) → SO(4) → 1. </span><span style="text-align: left;"> </span></blockquote><blockquote class="tr_bq" style="text-align: justify;"><span style="text-align: left;"><i>Amazingly, in this description the group of gauge transformations of the matter fields arises spontaneously as a normal subgroup of the generalized diffeomorphism group Aut(A). <u>It is the non commutativity of the algebra A which gives for free the group of gauge transformations of matter fields as a (normal) subgroup of the group of diffeomorphisms</u>.</i></span></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>What the present paper shows is that </i><u style="font-style: italic;">one should consider the internal gauge symmetries as part of the diffeomorphism group of the non commutative geometry, and the gauge bosons as the internal fluctuations of the metric. It follows then that the action functional should be of purely gravitational nature. We state the principle of spectral invariance, stronger than the invariance under diffeomorphisms</u><i>, which requires that the action functional only depends on the spectral properties of D=ds</i><sup><i>-1</i></sup><i> in H. This is verified by the action,</i> </blockquote><div style="text-align: center;"><blockquote class="tr_bq" style="text-align: justify;"><i>I =Trace (ϕ(ds/ℓ</i><i style="text-align: justify;"><sub style="text-align: justify;">p</sub></i><i>))+<Dψ, ψ></i> </blockquote></div><blockquote class="tr_bq" style="text-align: justify;"><i>for any nice function ϕ from R</i><sup><i>*</i></sup><i style="text-align: justify;"><sub style="text-align: justify;">+</sub></i><i> to R. We shall show in [CC] that this action gives the SM Lagrangian coupled with gravity.</i><i style="text-decoration: underline;">It would seem at first sight that the algebra A has disappeared from the scene when one writes down the above action, the point is that it is still there because it imposes the </i><i><u>constraints </u>[[D, a], b</i><i style="text-align: justify;"><sub style="text-align: justify;">0</sub></i><i>]=0 <u>∀ a, b ∈ A and</u> Σa</i><i style="text-align: justify;"><sub style="text-align: justify;">0i</sub></i><i>[D, a</i><i style="text-align: justify;"><sub style="text-align: justify;">1i</sub></i><i>]...[D, a</i><i style="text-align: justify;"><sub style="text-align: justify;">4i</sub></i><i>]= γ <u>coming from axioms [required to provide with the spectral calculus and the volume form]</u></i><i>. It is important at this point to note that the integrality, n ∈ N of the dimension of a non commutative geometry appears to be essential to define the </i><i>[algebraic formulation of a differential form called a] Hochschild cycle c∈Z</i><i style="text-align: justify;"><sub style="text-align: justify;">n</sub></i><i> and in turns the chirality γ. This is very similar to the obstruction which appears when one tries to apply dimensional regularization to chiral gauge theories.</i></blockquote><blockquote class="tr_bq"><div style="text-align: right;"><i><a href="http://arxiv.org/abs/hep-th/9603053" target="_blank">Gravity coupled with matter and foundation of non-commutative geometry</a></i></div><div style="text-align: right;"><a href="http://arxiv.org/find/hep-th/1/au:+Connes_A/0/1/0/all/0/1">A. Connes</a></div><div style="text-align: right;">(Submitted on 8 Mar 1996)</div></blockquote><br /><blockquote><div style="text-align: justify;"><i><u>This leads us to the postulate that: </u></i></div></blockquote><blockquote><div style="text-align: justify;"><div style="text-align: center;"><i><u>The symmetry principle in noncommutative geometry is invariance under the group Aut(A). </u></i></div></div></blockquote><blockquote><div style="text-align: justify;"><i><u>We now apply these ideas to derive a noncommutative geometric action unifying gravity with the standard model</u>. The algebra is taken to be A=</i><i style="text-align: justify;">C<sup>∞</sup></i><i style="text-align: justify;">(M)</i><i>⊗A</i><i style="text-align: justify;"><span style="font-style: normal;"><i style="text-align: justify;"><span style="text-align: left;"><sub>F</sub></span></i></span></i><i> where the algebra </i><i>A</i><i style="text-align: justify;"><span style="font-style: normal;"><i style="text-align: justify;"><span style="text-align: left;"><sub>F</sub></span></i></span></i><i> is finite dimensional, A<span style="text-align: justify;"><span style="font-style: normal;"><span style="text-align: justify;"><span style="text-align: left;"><sub>F</sub></span></span></span></span>=<span style="color: #222222; font-family: "stixgeneral"; line-height: 24.3936px; text-align: center; white-space: nowrap;">ℂ</span><span style="text-align: justify;"><span style="font-size: x-small;">⊕</span></span><span style="text-align: justify;"><span style="background-color: white; color: #222222; font-family: "stixgeneral"; line-height: 24.3936px; text-align: center; white-space: nowrap;">ℍ</span></span><span style="text-align: justify;"><span style="font-size: x-small;">⊕</span>M</span><span style="text-align: justify;"><sub>3</sub></span><span style="text-align: justify;">(</span><span style="background-color: white; color: #222222; font-family: "stixgeneral"; line-height: 24.3936px; text-align: center; white-space: nowrap;">ℂ</span><span style="text-align: justify;">)</span> and <span style="text-align: justify;"><span style="background-color: white; color: #222222; font-family: "stixgeneral"; line-height: 24.3936px; text-align: center; white-space: nowrap;">ℍ </span></span>⊂ <span style="text-align: justify;">M<sub>2</sub>(<span style="background-color: white; color: #222222; font-family: "stixgeneral"; line-height: 24.3936px; text-align: center; white-space: nowrap;">ℂ</span>)</span> is the algebra of quaternions, </i><i style="text-align: justify;"><span style="background-color: white; color: #222222; font-family: "stixgeneral"; line-height: 24.3936px; text-align: center; white-space: nowrap;">ℍ </span></i><i>... </i> </div></blockquote><blockquote><div style="text-align: justify;"><i><u>A is a tensor product which geometrically corresponds to a product space, an instance of spectral geometry for A is given by the product rule</u>, </i></div></blockquote><blockquote><div style="text-align: justify;"><div style="text-align: center;"><i>H = L</i><i style="text-align: justify;"><sup>2</sup></i><i>(M, S)⊗ H</i><i style="text-align: justify;"><span style="font-style: normal;"><i style="text-align: justify;"><span style="text-align: left;"><sub>F</sub></span></i></span></i><i> , D = <strike>∂</strike></i><i style="text-align: justify;"><span style="font-style: normal;"><i style="text-align: justify;"><span style="text-align: left;"><sub>M</sub></span></i></span></i><i> </i><i>⊗ 1 + γ</i><i style="text-align: justify;"><span style="font-style: normal;"><i style="text-align: justify;"><span style="text-align: left;"><sub>5</sub></span></i></span></i><i> ⊗ D</i><i style="text-align: justify;"><span style="font-style: normal;"><i style="text-align: justify;"><span style="text-align: left;"><sub>F</sub></span></i></span></i><i> </i></div></div></blockquote><blockquote><div style="text-align: justify;"><u><i>where (</i><i style="text-align: center;">H</i><i style="text-align: center;"><span style="font-style: normal;"><i style="text-align: justify;"><span style="text-align: left;"><sub>F</sub></span></i></span></i><i>, </i><i style="text-align: center;">D</i><i style="text-align: center;"><span style="font-style: normal;"><i style="text-align: justify;"><span style="text-align: left;"><sub>F</sub></span></i></span></i><i>) is a spectral geometry on </i><i>A</i><i style="text-align: justify;"><span style="font-style: normal;"><i style="text-align: justify;"><span style="text-align: left;"><sub>F</sub></span></i></span></i><i>, while both </i><i style="text-align: center;">L</i><i style="text-align: center;"><sup>2</sup></i><i style="text-align: center;">(M, S)</i><i> and the Dirac operator </i><i style="text-align: center;">∂</i><i style="text-align: center;"><span style="font-style: normal;"><i style="text-align: justify;"><span style="text-align: left;"><sub>M</sub></span></i></span></i></u><i><u> on M are as above</u>. The group Aut(A) of diffeomorphisms falls in equivalence classes under the normal subgroup Int(A) of inner automorphisms. In the same way the space of metrics has a natural foliation into equivalence classes. The internal fluctuations of a given metric are given by the formula,</i> </div></blockquote><div style="text-align: center;"><blockquote><div style="text-align: justify;"><i>D = D</i><i style="text-align: justify;"><sub style="text-align: justify;">0</sub></i><i> + A + JA</i><i style="text-align: center;">J </i><i style="text-align: center;"><sup>-1</sup></i><i>, A = Σ</i><i>a</i><i style="text-align: justify;"><sub style="text-align: justify;">i</sub></i><i>[</i><i>D</i><i style="text-align: justify;"><sub style="text-align: justify;">0</sub></i><i>, b</i><i style="text-align: justify;"><sub style="text-align: justify;">i</sub></i><i>] , </i><i>a</i><i style="text-align: justify;"><sub style="text-align: justify;">i</sub></i><i>, </i><i>b</i><i style="text-align: justify;"><sub style="text-align: justify;">i</sub></i><i> ∈ A and A = A</i><i style="text-align: justify;"><sup style="font-style: normal;">*</sup></i><i>... </i></div></blockquote></div><blockquote><div style="text-align: justify;"><i><u>For Riemannian geometry these fluctuations are trivial. </u></i></div></blockquote><blockquote><div style="text-align: justify;"><u><i>The hypothesis which we shall test in this letter is that there exist an energy scale Λ in the range 10</i><i style="text-align: justify;"><sup>15</sup></i><i>−10</i><i style="text-align: justify;"><sup>19</sup></i></u><i><u> Gev at which we have a geometric action given by the spectral action</u>... </i></div></blockquote><blockquote><div style="text-align: justify;"><i><u>We now describe the internal geometry. The choice of the Dirac operator and the action of AF in HF comes from the restrictions that these must satisfy</u>:</i><span style="text-align: left;"> </span></div></blockquote><blockquote><div style="text-align: justify;"><div style="text-align: center;"><i>J</i><i style="text-align: justify;"><sup style="font-style: normal;">2</sup></i><i> = 1 , [J, D] = 0, [a, J</i><i>b</i><i style="text-align: justify;"><sup style="font-style: normal;">*</sup></i><i>J </i><i style="text-align: justify;"><sup>-1</sup></i><i>]=0 , [[D, a], Jb</i><i style="text-align: justify;"><sup style="font-style: normal;">*</sup></i><i>J </i><i style="text-align: justify;"><sup>-1</sup></i><i>]=0 ∀ a, b. (4)</i><span style="text-align: left;"> </span></div></div></blockquote><blockquote><div style="text-align: justify;"><i><u>We can now compute the inner fluctuations of the metric and thus operators of the form</u>: A = </i><i>Σa</i><i style="text-align: justify;"><sub style="text-align: justify;">i</sub></i><i>[D, b</i><i style="text-align: justify;"><sub style="text-align: justify;">i</sub></i><i>]</i><i>. This with the self-adjointness condition A = A</i><i style="text-align: justify;"><sup style="font-style: normal;">*</sup></i><i> gives a U(1), SU(2) and U(3) gauge fields as well as a Higgs field... </i></div></blockquote><blockquote><div style="text-align: justify;"><i><u> It is a simple exercise to compute the square of the Dirac operator ... This can be cast into the elliptic operator form</u> [7]: </i></div></blockquote><blockquote><div style="text-align: center;"><div style="text-align: center;"><i>P = D</i><i style="text-align: justify;"><sup style="font-style: normal;">2</sup></i><i> = −(g</i><i style="text-align: justify;"><sup style="font-style: normal;">µν</sup></i><i style="text-align: justify;">∂<sub style="text-align: justify;">µ</sub></i><i>∂<sub>ν</sub> · 1I + A</i><i style="text-align: justify;"><i style="text-align: justify;">γ</i><sup style="font-style: normal;">µ</sup>∂<sub style="text-align: justify;">µ</sub></i><i> + B) </i></div></div></blockquote><blockquote><div style="text-align: justify;"><div style="text-align: justify;"><i>where 1I, A µ and B are matrices of the same dimensions as D. <u>Using the heat kernel expansion for Tr(e</u></i><i style="text-align: justify;"><sup style="font-style: normal;"><u>-tP</u></sup></i><i><u>) ... we can show that ... a very lengthy but straightforward calculation ... gives for the bosonic action ... {the standard model action coupled to Einstein and Weyl gravity}</u> </i><i>plus higher order non-renormalizable interactions suppressed by powers of the inverse of the mass scale in the theory}...</i> </div></div></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>We ... adopt Wilson’s view point of the renormalization group approach to field theory [<a href="http://k.g.%20wilson%2C%20rev.%20%20mod.%20%20phys.%2047%20%281975%29%2C%20773/" target="_blank">9</a>] where the spectral action is taken to give the bare action with bare quantities ... at a cutoff scale Λ which regularizes the action the theory is assumed to take a geometrical form. </i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>The renormalized action receives counterterms of the same form as the bare action but with physical parameters ... The renormalization group equations ... yield relations between the bare quantities and the physical quantities with the addition of the cutoff scale Λ. Conditions on the bare quantities would translate into conditions on the physical quantities. <u>The renormalization group equations of this system were studied by Fradkin and Tseytlin [<a href="http://www.sciencedirect.com/science/article/pii/0550321382904448?via%3Dihub" target="_blank">10</a>] and is known to be renormalizable, but non-unitary [<a href="http://journals.aps.org/prd/abstract/10.1103/PhysRevD.16.953" target="_blank">11</a>] due to the presence of spin-two ghost (tachyon) pole near the Planck mass. We shall not worry about non-unitarity (see, however, reference <a href="http://www.sciencedirect.com/science/article/pii/0370269377906785?via%3Dihub" target="_blank">12</a>), because in our view at the Planck energy the manifold structure of space-time will break down and must be replaced with a genuienly noncommutative structure</u>.</i></blockquote><blockquote><div style="text-align: justify;"><i>Relations between the bare gauge coupling constants as well as equations (3.19) have to be imposed as boundary conditions on the renormalization group equations [9]. The bare mass of the Higgs field is related to the bare value of Newton’s constant, and both have quadratic divergences in the limit of infinite cutoff Λ... </i></div></blockquote><blockquote><div style="text-align: justify;"><i>There are some relations between the bare quantities. The renormalized action will have the same form as the bare action but with physical quantities replacing the bare ones. <u>The relations among the bare quantities must be taken as boundary conditions on the renormalization group equations governing the scale dependence of the physical quantities. These boundary condition imply that the cutoff scale is of order ∼ 10</u></i><u><i style="text-align: justify;"><sup style="font-style: normal;">15</sup></i><i> Gev and sin</i><i style="text-align: justify;"><sup style="font-style: normal;">2</sup></i></u><i><u>θw∼0.21 which is off by ten percent from the true value. We also have a prediction of the Higgs mass in the interval 170 − 180 Gev. There is ... a stronger disagreement where Newton’s constant comes out to be too large</u>... Incidentally the problem that Newton’s constant is coming out to be too large is also present in string theory where also has unification of gauge couplings and Newton’s constant occurs [<a href="http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.52.883" target="_blank">15</a>]. <u>These results must be taken as an indication that the spectrum of the standard model has to be altered as we climb up in energy. The change may happen at low energies (just as in supersymmetry ...) or at some intermediate scale.</u></i><i><u> This also could be taken as an indication that the the concept of space-time as a manifold breaks down and the noncommutativity of the algebra must be extended to include the manifold part</u>.</i></div></blockquote><blockquote class="tr_bq"><div style="text-align: right;"><i><a href="https://arxiv.org/abs/hep-th/9606056" target="_blank">A Universal Action Formula</a></i></div><div style="text-align: right;"><a href="https://arxiv.org/find/hep-th/1/au:+Chamseddine_A/0/1/0/all/0/1">Ali Chamseddine</a>, <a href="https://arxiv.org/find/hep-th/1/au:+Connes_A/0/1/0/all/0/1">Alain Connes</a> </div><div style="text-align: right;">(Submitted on 11 Jun 1996)</div></blockquote><br /><br /><blockquote class="tr_bq" style="text-align: justify;"><i><u>The notion of spectral geometry has</u> deep roots in pure mathematics. They have <u>to do with the understanding of the notion of (smooth) manifold. While this notion is simple to define in terms of local charts i.e. by glueing together open pieces of finite dimensional vector spaces, it is much more difficult and instructive to arrive at a global understanding</u> ... What one does is to detect global properties of the underlying space with the goal of characterizing manifolds...<span style="text-align: left;"> </span><span style="text-align: left;">At the beginning of the 80’s, <u>motivated </u></span><span style="text-align: left;"><u>by numerous examples of noncommutative spaces arising naturally in geometry from foliations or in physics from the Brillouin zone in the work of Bellissard on the quantum Hall effect, I realized that specifying an unbounded representative of the <a href="https://ncatlab.org/nlab/show/Fredholm+operator" target="_blank">Fredholm operator</a> was giving the right framework for spectral geometry </u>...</span></i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><u>Over the years this new [noncommutative geometric paradigm of spectral nature] has been considerably refined ... The noncommutative geometry dictated by physics is the product of the ordinary 4-dimensional continuum by a finite noncommutative geometry which appears naturally from the classification of finite geometries of KO-dimension equal to 6 modulo 8 (cf. [<a href="https://arxiv.org/abs/0706.3688" target="_blank">15</a>, <a href="https://arxiv.org/abs/hep-th/0610241" target="_blank">18</a>]). The compatibility of the model with the measured value of the Higgs mass was demonstrated in [<a href="https://arxiv.org/abs/1208.1030" target="_blank">20</a>] due to the role in the renormalization of the scalar field already present in [<a href="https://arxiv.org/abs/1004.0464" target="_blank">19</a>]. </u></i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><u>In [<a href="https://arxiv.org/abs/1409.2471" target="_blank">21</a>,<a href="https://www.blogger.com/Geometry%20and%20the%20Quantum:%20Basics," target="_blank"> 22</a>], with Chamseddine and Mukhanov we gave the conceptual explanation of the finite noncommutative geometry from Clifford algebras and obtained a higher form of the Heisenberg commutation relations between p and q, whose irreducible Hilbert space representations correspond to 4-dimensional spin geometries</u>. The role of p is played by the Dirac operator and the role of q by the Feynman slash of coordinates using Clifford algebras. The proof that all spin geometries are obtained relies on deep results of immersion theory and ramified coverings of the sphere. <u>The volume of the 4-dimensional geometry is automatically quantized by the index theorem and the spectral model, taking into account the inner automorphisms due to the noncommutative nature of the Clifford algebras, gives Einstein gravity coupled with the slight extension of the standard model which is a Pati-Salam model. This model was shown in our joint work with A. Chamseddine and W. van Suijlekom [<a href="https://arxiv.org/abs/1304.8050" target="_blank">24</a>, <a href="https://arxiv.org/abs/1507.08161" target="_blank">25</a>] to yield unification of coupling constants</u>.</i> </blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><u>Th{e} quantization of the volume implies that the bothering cosmological leading term of the spectral action is now quantized and thus it no longer appears in the variation of the spectral action</u>. Thus provided one understands how to reinstate all the ne details of the nite geometry (the one encoded by the Clifford algebras) such as the nuance on the grading and the number of generations, the variation of the spectral action will reproduce the Einstein equations coupled with matter.</i></blockquote><blockquote class="tr_bq"><div style="text-align: right;"><i><a href="https://www.dropbox.com/s/gzrqzjvilvgwfk9/J-Kouneiher.pdf?dl=0" target="_blank">Geometry and the Quantum</a> </i></div><div style="text-align: right;">Alain Connes </div><div style="text-align: right;">Draft version from February 21, 2017</div></blockquote></div>Cédric Bardothttps://plus.google.com/104733107894701960711noreply@blogger.com0tag:blogger.com,1999:blog-3911792794793692366.post-40527445937237622692017-02-22T20:20:00.002+01:002017-02-24T20:57:08.380+01:00(How and when) Spectral Physics (was born) or first fragment of a Lover's Dictionary on...<div dir="ltr" style="text-align: left;" trbidi="on"><b><i>Spectral Physics</i> (draft for the core entry)</b><br /><b><br /></b><br /><div style="-webkit-text-stroke-width: 0px; color: black; font-family: "Times New Roman"; font-size: medium; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: normal; letter-spacing: normal; orphans: 2; text-align: justify; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px;"></div><div style="orphans: 2; text-align: justify; text-indent: 0px; widows: 2;"><div style="color: black; font-family: "times new roman"; font-size: medium; font-weight: normal; letter-spacing: normal; margin: 0px; text-transform: none; white-space: normal; word-spacing: 0px;"><blockquote class="tr_bq" style="font-style: normal; text-align: right;"><a href="http://rsta.royalsocietypublishing.org/content/roypta/373/2039/20140213.full.pdf" target="_blank">That God is colouring Newton does show, And the devil is a Black outline, all of us know. </a></blockquote><blockquote class="tr_bq" style="font-style: normal; text-align: right;">William Blake, ‘To Venetian Artists’</blockquote></div><div style="margin: 0px;"><div style="color: black; font-family: "times new roman"; font-size: medium; font-style: normal; font-weight: normal; letter-spacing: normal; text-transform: none; white-space: normal; word-spacing: 0px;"><br /></div><blockquote class="tr_bq" style="background-color: white; box-sizing: border-box; color: black; font-family: "times new roman", times, serif; font-size: 15px; font-weight: normal; letter-spacing: normal; line-height: 1.6; margin-bottom: 15px; padding: 0px; text-align: justify; text-transform: none; white-space: normal; word-spacing: 0px;"><i>... in the beginning of the year 1666 <span style="line-height: inherit;"><a href="https://www.blogger.com/null" id="l2" style="box-sizing: border-box; color: #8a775d; font-weight: bold; line-height: inherit; text-decoration: underline;"></a></span>(at which time I applyed my self to the grinding of Optick glasses <span style="line-height: inherit;"><a href="https://www.blogger.com/null" id="l3" style="box-sizing: border-box; color: #8a775d; font-weight: bold; line-height: inherit; text-decoration: underline;"></a></span>of other figures then Sphericall) I procured me a trian<span style="line-height: inherit;"><a href="https://www.blogger.com/null" id="l4" style="box-sizing: border-box; color: #8a775d; font-weight: bold; line-height: inherit; text-decoration: underline;"></a></span>gular glasse Prisme to try therewith the celebrated phænomena <span style="line-height: inherit;"><a href="https://www.blogger.com/null" id="l5" style="box-sizing: border-box; color: #8a775d; font-weight: bold; line-height: inherit; text-decoration: underline;"></a></span>of colours. And in order thereto having darkned my chamber <span style="line-height: inherit;"><a href="https://www.blogger.com/null" id="l6" style="box-sizing: border-box; color: #8a775d; font-weight: bold; line-height: inherit; text-decoration: underline;"></a></span>& made a small hole in my window-shuts to let in a convenient <span style="line-height: inherit;"><a href="https://www.blogger.com/null" id="l7" style="box-sizing: border-box; color: #8a775d; font-weight: bold; line-height: inherit; text-decoration: underline;"></a></span>quantity of the sun's light, I placed my Prism at its entrance <span style="line-height: inherit;"><a href="https://www.blogger.com/null" id="l8" style="box-sizing: border-box; color: #8a775d; font-weight: bold; line-height: inherit; text-decoration: underline;"></a></span>that it might be thereby refracted to the opposite wall. It <span style="line-height: inherit;"><a href="https://www.blogger.com/null" id="l9" style="box-sizing: border-box; color: #8a775d; font-weight: bold; line-height: inherit; text-decoration: underline;"></a></span>was at first a very pleasing divertisement to view the <span style="line-height: inherit;"><a href="https://www.blogger.com/null" id="l10" style="box-sizing: border-box; color: #8a775d; font-weight: bold; line-height: inherit; text-decoration: underline;"></a></span>vivid & intense colours produced thereby; but after a while <span style="line-height: inherit;"><a href="https://www.blogger.com/null" id="l11" style="box-sizing: border-box; color: #8a775d; font-weight: bold; line-height: inherit; text-decoration: underline;"></a></span>applying my selfe to consider them more circumspectly, I be<span style="line-height: inherit;"><a href="https://www.blogger.com/null" id="l12" style="box-sizing: border-box; color: #8a775d; font-weight: bold; line-height: inherit; text-decoration: underline;"></a></span>came surprized to see them in an oblong form, which according <span style="line-height: inherit;"><a href="https://www.blogger.com/null" id="l13" style="box-sizing: border-box; color: #8a775d; font-weight: bold; line-height: inherit; text-decoration: underline;"></a></span>to the received lawes of refraction I expected should have <span style="line-height: inherit;"><a href="https://www.blogger.com/null" id="l14" style="box-sizing: border-box; color: #8a775d; font-weight: bold; line-height: inherit; text-decoration: underline;"></a></span>been circular.</i><span style="background-color: transparent; font-family: "times new roman"; font-size: small; text-align: justify;"> </span></blockquote><blockquote class="tr_bq" style="background-color: white; box-sizing: border-box; color: black; font-family: "times new roman", times, serif; font-size: 15px; font-weight: normal; letter-spacing: normal; line-height: 1.6; margin-bottom: 15px; padding: 0px; text-align: justify; text-transform: none; white-space: normal; word-spacing: 0px;"><i>They were terminated at the sides with streight lines, but at <span style="line-height: inherit;"><a href="https://www.blogger.com/null" id="l15" style="box-sizing: border-box; color: #8a775d; font-weight: bold; line-height: inherit; text-decoration: underline;"></a></span>the ends the decay of light was so graduall that it was <span style="line-height: inherit;"><a href="https://www.blogger.com/null" id="l16" style="box-sizing: border-box; color: #8a775d; font-weight: bold; line-height: inherit; text-decoration: underline;"></a></span>difficult to determine justly what was their figure, yet <span style="line-height: inherit;"><a href="https://www.blogger.com/null" id="l17" style="box-sizing: border-box; color: #8a775d; font-weight: bold; line-height: inherit; text-decoration: underline;"></a></span>they seemed semicircular.</i><span style="background-color: transparent; font-family: "times new roman"; font-size: small; text-align: justify;"> </span></blockquote><blockquote class="tr_bq" style="background-color: white; box-sizing: border-box; color: black; font-family: "times new roman", times, serif; font-size: 15px; font-weight: normal; letter-spacing: normal; line-height: 1.6; margin-bottom: 15px; padding: 0px; text-align: justify; text-transform: none; white-space: normal; word-spacing: 0px;"><i>Comparing the length of this Coloured Spectrum with its bredth <span style="line-height: inherit;"><a href="https://www.blogger.com/null" id="l18" style="box-sizing: border-box; color: #8a775d; font-weight: bold; line-height: inherit; text-decoration: underline;"></a></span>I found it about five times greater, a disproportion soe <span style="line-height: inherit;"><a href="https://www.blogger.com/null" id="l19" style="box-sizing: border-box; color: #8a775d; font-weight: bold; line-height: inherit; text-decoration: underline;"></a></span>extravagant that it excited me to a more then ordinary <span style="line-height: inherit;"><a href="https://www.blogger.com/null" id="l20" style="box-sizing: border-box; color: #8a775d; font-weight: bold; line-height: inherit; text-decoration: underline;"></a></span>curiosity of examining from whence it might proceed; I could <span style="line-height: inherit;"><a href="https://www.blogger.com/null" id="l21" style="box-sizing: border-box; color: #8a775d; font-weight: bold; line-height: inherit; text-decoration: underline;"></a></span>scarce think that the various thicknesse of the glasse, or the <span style="line-height: inherit;"><a href="https://www.blogger.com/null" id="l22" style="box-sizing: border-box; color: #8a775d; font-weight: bold; line-height: inherit; text-decoration: underline;"></a></span>termination with shaddow or darknesse could have any influence <span style="line-height: inherit;"><a href="https://www.blogger.com/null" id="l23" style="box-sizing: border-box; color: #8a775d; font-weight: bold; line-height: inherit; text-decoration: underline;"></a></span>on light to produce such an effect, yet I thought it not <span style="line-height: inherit;"><a href="https://www.blogger.com/null" id="l24" style="box-sizing: border-box; color: #8a775d; font-weight: bold; line-height: inherit; text-decoration: underline;"></a></span>amisse to examine first those circumstances, & soe tryed what <span style="line-height: inherit;"><a href="https://www.blogger.com/null" id="l25" style="box-sizing: border-box; color: #8a775d; font-weight: bold; line-height: inherit; text-decoration: underline;"></a></span>would happen by transmitting light through parts of the glasse <span style="line-height: inherit;"><a href="https://www.blogger.com/null" id="l26" style="box-sizing: border-box; color: #8a775d; font-weight: bold; line-height: inherit; text-decoration: underline;"></a></span>of divers thicknesses, or through holes in the window of divers <span style="line-height: inherit;"><a href="https://www.blogger.com/null" id="l27" style="box-sizing: border-box; color: #8a775d; font-weight: bold; line-height: inherit; text-decoration: underline;"></a></span>bignesses, or by setting the Prism without, so that the light might <span style="line-height: inherit;"><a href="https://www.blogger.com/null" id="l28" style="box-sizing: border-box; color: #8a775d; font-weight: bold; line-height: inherit; text-decoration: underline;"></a></span>passe through it & bee refracted before it was terminated <span style="line-height: inherit;"><a href="https://www.blogger.com/null" id="l29" style="box-sizing: border-box; color: #8a775d; font-weight: bold; line-height: inherit; text-decoration: underline;"></a></span>by the hole: but I found none of those circumstances mate<span style="line-height: inherit;"><a href="https://www.blogger.com/null" id="l30" style="box-sizing: border-box; color: #8a775d; font-weight: bold; line-height: inherit; text-decoration: underline;"></a></span>riall. The fashion of the colours was in all these cases the <span style="line-height: inherit;"><a href="https://www.blogger.com/null" id="l31" style="box-sizing: border-box; color: #8a775d; font-weight: bold; line-height: inherit; text-decoration: underline;"></a></span>same.</i></blockquote><blockquote class="tr_bq" style="color: black; font-family: "times new roman"; font-size: medium; font-weight: normal; letter-spacing: normal; text-transform: none; white-space: normal; word-spacing: 0px;"><div style="text-align: right;"><i><a href="http://www.newtonproject.ox.ac.uk/view/texts/normalized/NATP00003" target="_blank">Draft of 'A Theory Concerning Light and Colors'</a></i></div><div style="text-align: right;">Isaac Newton</div><div style="text-align: right;">Trinity Coll Cambridge. Feb. 6. 1671/2</div></blockquote></div><div style="-webkit-text-stroke-width: 0px; color: black; font-family: "Times New Roman"; font-size: medium; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: normal; letter-spacing: normal; margin: 0px; text-transform: none; white-space: normal; word-spacing: 0px;"><br /></div><div style="color: black; font-family: "times new roman"; font-size: medium; font-weight: normal; letter-spacing: normal; margin: 0px; text-transform: none; white-space: normal; word-spacing: 0px;"><br />I envision s<i>pectral physics</i> as a scientific endeavour based on a set of experimental and conceptual spectroscopes to scrutinise and merge in a coherent picture the macroscopic and microscopic features of the phenomenological world physicists probe thanks to telescopes, high energy accelerators, extremely low temperature devices, very high magnetic fields ... etc, and confront with heuristic tools like quantum mechanics, thermal physics or general relativity while mathematicians formalise the computations confirmed by nature with theories like Euclidean geometry, calculus, Fourier analysis, Riemannian manifolds and their noncommutative extensions with a proper spectral calculus.<br /><br /><br /></div></div></div>Cédric Bardothttps://plus.google.com/104733107894701960711noreply@blogger.com0tag:blogger.com,1999:blog-3911792794793692366.post-79718505558323245422017-02-19T10:36:00.001+01:002017-02-20T18:41:32.837+01:00(Even more?) Simple GUTs come along with longer proton lifetime and hint of normal neutrino mass hierarchy<div dir="ltr" style="text-align: left;" trbidi="on"><b>From hidden simplicities to a conjectured quantum gravity condition on matter content</b><br /><div style="text-align: justify;">Here are ideas and speculations from a more than twenty year old article by Giovanni AMELINO-CAMELIA which resonates interestingly - in my ears at least - with <i><a href="https://arxiv.org/abs/1507.08161" target="_blank">grand unification in the Spectral Pati-Salam Model</a> </i>retrospectively (underlining and bold emphasis as well as {...} are mine as usual):</div><blockquote class="tr_bq" style="text-align: justify;"><i><u>It is probably worth emphasizing, at least for the benefit of the students ... that we have nothing (from the conceptual viewpoint) to assure us that nature should be describable in terms of simple laws. Still, most of us do expect this simplicity, probably extrapolating from the history of physics, which has proceeded through a series of steps of deeper understanding and simplification</u> (such as the description of the baryon spectrum in terms of the quark model). <u>From the point of view of this expected simplicity, the SM is quite unsatisfactory, since it leaves unanswered several questions</u>; in particular, </i></blockquote><blockquote class="tr_bq"><i>(Qa) Particle physics is described by a gauge theory with the peculiar gauge group GSM ≡SU(3)c⊗SU(2)L⊗ U(1)Y .<br />(Qb) The corresponding three coupling constants, αs, α2, and αY , are free parameters of the model. (Qc) A peculiar bunch of IRREPs (irreducible representations) of SU(3)c⊗SU(2)L hosts the quarks and leptons.<br />(Qd) The hypercharge assignments to the quark and lepton IRREPs are arbitrary. (Qe) The Yukawa couplings are arbitrary.<br />(Qf) The entries of the Cabibbo-Kobayashi-Maskawa matrix are arbitrary.<br />(Qg) Each of the quarks and leptons of the model is present in triplicate copy (family structure).<br /><u>(Qh) A peculiar (bunch of) IRREP(s) hosts the Higgs particles.<br />(Qi) The parameters of the Higgs potential, which determine the Higgs mass(es) and all the aspects of symmetry breaking, are arbitrary</u>.<br />(Qj) The anomaly cancellation is a (apparently accidental) result of the structure of the (arbitrarily selected) matter content of the model. </i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><u>GUTs [models with a (grand)unified description of particle interactions] have been investigated primarily because, as illustrated in the discussion of SO(10) GUTs given in the next section, they address/simplify (Qa)-(Qf) and, in some cases, (Qj), and are therefore good candidates for the description of particle physics if the trend of incremental simplifications of this description is to continue. However, it should be noted that not only GUTs bring no improvement in relation to (Qg), but they actually increase the complexity associated to (Qh) and (Qi)</u>. Therefore, from the “aesthetic” viewpoint, GUTs have merits and faults (with the merits outnumbering, but not necessarily outweighing, the faults). </i></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><i><u>Phenomenological encouragement for the GUT idea comes from the observed low-energy values of αs, α2, and αY , which appear to be arranged just as needed for unification</u>. Indeed, (although the simplest GUT candidate, minimal SU(5), does not pass this test[1]) there are several examples of GUTs which reproduce these data on the coupling constants while being consistent with the ... experimental lower limit on proton decay τ<sub>p→e+π0</sub> ≥ 9</i><i>×</i><i>10<sup>32</sup> years {in 1996 and τ</i><i><sub>p→e+π0 </sub></i><i>>1.6×10</i><i><sup>34</sup></i><i> years at 90% confidence <a href="https://arxiv.org/abs/1610.03597" target="_blank">using Super-Kamiokandedata from April 1996 to March 2015</a>}. <u>One important feature of phenomenologically consistent GUTs is that they must involve at least one extra scale, besides the unification scale MX, at which the RGEs (renormalization group equations) of the SM couplings are modified</u>... </i></div></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><i><u>Perhaps the simplest GUTs meeting the minimum requirement of agreement with the data on the coupling constants and with the experimental limit on proton decay are some SO(10) models, which are reviewed in the next section</u>. <u>They naturally (see next section) predict a two-scale breaking to GSM</u>; in fact, a typical SO(10) breaking chain is given by </i><br /><div class="separator" style="clear: both; text-align: center;"><i><a href="https://1.bp.blogspot.com/-IoXCdiKXupQ/WKhQk8pzxLI/AAAAAAAACA8/ywqaKMBBM6MuI3Mm7DVNdZ7MvIx2ITL8gCLcB/s1600/SO10.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="47" src="https://1.bp.blogspot.com/-IoXCdiKXupQ/WKhQk8pzxLI/AAAAAAAACA8/ywqaKMBBM6MuI3Mm7DVNdZ7MvIx2ITL8gCLcB/s400/SO10.JPG" width="400" /></a> </i></div><i></i></div></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><i>Importantly, in SO(10) the hypercharge Y is the combination of two generators belonging to the Cartan, Y = T3R + (B − L)/ 2 , (2) where B − L and T3R belong respectively to the SU(4)PS (the SU(4) containing SU(3)c and U(1)B−L, which was first considered by Pati and Salam) and the SU(2)R subgroups of SO(10). This leads to a high unification point MX if the intermediate symmetry group G′ contains SU(2)R and/or SU(4)PS, since then, between MZ and MR, the Abelian evolution of αY (predicted by SM) is replaced by the non-Abelian one of either component of Y . MX is connected with the masses of the lepto-quarks that can mediate proton decay, and this SO(10) mechanism for a higher unification point turns out to be useful in allowing to meet the condition </i><span style="text-align: left;"> </span></div></blockquote><blockquote class="tr_bq"><div style="text-align: center;"><i>MX ≥ 3.2<span style="text-align: justify;">×</span>10<span style="text-align: justify;"><sup>15</sup></span> GeV , (3) <span style="text-align: left;"> </span></i></div></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><i>which is necessary... for agreement with the present experimental limit on proton decay. </i><i><u>Although (relatively) simple GUTs, such as SO(10), can work, they are affected by the hierarchy problem, and this causes many to prefer SUSY (supersymmetric) GUTs... In this paper (but not necessarily elsewhere) I take the position that for the GUTs (whether they are SUSY or not) the aesthetic advantages and the consistency with the observed low-energy values of the gauge coupling constants outweigh the damage done in regard to (Qh) and (Qi). This motivates me to look for possible ways to associate hidden simplicities to the apparently complicated GUT structures affecting (Qh) and (Qi) (and (Qg))</u>; the reader is warned of the fact that the resulting discussion is accordingly quite speculative.</i></div><br /><div style="text-align: justify;"><i>From ... properties of the smallest IRREPs of SO(10) one can easily see that the typical pattern of SSB of SO(10) to GSM has two steps; indeed, with the exception of the singlet in the 144, the little group of all the above mentioned GSM singlets is larger than GSM. Actually, either for phenomenological or for technical reasons, some of the above mentioned GSM singlets, cannot be used for the first SSB step...The previous considerations lead to four scenarios, in which the first steps of breaking are:</i><span style="text-align: left;"> </span></div></blockquote><blockquote class="tr_bq"><div style="text-align: center;"><div style="text-align: left;"><i>(Ia) SO(10) → SU(3)c⊗SU(2)L⊗SU(2)R⊗U(1)B−L×D </i></div></div><div style="text-align: center;"><div style="text-align: left;"><i>(Ib) SO(10) → SU(4)PS⊗SU(2)L⊗SU(2)R </i></div></div><div style="text-align: center;"><div style="text-align: left;"><i>(Ic) SO(10) → SU(3)c⊗SU(2)L⊗SU(2)R⊗U(1)B−L </i></div></div><div style="text-align: center;"><div style="text-align: left;"><i>(II) SO(10) → SU(4)PS⊗SU(2)L⊗SU(2)R×D, <span style="text-align: left;"> </span></i></div></div></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>The type-I SO(10) models require that an appropriate vector3 in the space of GSM singlets of the 210 acquires a v.e.v. (vacuum expectation value) at the GUT scale. Analogously the type-II model requires that the GSM singlet of the 54 acquires a v.e.v. at the GUT scale. An appealing[<a href="http://inspirehep.net/record/141106?ln=fr" target="_blank">10</a>] possibility for the completion of the models of type-Ia,b,c and type-II is the one of realizing the second SSB step, at a scale MR, with the GSM singlet of the 126⊕126 representation, and the third SSB step with a combination of the SU(3)c⊗U(1)e.m.-invariant vectors of two 10’s, in such a way to avoid the unwanted relation mt = mb ... Through the see-saw mechanism, the scale MR is related to the masses of the (almost) left-handed neutrinos... </i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>The type-Ia,b,c and type-II models have been studied... and they have been found to be consistent with the unification of couplings and the experimental bound on the proton lifetime, although in the case of the type-II model the consistence with the experimental bound on the proton lifetime is only marginal... Within the see-saw mechanism, one also finds that these models predict masses for the (almost) left-handed neutrinos in an interesting range. </i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><u>This phenomenology depends however on the values of the parameters of the Higgs potential, which are free inputs of the model. Most importantly, as mentioned above, the parameters of the Higgs potential must be chosen so that the desired SSB pattern is realized. Although this does not involve a particular fine tuning[10, 11, 12, 13], it does introduce an element of undesirable arbitrariness in the models</u>. <u>Similarly, the “matter ingredients” of the models</u> (e.g., in the type-I models, 16⊕16⊕16 for the fermions plus 10⊕10⊕126⊕126⊕210 for the Higgs bosons) <u>is selected with the only constraint of reproducing observation (i.e. the matter content is not constrained by any requirement of internal consistency of the models)</u>... </i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><b>One way to render a GUT more predictive would be the discovery of a dynamical mechanism (quasi) fixing the values of the parameters of the Higgs potential at the GUT scale MX</b>. In this section I discuss one such mechanism which might be available when looking at the GUT as an effective low-energy description of a more fundamental theory (possibly including gravity). </i></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><i>I observe that, <u>besides leading to the possibility of an increased predictivity (in the sense clarified above) of the SSB pattern, viewing GUTs as effective low-energy descriptions of a more fundamental theory, with the associated RG implications, requires a modification of the conventional tests of the naturalness of a GUT. These conventional tests typically assign a “low grade” to GUTs in which a fine tuning of the Higgs parameters is needed for a phenomenological SSB pattern; however, the </u></i><i><u>effective-theory viewpoint on GUTs would require to check whether the phenomenological SSB pattern corresponds to fine tuning of the Higgs parameters at the scale M∗. It is plausible that a scenario requiring no fine tuning of the Higgs parameters at M∗ might correspond via the RG running (for example in presence of an appropriate infra-red fixed point) to a narrow region (apparent fine tuning) of the Higgs parameter space at MX , where the SSB is decided</u>. On the other hand, it is also plausible that a SSB pattern corresponding to a significant portion of the Higgs parameter space </i><i>actually requires some level of fine tuning at M∗ (for example, the considered portion </i><i>of Higgs parameter space might be “disfavored” by the RG running).</i><span style="text-align: left;"> </span></div></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><i>Concerning the scale M∗ at which the GUT becomes relevant as an effective low-energy theory, it should be noticed that, while any scenario with M∗ >MX is plausible, the present (however limited) understanding of physics beyond the GUT scale MX suggests that M∗ could be within a few orders of magnitude of the Planck scale MP . <u>In fact, it is reasonable to expect that beyond the GUT there is a theory incorporating </u><u>gravity (a quantum gravity), and MP is the scale believed to characterize this more fundamental theory.</u></i><span style="text-align: left;"> </span></div></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><i><u>It is also important to realize that the type of RG naturalness that I am requiring for GUTs is really a minimal requirement once the GUT is seen as an effective low-energy description of a more fundamental theory</u>. In order to get a consistent GUT from this viewpoint one would also want that “nothing goes wrong” in going from the scale M∗ to the scale MX . For example, SSB should not occur “prematurely” at a scale µSSB such that MX <µSSB <M∗ , and the running of the masses involved in the RGEs should be taken into account. In relation to this point, it is interesting that the investigation of the RG naturalness of the parameters of the Higgs potential might ultimately help understanding also the emergence of the GUT scale. At present this scale is just a phenomenological input of a GUT, resulting from the observed (low-energy) values of the GSM coupling constants, but it would be interesting to see it emerging as a scale within the GUT. By studying the RGEs for the parameters of the Higgs potential one might find such a scale; for example, assuming not-too-special </i><i>initial conditions for the parameters at the scale M∗, one might find that the running of the parameters is such that SSB of the GUT occurs typically in the neighborhood of a certain scale hopefully a phenomenologically reasonable one). </i><span style="text-align: left;"> </span></div></blockquote><blockquote class="tr_bq"><u></u><br /><div style="text-align: justify;"><u><i><u>I also want to stress that one could consider additional consistency/naturalness conditions in order to render the GUT consistent with a working cosmological (early universe evolution) scenario. Such conditions should be properly formulated in the language of finite temperature field theory, and should take into account the fact that (contrary to the expectations often expressed in the literature) the dependence of couplings on the renormalization scale is different from their temperature dependence</u>... </i></u></div><u></u></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><i><u>As illustrated by the review of SO(10) GUTs ... GUTs typically involve a remarkably complex matter content.</u> Most notably, the Higgs sector consists of several carefully selected IRREPs of the GUT group, and, like in the SM, the fermionic sector of leptons and quarks is arbitrary and is plagued by the family triplication. <u>This complexity might well be telling us that the GUT idea needs drastic revisions; however, in this paper I take the point of view that the complexity of the matter content might be only apparent</u>. I therefore want to mention a few appealing scenarios in which this complexity might arise from a fundamental simplicity. <u>For continuity with the line of argument advocated in the previous section, let me start by mentioning the possibility that as an effective low-energy description of a more fundamental theory, the (effective) matter content of the GUT at the scale MX might be fixed by the RG running</u>. It is in fact plausible that some IRREPs tend to get heavy masses via RG running, whereas the masses of other IRREPs (the ones relevant for symmetry breaking and low-energy phenomenology) might tend to be light (i.e. order MX or less). <u>This type of running of masses (or other parameters) might even be responsible for the cancellation of anomalies at low energies; indeed, the RG running is known to be easily driven by symmetries</u>...</i><span style="text-align: left;"> </span></div></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><i><b>Another hypothesis</b> which has been gaining some momentum in the literature on low-dimensional Quantum-Gravity toy models <b>is that Quantum Gravity might be quite selective concerning the type of matter “it likes to deal with”, i.e. the requirement of overall consistency of Quantum Gravity might fix the matter content</b>. Results pointing (however faintly) in this direction can be found for example in certain studies of discretized two-dimensional Quantum Gravities[<a href="https://arxiv.org/abs/hep-th/9312002" target="_blank">25</a>], and studies of the Dirac quantization of certain two-dimensional Quantum Gravities in the continuum [<a href="https://arxiv.org/abs/hep-th/9405119" target="_blank">26</a> {<a href="https://arxiv.org/abs/gr-qc/9511048" target="_blank">26'</a>}]...</i><span style="text-align: left;"> </span></div></blockquote><blockquote class="tr_bq"><i><u></u></i><br /><div style="text-align: justify;"><i><b>Perhaps the only robust concept discussed in this paper is the one concerning the way in which the conventional tests of the naturalness of a GUT need to be modified if the GUT is seen as a low-energy effective description of a more fundamental theory.</b></i><span style="text-align: left;"> </span></div></blockquote><blockquote class="tr_bq"><i><u></u><u></u></i><br /><div style="text-align: justify;"><i><u><u>On a more speculative side, I also articulated the hope that the correct GUT (if there is one) could be such that its SSB pattern is essentially predicted </u>(in the sense of the RG naturalness I discussed) rather than being a free input; <u>this would fit well the general trend of increased predictivity at each new stage of our understanding of particle physics</u>.<span style="text-align: left;"> </span></u></i></div><i><u></u></i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><u>I have also looked at the complexity of the matter content of GUTs, and explored the possibility that this might be an apparent complexity, hiding a fundamental simplicity</u>... I have speculated on a few appealing candidates for this simplicity; however, <u>it is reasonable to expect that real progress in this direction will require dramatic new developments.</u> </i></blockquote><blockquote class="tr_bq"><div style="text-align: right;"><i><a href="https://arxiv.org/abs/hep-ph/9610298" target="_blank">Simple GUTs</a></i></div><div style="text-align: right;"><a href="https://arxiv.org/find/hep-ph/1/au:+Amelino_Camelia_G/0/1/0/all/0/1">G. Amelino-Camelia</a></div><div style="text-align: right;">(Submitted on 9 Oct 1996)</div></blockquote><br /><b><br /></b><br /><div style="text-align: justify;"><b>Two challenges for some courageous graduate students in particle physics phenomenology and cosmology:</b></div><ul style="text-align: left;"><li style="text-align: justify;">Explore the phenomenological consequences of the spectral Pati-Salam model(s) in particular those concerning neutrino masses and mixing* and check its compatibility with current low-energy data and potential falsifiability with future planned experiments. Investigate the possible "Renormalisation Group naturalness" of this simple(r?) GUT(s). </li></ul><ul style="text-align: left;"><li style="text-align: justify;">Build a cosmological model with a scope from a 1<span style="text-align: center;">0<span style="text-align: justify;"><sup>12</sup></span></span> GeV leptogenesis horizon to the current 0.23 eV scale, compatible with current astrophysical data and based only on the matter content of the spectral Pati-Salam model and the phenomenology of mimetic gravity consistent with the spectral action principle. Explore the phenomenological implications in particular concerning the different cosmological backgrounds (gravitational, electromagnetic and neutrino sectors).</li></ul><br /><br /><b>* Neutrino may sing "from their GUTs"</b><br /><div style="text-align: justify;">From a particle physics phenomenologist perspective, spectral models may appear not very appealing as the matter content does not offer great perspective regarding the discovery of an exotic particle at a man made accelerator or even detector: no sparticle or wimp for instance. Nevertheless the recent article summarized below shows how some minimal grand unified models can help us to stay tuned on the faint neutrino song:</div><blockquote class="tr_bq" style="text-align: justify;"><i><u>Minimal SO(10) grand unified models provide phenomenological predictions for neutrino mass patterns and mixing</u>. These are the outcome of the interplay of several features, namely: i) the seesaw mechanism; ii) the presence of an intermediate scale where B-L gauge symmetry is broken and the right-handed neutrinos acquire a Majorana mass; iii) a symmetric Dirac neutrino mass matrix whose pattern is close to the up-type quark one. In this framework two natural characteristics emerge. <u>Normal neutrino mass hierarchy is the only allowed, and there is an approximate relation involving both light-neutrino masses and mixing parameters. This differs from what occurring when horizontal flavour symmetries are invoked</u>. In this case, in fact, neutrino mixing or mass relations have been separately obtained in literature. <u>In this paper we discuss an example of such comprehensive mixing-mass relation in a specific realization of SO(10) and, in particular, analyse its impact on the expected neutrinoless double beta decay effective mass parameter hmeei, and on the neutrino mass scale. Remarkably a lower limit for the lightest neutrino mass is obtained (m</u></i><u><i style="text-align: justify;"><span style="font-size: 13.3333px;"><i style="font-size: medium;"><sub>lighest </sub></i></span></i><i> </i>≥ <i>7.5×10</i><span style="text-align: center;"><span style="text-align: justify;"><sup>-4</sup></span></span><span style="text-align: justify;"> </span></u><i><u>eV, at 3 σ level)</u>. </i></blockquote><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-Ur7iKNeIsvE/WKhquBld_EI/AAAAAAAACBM/LAG8owK-HFQKGprCED_sZRfv9vvECL6eQCLcB/s1600/Buccella1.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://2.bp.blogspot.com/-Ur7iKNeIsvE/WKhquBld_EI/AAAAAAAACBM/LAG8owK-HFQKGprCED_sZRfv9vvECL6eQCLcB/s1600/Buccella1.JPG" /></a></td></tr><tr><td class="tr-caption" style="text-align: justify;"><blockquote class="tr_bq"><i><span style="font-size: small;">T</span></i><i><span style="font-size: small;">he solid (dashed) lines bound the allowed region in the m</span></i><span style="font-size: small;"><i style="text-align: justify;"><span style="font-size: 13.3333px;"><i style="font-size: medium;"><sub>lighest </sub></i></span></i></span><i style="font-size: medium;">–(m</i><span style="font-size: small;"><i style="text-align: justify;"><span style="font-size: 13.3333px;"><i style="font-size: medium;"><sub>ee</sub></i></span></i></span><i style="font-size: medium;">) plane obtained by spanning the 3 σ ranges for the neutrino mixing parameters [<a href="https://arxiv.org/abs/1601.07777" target="_blank">9</a>] in case of NH (IH). The dotted (dot-dashed) line is the prediction of eq. (9) on the effective mass, once the NH (IH) best-fit values of the neutrino mixing parameters are adopted [9]. The shaded region represents the 3 σ area obtained according to the neutrino mass-mixing dependent sum rule of eq. (9).</i></blockquote></td></tr></tbody></table><div><blockquote class="tr_bq"><div style="text-align: right;"><i><a href="https://arxiv.org/abs/1701.00491" target="_blank"><br />A neutrino mass-mixing sum rule from SO(10) and neutrinoless double beta decay</a></i></div><div style="text-align: right;"><a href="https://arxiv.org/find/hep-ph/1/au:+Buccella_F/0/1/0/all/0/1">F. Buccella</a>, <a href="https://arxiv.org/find/hep-ph/1/au:+Chianese_M/0/1/0/all/0/1">M. Chianese</a>, <a href="https://arxiv.org/find/hep-ph/1/au:+Mangano_G/0/1/0/all/0/1">G. Mangano</a>, <a href="https://arxiv.org/find/hep-ph/1/au:+Miele_G/0/1/0/all/0/1">G. Miele</a>, <a href="https://arxiv.org/find/hep-ph/1/au:+Morisi_S/0/1/0/all/0/1">S. Morisi</a>, <a href="https://arxiv.org/find/hep-ph/1/au:+Santorelli_P/0/1/0/all/0/1">P. Santorelli</a></div><div style="text-align: right;">(Submitted on 2 Jan 2017 (<a href="https://arxiv.org/abs/1701.00491v1">v1</a>), last revised 11 Jan 2017 (this version, v2))</div></blockquote><br /><br />//Last edit February 20, 2017</div></div>Cédric Bardothttps://plus.google.com/104733107894701960711noreply@blogger.com0tag:blogger.com,1999:blog-3911792794793692366.post-62518315176417519762017-02-18T17:05:00.000+01:002017-02-22T13:45:10.406+01:00All roads lead to Clifford algebra (and praise the spinors for that)!<div dir="ltr" style="text-align: left;" trbidi="on"><b>More of algebra <strike>p</strike>fest...</b><br /><div style="text-align: justify;">... in a very recent <i>geometric algebra</i> perspective on the discrete parameters and symmetries of the standard model:</div><blockquote class="tr_bq" style="text-align: justify;"><i><u>A simple geometric algebra is shown to contain automatically the leptons and quarks of a generation of the Standard Model (SM), and the electroweak and color gauge symmetries...</u></i><i>{<u>Any structure aiming to describe the particles and forces of the SM has to include two instances of the complex Clifford algebra <span style="text-align: left;">Cℓ</span><span style="text-align: justify;"><sub>6</sub></span>. Since the two instances are isomorphic, the minimal solution is to identify them</u>. This minimal algebraic structure is the Standard Model Algebra, A<span style="text-align: justify;"><sub>SM</sub></span></i><span style="text-align: left;">:=</span><i><span style="text-align: left;">Cℓ(χ<span style="text-align: justify;"><sup>†</sup></span>⊕ χ)</span></i><i><span style="text-align: left;">≅ </span></i><i><span style="text-align: left;">Cℓ</span><span style="text-align: justify;"><sub>6</sub></span></i><i><span style="text-align: left;"> </span></i><i>with a preferred Witt decomposition that splits the algebra into minimal left ideals: </i><i><span style="text-align: left;">χ<span style="text-align: justify;"><sup>†</sup></span>⊕ χ </span></i><i><span style="text-align: left;">where </span><span style="text-align: left;">χ is a </span><span style="text-align: left;">complex three-dimensional vector space</span></i><i>.} The minimal left ideals determined by the Witt decomposition correspond naturally pairs of leptons or quarks whose left chiral components interact weakly. The Dirac algebra is a distinguished subalgebra acting on the ideals representing leptons and quarks. <u>The resulting representations on the ideals are invariant to the electromagnetic and color symmetries, which are generated by the bivectors of the algebra. The electroweak symmetry is also present, and it is already broken by the geometry of the algebra. The model predicts a bare Weinberg angle </u></i><u><i>θ<span style="text-align: justify;"><sub style="text-align: justify;">W</sub></span></i><i> given by </i><i>sin<span style="text-align: justify;"><span style="text-align: justify;"><span style="text-align: center;"><span style="text-align: justify;"><sup>2</sup></span></span></span></span>(θ<span style="text-align: justify;"><sub style="text-align: justify;">W</sub></span>)</i></u><i><u>=0.25</u>... <u>{which} seems more encouraging that that of 0.375 predicted by the SU(5), SO(10), and other GUTs.</u> But it is still not within the range estimated experimentally. Depending on the utilized scheme, the experimental values for sin<span style="text-align: justify;"><span style="text-align: justify;"><span style="text-align: center;"><span style="text-align: justify;"><sup>2</sup></span></span></span></span>(θ<span style="text-align: justify;"><sub style="text-align: justify;">W</sub></span>), range between ≃ 0.223 and ≃ 0.24 (Erler and Freitas, 2015). In particular, CODATA gives a value of 0.23129(5) (Mohr and Newe, 2016). As in the case of the SU(5) prediction ... a correct comparison would require taking into account the running of the coupling constants due to higher order perturbative corrections...</i><span style="text-align: left;"> </span></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><u>The most known GUT models based on the inclusion of the Standard Model group into a larger simple Lie group range from SU(5)</u> (Georgi and Glashow, 1974) <u>and Spin(10) </u>(Georgi, 1975), and their supersymmetric versions, <u>to much larger extensions</u>. <u>The model proposed in this article has something in common with them, by using representations of the gauge groups on exterior algebras. It differs by not predicting new bosons and proton decay, by explaining why not any Lie group and not any representation appear to be manifested as particles, and by a different value of the Weinberg angle</u>...<span style="text-align: left;"> </span></i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><u>The proposed model, by unifying various aspects of the Standard Model, may also be a first step toward a simpler and more insightful Lagrangian. This model clearly cannot include gravity on equal footing with the other forces</u>, but its geometric nature and the automatic inclusion of the Dirac algebra associated with the metric may allow finding new connections with general relativity and gravity. At this stage these prospects are speculative, but this is just the beginning. <u>Another future step is to investigate the quantization within this framework. Since the model does not make changes to the SM, it may turn out that the Lagrangian and the quantization are almost the same as those we know. But the constraints introduced by the Standard Model Algebra </u></i><i><u>may be helpful in these directions too. An interesting difference is the electroweak symmetry breaking induced purely by geometry</u>... The Higgs boson is not forbidden by the model, being allowed to live in its usual space associated with the weak symmetry, and it is useful to generate the masses of the particles. But it gained a more geometric interpretation, which may find applications in future research. <u>The proposed model does not make any assumptions about the neutrino, except that it is represented as a four-spinor. This includes the possibility that the neutrino is a Weyl spinor, refuted, and that it is a Dirac or Majorana spinor, which is still undecided. This again depends on the dynamics. It is not excluded that subsequent development of this model may decide the problem in one way or another, at theoretical level</u>.</i></blockquote><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-16MqZua66eo/WKWnRwkNsSI/AAAAAAAAB_s/khpEAs6lf-U-D3VSroGWE8VNpb2K1vCQgCLcB/s1600/SMgeometricAlgebra.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://1.bp.blogspot.com/-16MqZua66eo/WKWnRwkNsSI/AAAAAAAAB_s/khpEAs6lf-U-D3VSroGWE8VNpb2K1vCQgCLcB/s1600/SMgeometricAlgebra.JPG" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="font-size: small;"><i> Discrete properties of leptons and quarks in the Standard Model Algebra.</i></span></td></tr></tbody></table><blockquote class="tr_bq"><div style="text-align: right;"><i><a href="https://arxiv.org/abs/1702.04336" target="_blank"><br />The Standard Model Algebra</a></i></div><div style="text-align: right;"><a href="https://arxiv.org/find/hep-th/1/au:+Stoica_O/0/1/0/all/0/1">Ovidiu Cristinel Stoica</a></div><div style="text-align: right;">(Submitted on 14 Feb 2017)</div></blockquote><b>Comment</b><br /><div style="text-align: justify;">I find this article interesting for several reasons. First it shows on one side the powerfulness of Clifford algebras, one particular mathematical facet of noncommutativity, to describe in a compact way the <i>discrete</i> parameters of the Standard model. But on the other side it exemplifies the limited scope of this geometric algebra perspective: if one wants to add gravity and its continuous parameters in a unified picture then another mathematical aspect of noncommutativity provides invaluable services thanks to a powerful analytical machinery namely spectral geometry as envisioned byConnes and his collaborator Chamseddine: </div><blockquote class="tr_bq" style="text-align: justify;"><i>... <u>the study of pure gravity for spectral geometries involving the algebra B=M<sub>n</sub>(C<sup>∞</sup>(M)) instead of the usual commutative algebra </u></i><i><u>C<sup>∞</sup>(M)</u></i><i><u> of smooth functions, yields Einstein gravity on M minimally coupled with Yang-Mills theory for the gauge group SU(n)</u>. The Yang-Mills gauge potential appears as the inner part of the metric, in the same way as the group of gauge transformations (for the gauge group SU(n)) appears as the group of inner diffeomorphisms. This simple example shows that <u>the noncommutative world incorporates the internal symmetries in a natural manner as a slight refinement of the algebraic rules on coordinates. There is a certain similarity between this refinement of the algebraic rules and what happens when one considers super-space in supersymmetry, but unlike in the latter case the algebraic rules are semi-simple rather than nilpotent. The effect is also somewhat similar to what happens in the Kaluza-Klein scenario since it is pure gravity on the new geometry that produces the mixture of gravity and gauge theory. But there is a fundamental difference since the construction does not alter the metric dimension and thus does not introduce the infinite number of new modes which automatically come up in the Kaluza-Klein model.</u> In this manner one stays much closer to the original input from physics and does not have to argue that the new modes are made invisible because they are very massive. </i></blockquote><blockquote class="tr_bq" style="text-align: right;"><a href="https://arxiv.org/abs/1008.0985">Space-Time from the spectral point of view</a><a href="https://arxiv.org/find/hep-th/1/au:+Chamseddine_A/0/1/0/all/0/1">Ali H. Chamseddine</a>, <a href="https://arxiv.org/find/hep-th/1/au:+Connes_A/0/1/0/all/0/1">Alain Connes</a>(Submitted on 5 Aug 2010)</blockquote><div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Of course my last remark doesn't intend to underestimate the scientific work of neither O. Stoica (of whom I follow the interesting blog) nor other geometric algebra practitioners. Nevertheless most physicists have not yet appropriated themselves Clifford algebras despite the fact that quantum physics seems to provide naturally (some of?) them. Probably they need more <a href="https://www.math.leidenuniv.nl/~gill/GA.pdf" target="_blank">experimental or conceptual incentives</a>. Moreover history has proved that it <a href="https://arxiv.org/abs/1109.0535" target="_blank">happened to be misused</a> in the past. Time will tell then if the first article highlighted in this post will help. </div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">As far as noncommutative geometry is concerned I think <a href="https://www.dropbox.com/s/gzrqzjvilvgwfk9/J-Kouneiher.pdf?dl=0" target="_blank"><i>the mathematical demonstration that the two very specific Clifford algebra required for a Pati-Salam gauge unification model are <span style="color: blue;">exactly the pair </span><span style="color: blue;">required in the Feynman slash of</span> the proper coordinates to recover with a generalized Dirac operator any 4 dimensional Riemannian manifold with a quantized volume</i> </a>is already a potential strong incentive for physicists!</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">I would like to conclude with the following text by Claude Daviau that summarizes in an exemplary way I think some real benefits and potential dangers of clifford algebras in physics:</div><blockquote class="tr_bq"><div style="text-align: justify;"><div style="text-align: justify;"><i>L'univers qui nous entoure est encore très largement à découvrir et la physique est loin d'avoir fini d'en faire le tour. Nous devons nous souvenir qu'à la fin du XIXème siècle certains physiciens pensaient que l'essentiel était déjà compris. Il n'y avait plus que quelques problèmes irritants, comme celui du corps noir. Mais de ces quelques difficultés qui restaient sont sorties des choses aussi importantes que la physique quantique et la relativité...</i><span style="text-align: left;"> </span></div></div></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><div style="text-align: justify;"><i>Entre la physique de 1860 et la physique de 2010, de nombreuses différences mineures cachent deux différences fondamentales. La première est en apparence purement physique, c'est l'existence de la constante de Planck. La seconde concerne aussi les mathématiques, c'est l'utilisation des nombres complexes. Ces deux différences sont liées: avant les quanta, les nombres complexes n'avaient pas pris pied en physique. Ils s'y sont introduits, à la marge, parce que l'exponentielle complexe permet d'écrire simplement la trigonométrie... <u>C'est Schrödinger qui, le premier, s'est aperçu... que l'onde {de l'électron} était à valeur complexe et non pas réelle. Pourquoi en est-il ainsi ? La réponse que l'on peut faire du point de vue mathématique, est simple : l'espace physique étant de dimension 3, son algèbre de Clifford contient des objets de carré -1. Encore faut-il alors justifier la nécessité physique de l'utilisation des algèbres de Clifford.</u></i><span style="text-align: left;"><u> </u></span></div></div></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><div style="text-align: justify;"><i><u>Cette nécessité physique vient de l'existence de particules de spin 1/2. Nous avons expliqué plus haut comment l'invariance relativiste, pour une particule de spin 1/2, nécessite l'utilisation de l'algèbre de Clifford d'espace, donc entraîne l'utilisation des nombres complexes</u>. <u>La découverte du spin de l'électron remonte à 1926, elle n'avait pas été prévue avant par la théorie physique. Longtemps la physique a sous-estimé les nouveautés que cela implique</u>...</i><span style="text-align: left;"> </span></div></div></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><div style="text-align: justify;"><i><u>La ... raison pour laquelle on n'a pas compris vraiment la nouveauté c'est la difficulté de l'outillage mathématique</u>. Tant que l'on utilise des opérateurs infinitésimaux, c'est à dire que l'on confond groupe de Lie et algèbre de Lie du groupe, on ne peut pas faire la différence entre les groupes d'invariance en jeu : les groupes sont globalement différents, mais localement identiques ! <u>Il faut être vraiment vigilant et pointilleux pour comprendre qu'il y a un problème entre l'axiomatique de la théorie quantique et l'équation de Dirac pour l'électron... </u></i></div></div></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><div style="text-align: justify;"><i><u>... on a tout interprété à partir des seules équations d'onde non relativistes</u>. C'était choquant pour Louis de Broglie, qui avait conçu l'idée de l'onde à partir de la cinématique relativiste... la théorie quantique axiomatisée postule pour le vecteur d'état qu'il doit suivre une équation de Schrödinger. <u>Comme c'est l'équation de Dirac...qui fonctionne pour l'atome d'hydrogène, la théorie axiomatisée n'est pas en droit de contraindre tout modèle à suivre ses règles</u>... </i><span style="text-align: left;"> </span></div></div></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><div style="text-align: justify;"><i>En remettant au coeur de la théorie physique les groupes d'invariance qui sont réellement nécessaires, on peut apercevoir que le groupe d'invariance de l'électromagnétisme est plus vaste que ce que l'on avait cru jusqu'ici. En conséquence les invariants sont moins nombreux, les contraintes sont plus grandes.</i><span style="text-align: left;"> </span></div></div></blockquote><blockquote class="tr_bq" style="text-align: justify;"><div style="text-align: right;"><div style="text-align: right;"><i><a href="https://ebook.nolim.fr/ebook/9782953913408/l-espace-temps-double-claude-daviau" target="_blank">L'espace-temps double</a></i></div></div><div style="text-align: right;"><div style="text-align: right;">Claude Daviau, </div></div><div style="text-align: right;"><div style="text-align: right;">Je publie 2011</div></div></blockquote><div style="text-align: justify;"><div style="text-align: justify;"><i><br /></i></div></div><div style="text-align: justify;"><div style="text-align: justify;">About this last author I must confess I am very respectful for his long march through Clifford algebras from the Dirac equation to his own <a href="http://file.scirp.org/pdf/JMP_2016083114210126.pdf" target="_blank">spinor wave equation for all objects of the first generation of fermions</a> (electron, neutrino, quarks u and d with three states of color each) which is form invariant under a greater group than the relativistic group. I am also intrigued by some of its consequences <span style="color: blue;">and I have heuristical inclination towards a research program to deepen the "complex" information stored in the wave function or rather density operator. I know of course </span><i><a href="https://transcyberphysix.blogspot.fr/2017/02/bohmian-mechanics-is-subtle-and.html" target="_blank">it is ... dangerous, to attribute any additional "real" meaning to them</a> </i>but I believe about<span style="color: blue;"> the possibility that some imaginary parameters [in quantum physics] possess a "hidden reality" endowed with the assumed power of exerting "gespenstische Fernwirkungen" (Einstein)</span>. <span style="color: blue;">And indeed</span> I can't follow <span style="color: blue;">Daviau</span> in his speculations about monopoles because I am utterly skeptical about the claimed experimental evidences they rely on.<br /><br /><span style="color: blue;">//last edit on February 22, 2017</span></div></div></div></div>Cédric Bardothttps://plus.google.com/104733107894701960711noreply@blogger.com0tag:blogger.com,1999:blog-3911792794793692366.post-75356765881222283612017-02-17T18:18:00.001+01:002017-02-17T18:58:00.820+01:00Deux quanta de géométrie vallent bien une maille de supersymétrie<div dir="ltr" style="text-align: left;" trbidi="on"><div style="text-align: justify;"><b>For physicists</b><br />As an addendum to the former post I recommend warmly to watch the very lively lecture of Ali Chamseddine below. It is about the quanta of geometry the Higgs boson has "brought" us thanks to the noncommutative spectroscope. Chamseddine deals also with the physical consequences and answers nicely the many questions from the physicist hearing even the ones about supersymmetry or string theory and he does it in his own prejudice-free or balanced way (see the next paragraph).<br /><br /><blockquote class="tr_bq" style="text-align: center;"><div style="text-align: right;"><div><br /></div></div></blockquote></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/J4N3TTt9h8A/0.jpg" frameborder="0" height="266" src="https://www.youtube.com/embed/J4N3TTt9h8A?feature=player_embedded" width="320"></iframe></div><div style="text-align: center;"><i>Quanta of geometry Lecture</i> by Ali Chamseddine <br />Future Prospects for Fundamental Particle Physics and Cosmology Workshop<br /> May 4 – 8, 2015<br /><br /><br /><div style="text-align: justify;"><b><br /></b></div><div style="text-align: justify;"><b>Just an anecdote</b></div><blockquote class="tr_bq" style="text-align: justify;"><i>In 1973 I got a scholarship from government of Lebanon to pursue my graduate studies at Imperial College, London. Shortly after I arrived, I was walking through the corridor of the theoretical physics group, I saw the name Abdus Salam on a door. At that time my information about research in theoretical physics was zero, and since Salam is an Arabic name, and the prime minister in Lebanon at that time was also called Salam, I knocked at his door and asked him whether he is Lebanese. He laughed and explained to me that he is from Pakistan. He then asked me why I wanted to study theoretical physics. I said the reason is that I love mathematics. He smiled and told me that I am in the wrong department. <u>In June 1974, having finished the Diploma exams I asked Salam to be my Ph.D. advisor and he immediately accepted and gave me two preprints to read and to chose one of them as my research topic. The first paper was with Strathdee [1] on the newly established field of supersymmetry (a word he coined), and the other is his paper with Pati [2] on the first Grand Unification model, now known as the Pati-Salam model. Few days later I came back and told Salam that I have chosen supersymmetry which I thought to be new and promising. Little I knew that the second project will come back to me forty years later from studying the geometric structure of space-time, as will be explained in what follows</u>. In this respect, Salam was blessed with amazing foresight.</i></blockquote><blockquote class="tr_bq"><div style="text-align: right;"><i><a href="https://arxiv.org/abs/1606.01189" target="_blank">Quanta of Geometry and Unification</a></i></div><div style="text-align: right;"><a href="https://arxiv.org/find/hep-th/1/au:+Chamseddine_A/0/1/0/all/0/1">Ali H. Chamseddine</a></div><div style="text-align: right;">(Submitted on 3 Jun 2016)</div></blockquote><br /></div></div>Cédric Bardothttps://plus.google.com/104733107894701960711noreply@blogger.com0tag:blogger.com,1999:blog-3911792794793692366.post-5417396176091527982017-02-17T00:13:00.002+01:002017-02-21T19:44:34.091+01:00Why we could be very happy that a Higgs boson has been discovered<div dir="ltr" style="text-align: left;" trbidi="on"><div class="tr_bq"><b>Possible insights from the 125 GeV Higgs boson in a spectral hypothesis perspective</b><br /><div style="text-align: justify;">After reading a <a href="http://www.math.columbia.edu/~woit/wordpress/?p=9110" target="_blank">recent post</a> by Peter Woit on his blog <i>Not Even Wrong</i>, I left there an accepted <a href="http://www.math.columbia.edu/~woit/wordpress/?p=9110#comments" target="_blank">comment</a> that retrospectively appears to me as a bold attempt to put across the exact opposite of the following views:</div><br /><blockquote class="tr_bq" style="text-align: justify;"><i>The only place left to look for a way out of this swamp [the variety of electroweak symmetry breaking theories], it seems to me, is in strongly interacting chiral gauge theories. Many talented theorists have thought about this.... There are surely wonders hidden in the subject of strongly interacting chiral gauge theories. If we are forced to deal with them to deal by physics at the SU(2)×U(1) breaking scale, we may find them. If instead a Higgs is discovered and the physics at the SU(2)×U(1) breaking scale can be described by perturbation theory, we probably never will. This would be the real source of my sadness if a Higgs were discovered. It would mean that nature had missed a chance to teach us some new and interesting field theory. Personally, I don’t think that she would be so malicious.</i></blockquote><blockquote class="tr_bq"><div style="text-align: right;"><a href="https://books.google.fr/books?id=Rg_tCgAAQBAJ&pg=PA383&lpg=PA383&dq=Why+I+would+be+very+sad+if+a+Higgs+boson+were+discovered&source=bl&ots=90DXhKYsLS&sig=gy3qgsYVJe0UNihl63IbiQwJNPY&hl=fr&sa=X&ved=0ahUKEwjhmfqGw5TSAhVFVhoKHQ4SBNMQ6AEIOzAF#v=onepage&q=Why%20I%20would%20be%20very%20sad%20if%20a%20Higgs%20boson%20were%20discovered&f=false"><i>Why I would be very sad if a Higgs boson were discovered.</i></a></div><div style="text-align: right;">Howard Georgi </div><div style="text-align: right;">Perspective on Higgs Physics II, ed. G.L. Kane. World Scientific, 1997.</div></blockquote></div><div class="tr_bq"><div style="text-align: right;"><br /></div><div style="text-align: justify;">I do not think either that nature is malicious but subtle, just like the Lord ... or quantum field theory. </div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Indeed as regular posts in this blog try to argue, nature or more specifically the 125 GeV Higgs boson has already not missed the opportunity to teach us - but in a barely audible voice - some new and interesting quanta of geometry that might provide insight about the ultra-high scale of seesaw mechanism and leptogenesis and hints to enlighten the <i>adelic </i><i>sectors</i><i style="text-align: justify;"><b><sup style="text-align: center;">*</sup></b></i><i> </i>of astrophysics and cosmology namely<i> </i>black holes, dark matter and dark energy (<i style="text-align: justify;"><b><sup style="text-align: center;">*</sup></b></i>this neologism, beyond a wink to the suffix used to create adjectives imparting a specific form of verve, is inspired by the greek adjective ἄδηλος which means literally "not self-evident" and figuratively "obscure").</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">I talk about "a barely audible voice" for two reasons. The first one is anecdotal and has to do with the fact that contemporary high energy physics papers reporting about noncommutative spectral developments derived from the 125 GeV Higgs boson are <a href="https://arxiv.org/abs/1303.7244" target="_blank">relevant</a> but rare while it appears to me that the spectral noncommutative geometrization of the Higgs could find a place in <i><a href="https://arxiv.org/abs/1609.04268" target="_blank">the theoretical physics ecosystem behind the discovery of the Higgs boson</a> </i>as it is<i> </i>nicely reviewed by James D. Wells (in an article from which I borrowed the above Georgi's quote). The second one is more substantial and refers to the fact that the insight physicists could gain from taking at face value the spectral noncommutative post-diction of the Higgs boson 125 GeV mass relies on the effectively very weak mixing (10<sup style="text-align: justify;">-9</sup>) between the electroweak higgs doublet and a computed <a href="https://arxiv.org/abs/1208.1030" target="_blank">ultra heavy higgs standard model</a> singlet <a href="https://arxiv.org/abs/1304.8050" target="_blank">responsible for the seesaw mechanism </a>and the spontaneous <a href="https://arxiv.org/abs/1507.08161" target="_blank">breaking of a Pati-Salam gauge group</a>.<br /><br />One can criticize my argument about a "spectral higgs brother hypothesis" (not to mention the <a href="https://arxiv.org/abs/1606.01189" target="_blank">quanta of geometry</a>) as immoderate speculation(s) of course. But with the hindsight from history<span style="text-align: left;"> J.D Wells writes : </span><br /><blockquote class="tr_bq"><i>... the Higgs boson hypothesis was an immoderate speculation, and therefore faith in theory argumentation and speculation was mandatory for the discovery program to proceed and reach its fulfillment. The Higgs boson could not have been discovered experimentally by accident. </i> </blockquote></div><div style="text-align: justify;"><br /><div style="text-align: justify;">Then I ask my reader : why do we not try to take advantage of a mathematically coherent formalism that provides effective computational tools to follow the breadcrumb trail from<span style="color: blue;"> the standard model higgs</span> <span style="color: blue;">at the</span> TeV <span style="color: blue;">scale</span> to <span style="color: blue;"><span style="background-color: white;">his big brother at</span> the</span> ZeV <span style="color: blue;">one </span><strike>or even YeV,</strike> investigate the possibility that<span style="text-align: left;"> </span><span style="text-align: left;">electroweak symmetry breaking is related to gravity through an almost commutative extension of spacetime and is triggered somehow by noncommutative fluctuations that impart a proper dynamics to geometry with consequences as mimetic dark matter, dark energy and a limiting spacetime curvature? </span><br /><br />Nature is not malicious but the human Hi(gg)story of the understanding of the electroweak symmetry breaking definitely proves to be devilish.</div><div style="text-align: justify;"><br /><span style="color: blue;">At least it was for spectral noncommutative geometers of whom it is worth reminding here the basic paradigm:</span><br /><blockquote class="tr_bq"><u style="text-align: left;"><i><span style="color: blue;">We thus view a given geometry as an irreducible representation of the algebraic relations between the coordinates and the line element, while the choice of such representations breaks the natural invariance group of the theory. The simplest instance of this view of geometry as a symmetry breaking phenomenon is what happens in the Higgs sector of the standard model.</span></i></u></blockquote><blockquote class="tr_bq"><div style="text-align: right;"><span style="color: blue;"><i><a href="http://www.alainconnes.org/docs/gelfand.pdf" target="_blank">ON THE FOUNDATION OF NONCOMMUTATIVE GEOMETRY</a></i> </span></div><div style="text-align: right;"><span style="color: blue;">Alain Connes </span></div></blockquote><span style="color: blue;"><br /></span><span style="color: blue;">These new geometers of physics have failed first to predict the correct mass of the standard model Higgs boson. But they learned from its very value and works it triggered among physicists worried about the stability of the Higgs potential at ultra heavy scales how to remove an incorrect assumption they made. To improve then the coherence of their framework they have subsequently understood how to give up an axiom of noncommutative geometry and uncovered new inner fluctuations of geometry that impact the structure of the Higgs fields and make them composite somehow. As a consequence they could postdict - following a more constrained theory - the correct SM Higgs boson mass, predicting a mixing with another scalar field responsible for the spontaneous symmetry breaking of a Pati-Salam gauge symmetry as I have already reported above. Last but not least, this new impetus has lead them to write an elaborate Heisenberg-like equation and they have established <i>the mathematical demonstration that the two very specific Clifford algebra required for a Pati-Salam gauge unification model in the spectral point of view are </i></span><i><span style="color: red;">exactly the pair required in the Feynman slash of</span><span style="color: blue;"> </span></i><i style="color: blue;">the proper coordinates to recover with a generalized Dirac operator any 4 dimensional Riemannian manifold with a quantized volume</i><span style="color: blue;">! </span><span style="color: red;">(19/02/2017 update: A. Connes has made available yesterday <a href="https://www.dropbox.com/s/gzrqzjvilvgwfk9/J-Kouneiher.pdf?dl=0" target="_blank">a new paper</a> in English that covers specifically this point that is the core of the first six hours of last lecture at the Collège to reach an audience as broad as possible).</span><br /><br /><span style="color: blue;">So to conclude let me come back to Howard Georgi and be bold once again to write him the following message:</span><br /><blockquote class="tr_bq"><span style="color: blue;">Dear Sir, </span></blockquote><blockquote class="tr_bq"><span style="color: blue;"><span style="color: blue;">I hope</span><span style="color: blue;"> you have welcomed too the discovery of the 125 GeV Higgs boson in 2012 even if you had some doubts or prejudices against its existence. I cannot say if the wonders lying in strongly interacting chiral gauge theories are realy hidden by this scalar boson but </span></span><span style="color: red;">I notice you have not lost the expectation <a href="https://arxiv.org/abs/1607.00369" target="_blank">to connect the Higgs phase and the confining phase</a>. </span> </blockquote><blockquote class="tr_bq"><span style="color: blue;"><span style="color: blue;">I wonder what would be your take on the possible spectral noncommutative world </span></span><span style="color: blue;">hidden </span><span style="color: blue;"><span style="color: blue;">behind the </span><span style="color: red;">specific</span><span style="color: blue;"> electroweak symmetry breaking nature has chosen for us</span><i><span style="color: blue;">.</span><span style="color: red;"> </span></i></span><span style="color: red;">Insofar as this new geometric paradigm suggests an extension of space where the program of unification of </span><span style="color: red;">the standard model gauge </span><span style="color: red;">interactions that you initiated with a few others is the natural result of a subtle dynamic extending that of gravity, I do not doubt that you would be interested to learn how discrete extra dimensions or rather some </span><span style="color: red;"><a href="http://www.alainconnes.org/docs/shahnlong.pdf" target="_blank">fine structure of spacetime</a> could be more than a metaphor thanks to the Higgs boson discovery.</span></blockquote><blockquote class="tr_bq"><span style="color: blue;">Yours respectfully.</span></blockquote><div style="text-align: center;"><br /></div></div><div style="text-align: justify;">This post is dedicated to a spectral heroine <span style="color: red;">researcher</span> : Charlotte Dempière <span style="color: red;">and a fantasized student of her dreaming</span><span style="color: blue;"> </span><span style="color: red;"><span style="color: blue;">of a <strike>subtle</strike> </span><span style="color: blue;">loose </span><span style="color: blue;">way to connect <a href="https://arxiv.org/pdf/hep-ph/0703260.pdf" target="_blank">unparticle physics</a>, <a href="https://arxiv.org/abs/1605.07458" target="_blank">scale invariance at low accelerations</a> </span><span style="color: blue;">and <a href="https://arxiv.org/pdf/1612.08661.pdf" target="_blank">mimetic matter</a> </span><span style="color: blue;">in a new quantum world.</span></span><br /><br /><span style="color: red;">// Last edit 18 february 2017</span></div></div></div></div>Cédric Bardothttps://plus.google.com/104733107894701960711noreply@blogger.com0tag:blogger.com,1999:blog-3911792794793692366.post-51807979355598854752017-02-15T13:47:00.003+01:002017-02-15T15:23:11.848+01:00Thank you Alain Connes<div dir="ltr" style="text-align: left;" trbidi="on"><div style="text-align: justify;">Today, I take the opportunity that the <a href="https://www.college-de-france.fr/site/alain-connes/course-2017-02-09-15h45.htm" target="_blank">last session</a> of A. Connes' lectures at Collège de France is available online to greet him with the following special post, full of enthusiasm and devoid of any boasting I hope even if probably pompous I confess:</div><br /><blockquote class="tr_bq">Dear Professor,</blockquote><div style="text-align: justify;"><blockquote class="tr_bq">I thank you very much to have accepted your 2017 lectures at Collège de France be broadcasted.<br />I was pleased you spent some time to discuss in French your operator algebraic Heisenberg-like equation dealing with quantization of volume of manifolds and its particular solution in four dimensions that proves the geometric origin of the symmetries of the noncommutative spectral model of particle physics. </blockquote><blockquote class="tr_bq">Allow me to express now my deep gratitude for your fight to distill significant insights <i>from an inflexible Nature, who says so distinctly "No" and so indistinctly "Yes" to our theories*. </i> </blockquote><blockquote class="tr_bq"><i></i>I wish you the best in the continuation of the noncommutative geometric program in both its mathematical and physics aspects.<br />As a physicist I hope a time comes soon when some of your collaborator or another brilliant visionary may understand how <a href="https://quantumostinato.blogspot.fr/2015/07/a-tale-of-two-tt-oms-new-hypotheses.html" target="_blank">attoms</a> of spacetime are as easy to observe today as are atoms of matter. </blockquote><blockquote class="tr_bq">In your last lectures, prof. Connes, you quote Riemann, Einstein and Grothendieck : great figures from the distant or closer past; I am looking forward to hearing from you discussing one day how your work has taken up (supersedes?) some of the <a href="https://quantumostinato.blogspot.fr/2015/11/celebrating-100th-anniversary-of.html" target="_blank">challenges</a> described by the contemporary Freeman Dyson in his text <i><a href="http://www.ams.org/journals/bull/1972-78-05/S0002-9904-1972-12971-9/S0002-9904-1972-12971-9.pdf" target="_blank">Missed Opportunities</a></i>. </blockquote><blockquote class="tr_bq">I have the honor to be, Sir, yours faithfully.</blockquote></div><div style="text-align: right;"><blockquote class="tr_bq">Cédric Bardot</blockquote></div><div><br /></div><div><br />* Note : quote from the introduction to <i><a href="http://ftp.yazd.ac.ir/FTP/E-Book/Chemistry/Physical%20Chemistry/theory%20of%20groups%20&%20quantum%20mechanics,%202nd%20ed%20(1930)%20%5Bweyl%5D.pdf" target="_blank">The theory of groups</a> </i>by Hermann Weyl<br /><br /></div></div>Cédric Bardothttps://plus.google.com/104733107894701960711noreply@blogger.com0tag:blogger.com,1999:blog-3911792794793692366.post-83570151573730984862017-01-21T18:32:00.000+01:002017-03-16T22:52:16.251+01:00S'il vous plaît M. 't Hooft... chante nous un cℏoeur quantique d'espace-temps<div dir="ltr" style="text-align: left;" trbidi="on"><b>(Dreaming of) A portrait of a black hole horizon (as a quantum cℏoir of spacetime)...</b><br />... reading 't Hooft last preprint on his proposed new constraints on the topology and the boundary conditions of general coordinate transformations to solve both the firewall and information problems in black hole physics :<br /><blockquote class="tr_bq"><div style="text-align: justify;"><i>In this paper, we shall primarily make use of a partial answer that we claim to have arrived at recently [10]: <u>the necessity of revising the boundary conditions for Nature’s degrees of freedom at the horizon of a black hole.</u> Since our analysis started out with our desire for consistent descriptions of stationary (or approximately stationary) black holes, it was not immediately clear how the revised boundary conditions should have been enforced during the formation of a black hole, but, <u>in a somewhat formal fashion, one may well argue that, during black hole formation, the horizon starts out stretching over an infinitesimally tiny region; it opens up at a single point </u>[Upon close inspection, one might conclude that the horizon first forms on a fractal subspace of spacetime, but since the scale at which this fractal extends may end up to be small even in Planck units, we ignore this complication in this paper.] <u>in space and time. At that single point, it now appears to be necessary to revise the structure of this infinitesimal horizon to obey the new boundary condition</u>, but since all this should happen at Planckian dimensions, the revision needed in our laws of Nature here can easily be argued to have escaped our notice up to today. </i></div><div style="text-align: justify;"><i><br /></i></div><div style="text-align: justify;"><i><u style="text-decoration: underline;">After the horizon opens up, a black hole can grow quite big; the black hole horizon area grows rapidly towards macroscopic sizes during collapse, and as our modified boundary condition keeps track, it turns space and time into a non-trivial topological manifold</u><u>. As our new boundary condition must end up as being indestructible, its implications will be sizeable. We emphasise that, nevertheless, our modified boundary condition will not affect the visible properties of a black hole in the classical limit.</u> Also, we shall ensure that the modified boundary condition is of a kind that is not directly observable for a local observer. </i></div><u></u><br /><div style="text-align: justify;"><i>The boundary condition that we shall arrive at is characterised as an antipodal identification. In short, what it means is that <u style="text-decoration: underline;">the region of space-time inside the horizon is removed completely, as if by surgery, after which the edges are glued together by identifying the antipodes</u><u>. This is continued throughout the lifetime of the black hole [Do keep in mind that, strictly speaking, the horizon is entirely timeless.] It is important, subsequently to insist that, locally, space and time remain smooth across the seams, while particles, including the information they carry, can cross. The seams must be locally invisible—only global observers notice this boundary condition. We argue that the antipodal mapping is the only way to attach the edges together such that strict geometrical conditions are obeyed. </u></i></div><u></u><br /><div style="text-align: justify;"><i><br /></i></div><div style="text-align: justify;"><i><u>It boils down to a single “new physics” ingredient in black hole physics as soon as quantum effects are being considered</u>: </i></div></blockquote><blockquote class="tr_bq" style="text-align: justify;"><ul><li><i>from now on, when quantised particles and fields are considered, only those general coordinate transformations are permitted that map space and time continuously, and they must be one-to-one,</i></li></ul></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><i>a condition not obeyed by the standard, classical Schwarzschild metric: every space-time point in the physically observable part of the universe is mapped onto two points in the Kruskal-Szekeres coordinates. </i></div><div style="text-align: justify;"><i><br /></i></div><div style="text-align: justify;"><i>As will be demonstrated (subsection 3.1), <u>mapping the Schwarzschild metric onto the space-time metric of a local observer forces us to glue together regions in such a way that time-inversion takes place. Inverting the time direction is associated with an interchange of creation operators and annihilation operators. This implies that a region almost devoid of particles for one observer, is mapped onto a region almost filled with particles for the other observer. At first sight, this seems to be an unfamiliar and unwanted complication, but it is unavoidable</u>...</i></div><div style="text-align: justify;"><i><br /></i></div><div style="text-align: justify;"><i>At first sight,<u> it may seem that our way of handling space and time near a black hole, will make a decent quantum field theoretic description of the elementary particles in there, hopelessly inadequate but the contrary is true.</u> </i><i style="background-color: rgba(255 , 255 , 255 , 0); font-family: "helvetica neue light" , , "helvetica" , "arial" , sans-serif;">[... <u>in earlier reports, the author had expressed his opinion that the causal order of events has to be respected by the coordinate transformations used; we now found compelling reasons to abandon that demand</u>]. </i><i style="font-family: 'Helvetica Neue Light', HelveticaNeue-Light, helvetica, arial, sans-serif;"><u>The apparently drastic rearrangement of the space-time continuum is exactly what is needed to arrive at pure quantum states for the black hole, and to obtain a unitary scattering matrix, so as to eradicate both the black hole information problem and the firewall problem, while accurately respecting the laws of general relativity.</u></i></div><div style="text-align: justify;"><i><br /></i></div><div style="text-align: justify;"><i>There is a number of points that we should keep in mind. One is that wild guesses concerning possible answers, such as ‘novel uncertainty relations’, will be almost fruitless, as history shows*. The best thing to do is to split our problems into small pieces, and try to address each of these small fragments of questions in turn. Every now and then, such fragmented questions will lead to surprises. It helps enormously if we can convince ourselves of the correctness of our partial answers, and it is these that we should be able to use as new starting points for our next steps. </i> </div></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><i>On the other hand, <u>we do not claim that all mysteries are resolved now. A systematic procedure must be found for a one-to-one mapping of the states generated by the spherical waves of momentum distributions and positions, onto states of the Fock space of a quantum field theory </u>(some grand unified version of the standard model, relevant in the vicinity of the Planck scale, simply referred to as “standard model” elsewhere in this paper). It is here that the machinery of string theory might be of much help.</i> </div></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><i><u>Another point where our theory becomes vague is where the Planckian dimensions are reached</u>. Usually it is assumed that string theory will provide all the answers, but string theory did not tell us about gravitational back reaction or antipodal identification, so we respectfully conclude that string theory is not fool-proof. </i></div></blockquote><div style="text-align: justify;"><blockquote class="tr_bq" style="text-align: left;"><div style="text-align: right;"><a href="https://arxiv.org/abs/1612.08640"><i>The firewall transformation for black holes and some of its implications</i></a></div><div style="text-align: right;"><a href="https://arxiv.org/find/gr-qc/1/au:+Hooft_G/0/1/0/all/0/1"></a><a href="https://arxiv.org/find/gr-qc/1/au:+Hooft_G/0/1/0/all/0/1">Gerard 't Hooft</a> (Submitted on 27 Dec 2016) </div></blockquote></div><div style="text-align: justify;"><i><br /></i></div><div style="text-align: justify;"><i>* </i>Personal comment or wishful(l) thinking : more <a href="https://arxiv.org/abs/1411.0977" target="_blank">recent history</a> might prove this 't Hooft statement is not exactly right...</div><div style="text-align: justify;"><br /></div><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-y3b-LmqK6wg/WIONBEQ-9_I/AAAAAAAAB-U/Qgb93V_bI48H6dastZPIXQQYZ43lzeywQCLcB/s1600/BlackHolesChandraDeepField.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://2.bp.blogspot.com/-y3b-LmqK6wg/WIONBEQ-9_I/AAAAAAAAB-U/Qgb93V_bI48H6dastZPIXQQYZ43lzeywQCLcB/s1600/BlackHolesChandraDeepField.jpg" /></a></td></tr><tr><td class="tr-caption">Credit: X-ray: NASA/CXC/Penn State/B.Luo et al.<br /><a href="http://chandra.harvard.edu/photo/2017/cdfs/" style="background-color: white; color: #73767b; font-family: sans-serif; font-size: 10px; text-decoration: none;">Press Image and Caption</a></td></tr></tbody></table><div><blockquote class="tr_bq"><div style="text-align: justify;"><i><span style="text-align: center;">This is the deepest X-ray image ever obtained... collected in eleven and a half weeks, of Chandra spatial telescope observing time. The image comes from what is known as the Chandra Deep Field-South. The central region of the image contains the highest concentration of supermassive black holes ever seen, equivalent to about 5,000 objects that would fit into the area on the sky covered by the full Moon and about a billion over the entire sky...</span></i></div><i></i><br /><div style="text-align: justify;"><i><i><span style="text-align: center;">About 70% of the objects in the ... image are supermassive black holes, which may range in mass from about 100,000 to ten billion times the mass of the Sun. Gas falling towards these black holes becomes much hotter as it approaches the event horizon, or point of no return, producing bright X-ray emission.</span></i></i></div><i></i></blockquote><blockquote class="tr_bq"><div style="text-align: right;"><i><a href="http://chandra.harvard.edu/press/17_releases/press_010517cdfs.html" target="_blank">Deepest X-ray Image Ever Reveals Black Hole Treasure Trove</a></i></div><div style="text-align: right;">For Release: January 5, 2017</div></blockquote><br />This post is dedicated to a hiker friend, Emmanuel ;-)<br /><div style="text-align: right;"><span style="font-size: 12.8px;"><br /></span></div></div></div>Cédric Bardothttps://plus.google.com/104733107894701960711noreply@blogger.com1tag:blogger.com,1999:blog-3911792794793692366.post-32713489032308666792017-01-17T16:40:00.003+01:002017-01-17T16:48:22.632+01:00Physics has one quantum (or rather two quanta?) to pick with mathematics / Les mathématiques ont maille à partir avec la physique quantique (ou plutôt deux quanta à partager?)<div dir="ltr" style="text-align: left;" trbidi="on"><div class="separator" style="clear: both; text-align: justify;">The videos of the second Alain Connes' lecture at <i>Collège de France</i> for 2017 (entitled "La géométrie et le quantique") that took place last week are available now (<a href="https://www.college-de-france.fr/site/alain-connes/course-2017-01-12-14h30.htm" target="_blank">same site</a> as last ones mentioned in the former post).</div><div class="separator" style="clear: both; text-align: justify;">Some slides to illustrate the title of this post:</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-zTbqIJgjB1s/WH4ru_uLdMI/AAAAAAAAB90/0pvA_b0_QbQMBvEVMdzwXaV0HIiMqkWWwCLcB/s1600/GNC2a.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-zTbqIJgjB1s/WH4ru_uLdMI/AAAAAAAAB90/0pvA_b0_QbQMBvEVMdzwXaV0HIiMqkWWwCLcB/s1600/GNC2a.JPG" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-YPl6GN4C7CI/WH4ruzCXekI/AAAAAAAAB94/jmarlbtxOO0f422ZkJ8RZI1WUB3PLp-QACLcB/s1600/GNC2c.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-YPl6GN4C7CI/WH4ruzCXekI/AAAAAAAAB94/jmarlbtxOO0f422ZkJ8RZI1WUB3PLp-QACLcB/s1600/GNC2c.JPG" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-lgzIO6grPik/WH4ruxv3tmI/AAAAAAAAB9w/yuoGNcjeFJ48mosV1vCgz3Rkkyu6mZlNACLcB/s1600/GNC2b.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-lgzIO6grPik/WH4ruxv3tmI/AAAAAAAAB9w/yuoGNcjeFJ48mosV1vCgz3Rkkyu6mZlNACLcB/s1600/GNC2b.JPG" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-VzVpMF65bu8/WH4rvPRKobI/AAAAAAAAB98/UjggWeZvr8MeaDxDlsUtFR-ILROY55TNgCLcB/s1600/GNC2d.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-VzVpMF65bu8/WH4rvPRKobI/AAAAAAAAB98/UjggWeZvr8MeaDxDlsUtFR-ILROY55TNgCLcB/s1600/GNC2d.JPG" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><i><a href="https://www.college-de-france.fr/site/alain-connes/course-2017-01-12-14h30.htm" target="_blank">Source</a></i></div><br /><div style="text-align: justify;">As a teaser to the third lecture (on next Thursday 19 January) let's note that in the last six minutes of the second lecture (video "12 janvier 15h45-17h") Connes provides his general philosophy to address "quantum gravity" problems with functional integral calculation on 4D Euclidean geometries with 3D+1 Minkowski space-time "boundaries" (<a href="https://arxiv.org/abs/1008.3980" target="_blank">fitting with Hawking and Gibbons results</a>)...</div><br /></div>Cédric Bardothttps://plus.google.com/104733107894701960711noreply@blogger.com0tag:blogger.com,1999:blog-3911792794793692366.post-15336047013047842902017-01-12T10:56:00.003+01:002017-06-10T16:01:33.466+02:00A quantum leap beyond classical Riemannian geometry brought up in the realm of experimental physics <div dir="ltr" style="text-align: left;" trbidi="on"><div style="text-align: justify;">If I <a href="http://www.noncommutativegeometry.nl/last-lecture-series-alain-connes-cdf/" target="_blank">understand correctly</a>, it seems for the first time Alain Connes accepted his 2017 (possibly last?) lectures at College de France be filmed. I remember a few years ago he explained to his audience he was reluctant to accept a broadcasting of these particular lectures because he was afraid it could impart his freedom to think aloud. </div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">It is a great opportunity to all ingenious undergraduate seniors at a university anywhere in the world (see former post) and the luckiest students in Paris area to engage in a fascinating but challenging* conceptual trip (*these Connes lectures are in French ;-) </div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">The first "episode" (two videos) is available <a href="https://www.college-de-france.fr/site/alain-connes/course-2017-01-05-14h30.htm" target="_blank">here</a>. </div><div style="text-align: justify;">The second one is today (I don't know but I wish it will broadcasted too!)</div><div style="text-align: justify;"><br /></div><div style="text-align: justify;">Here are a few slides from the first videos as an <i><a href="http://web.mit.edu/mlcar/www/personal/performances/translations/invitation.html" target="_blank">invitation to a journey</a></i> with a mathematician who unfolded spacetime from X-rays to Higgs.</div><div style="text-align: justify;">Voici quelques captures d'écran du premier cours en guise d'<i><a href="http://web.mit.edu/mlcar/www/personal/performances/translations/invitation.html" target="_blank">invitation au voyage</a> </i>avec un mathématicien qui a déplié l'espacetemps des rayons X au boson de Higgs.</div><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-DTGMgOLiol4/WHdH0EP_V6I/AAAAAAAAB8M/E62RbeAyBWEq3jVK98a7atx_V4BxHeFeQCLcB/s1600/GNC2017h.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://3.bp.blogspot.com/-DTGMgOLiol4/WHdH0EP_V6I/AAAAAAAAB8M/E62RbeAyBWEq3jVK98a7atx_V4BxHeFeQCLcB/s1600/GNC2017h.JPG" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><span style="color: #999999;">(addendum 10 June 2017: this quote is from Newton's <i><a href="https://en.wikipedia.org/wiki/The_Queries" target="_blank">Queries</a></i> (<a href="https://classesv2.yale.edu/wiki/site/chem124_f08/newton%27s_query_31.html" target="_blank">#31</a>) </span></div><div class="separator" style="clear: both; text-align: center;"><span style="text-align: left;"><br /></span></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-0g-qgkMsiko/WHdL3AooE8I/AAAAAAAAB8Y/RE2Q_OhVvhcofAE3IN5we4_t-8qEjJ_9wCLcB/s1600/GNC2017c.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-0g-qgkMsiko/WHdL3AooE8I/AAAAAAAAB8Y/RE2Q_OhVvhcofAE3IN5we4_t-8qEjJ_9wCLcB/s1600/GNC2017c.JPG" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-j_lDN_hqvzo/WHdL81uMGzI/AAAAAAAAB8c/MptUHmvIx20RtTmfleUe5DAeL1x5xj5HACLcB/s1600/GNC2017d.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-j_lDN_hqvzo/WHdL81uMGzI/AAAAAAAAB8c/MptUHmvIx20RtTmfleUe5DAeL1x5xj5HACLcB/s1600/GNC2017d.JPG" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-sS_gOep1bnU/WHdMJ2RQdaI/AAAAAAAAB8g/vovpikb39ssRP-Xp34WBNWJd4qzA1bDTQCLcB/s1600/GNC2017j.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-sS_gOep1bnU/WHdMJ2RQdaI/AAAAAAAAB8g/vovpikb39ssRP-Xp34WBNWJd4qzA1bDTQCLcB/s1600/GNC2017j.JPG" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-VfD9Fk2BHjw/WHdSosD9k-I/AAAAAAAAB80/5xmKDJBXI1k9FsPql1Wg2-DeB6PfrsyBwCLcB/s1600/GNC2017k.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-VfD9Fk2BHjw/WHdSosD9k-I/AAAAAAAAB80/5xmKDJBXI1k9FsPql1Wg2-DeB6PfrsyBwCLcB/s1600/GNC2017k.JPG" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-nFdAXtRuY2c/WHdSswjeqfI/AAAAAAAAB84/mWFD_zZ3_tYZhpnJtBSX7IDCohKiVoCQQCLcB/s1600/GNC2017l.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-nFdAXtRuY2c/WHdSswjeqfI/AAAAAAAAB84/mWFD_zZ3_tYZhpnJtBSX7IDCohKiVoCQQCLcB/s1600/GNC2017l.JPG" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><br /></div>Cédric Bardothttps://plus.google.com/104733107894701960711noreply@blogger.com0tag:blogger.com,1999:blog-3911792794793692366.post-24320030277759469152017-01-12T10:01:00.001+01:002017-01-21T18:02:07.554+01:00From electroweak energy scale to the top and down back (2017 Challenge for youngsters and others)<div dir="ltr" style="text-align: left;" trbidi="on"><span style="clip: rect(3.2em, 1000.72em, 4.09em, -1000em); left: 0em; position: absolute; top: -3.99em;"><span class="mi" id="MathJax-Span-4" style="font-family: MathJax_Math-Web; font-style: italic;">Z</span> </span><span style="left: 0.78em; position: absolute; top: -4.35em;"><span class="mo" id="MathJax-Span-5" style="font-family: MathJax_Main-Web; font-size: 70.7%;"><span style="font-size: small;">′</span></span> </span><br /><span style="left: 0.78em; position: absolute; top: -4.35em;"> </span>Reader information: if you are looking for exotica you are on the quite wrong blog, keep up with "M. Trump goes to Washington, D.C." and his twitter feed instead ;-)<br /><div align="LEFT"><br /><br /><b>A reasonably simple informative 2016 paper </b><b>(not cited yet*) </b><b>on high energy physics...</b><br /><div style="text-align: justify;">...for the education of my best gifted high school student *with a node to a recent <a href="http://motls.blogspot.fr/2017/01/disappointing-composition-of-top-cited.html" target="_blank">post of another gifted but former high school student</a>, Lubos Motl, who complained about the <a href="http://motls.blogspot.com/2017/01/disappointing-composition-of-top-cited.html">disappointing composition of top-cited 2016 HEP papers</a>.</div><div style="text-align: justify;"><br /></div></div><blockquote class="tr_bq" style="text-align: justify;"><i><u>An extra U(1)' gauge symmetry is a common presence in many attempts to go beyond the Standard Model (SM). It represents, from a low-energy perspective, the simplest extension that can be attached to the SM gauge group, at the same time, from the opposite high-energy point of view, an extra abelian factor is almost an unavoidable leftover from the breaking of many GUT scenarios</u> [1].</i> </blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><u>If we adopt a (grand) unification paradigm, it is therefore feasible that a regime ruled by the gauge structure </u></i><i style="text-align: left;">SU(3)<span style="text-align: justify;"><span style="text-align: left;"><sub>C</sub></span></span></i><span style="font-size: x-small; text-align: left;">⊗</span><i style="text-align: left;">SU(2)<span style="text-align: justify;"><span style="text-align: left;"><sub>L</sub></span></span></i><span style="font-size: x-small; text-align: left;">⊗</span><i style="text-align: left;">U(1)<span style="text-align: justify;"><span style="text-align: left;"><sub>Y</sub></span></span></i><span style="font-size: x-small; text-align: left;">⊗</span><i style="text-align: left;">U(1)<span style="font-size: 13.3333px;">'</span></i><i><u> could populate the sequence of effective descriptions scaling from the GUT energy, before breaking into the SM one. The last step may be triggered by the nontrivial vacuum expectation of a scalar field χ, that is, consequently, required to be SM-singlet. If such U(1)' breaking is realised at the TeV scale, then there are realistic prospects of an interesting interplay with the current LHC probe</u>, the precise traits of such phenomenological characterisation being dictated by the extended matter content ([2–6]). <u>Beyond the scalar sector, where a SM-singlet accounts for the extra U(1)' breaking, and the neutral vector Z' , to accomplish gauge invariance, one extra fermion per generation is needed to cancel gauge and gravitational anomalies in a minimal way</u>. This scenario has been the subject of a recent up-to-date investigation [7] where we exploited the bounds and the discovery potential of current and forthcoming collider searches. <u>The more promising regions of the allowed parameter space have supplied the boundary conditions for a Next-to-Leading-Order (NLO) vacuum stability analysis, that we performed extrapolating the model to higher energies with two-loop β functions. As a result, the explored regions have been labeled with the maximal energy scale up to which they would provide a coherent (stable and perturbative) extrapolation of the model</u>.</i> </blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>The role of the Renormalisation Group (RG) extrapolation does not exhaust its insight power with the stability analysis. As we will illustrate, <u>for the particular case of our minimal SM⊗U(1)' regime, the RG may draw clear indications also about the high-energy regime that is expected to take place. In a combined effort, all the phenomenological and formal aspects of this analysis will contribute to unveil a consistent link between the low-energy model characterisation, and a stable, perturbative, ultraviolet (UV) completion</u>...</i> </blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><u>The class of models encompassed in [<a href="http://arxiv.org/abs/1605.02910" target="_blank">7</a>] adds, to the SM field content, a massive neutral gauge boson plus a scalar and three extra fermions</u>, all transforming trivially under the SM gauge group. This extended spectrum is naturally introduced to minimally account for gauge invariance, anomaly freedom and the requirement of a massive Z' . <u>We notice, as a valuable consequence of the previous setting, that the presence of a new abelian factor has forced the introduction of states that complete the 16-dimensional representation of SO(10) which is a further motivation to explore the possible UV fate of such model. Anomaly cancellation also rules the possible U(1)’ charges, leaving to the ratio of just two parameters the definition of the allowed charge assignments</u>. In a low-energy investigation the common choice is to highlight the Hypercharge operator Y, so that the generator of the extra U(1)' is constrained to the form Y' = (B − L) + (<span style="text-align: left; text-decoration: overline;">g</span>/g'1)Y, where B and L are, respectively, the Baryon and the Lepton number of the fields. The overall gauge strength g'1 and the mixing g rule, therefore, the content of the B − L and the Hypercharge operators in Y'. <u>The renormalisable interactions that arise from the extended field content can promptly realise a Type I seesaw mechanism to account for neutrino masses.</u></i></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i>... <u>the past investigations of the Z' have been strongly affected by bounds coming from EW Precision Tests (EWPTs) from LEP2. The first Run of LHC at 8 TeV and L = 20 fb−1 has generated even more stringent bounds at the TeV scale</u>. These can be extracted using a signal-to-background analysis for the Drell-Yan channel... Also the extended scalar sector creates numerous chances to reveal and characterise the class of models under study. We have limited the related new parameter space, that we parameterised with the new scalar mass m</i><i style="text-align: center;"><span style="text-align: justify;"><sub style="text-align: justify;">H2</sub></span></i><i> and the mixing angle α, considering the bounds from the direct detection probes, and comparing the signal produced with the one measured of the discovered Higgs at 125.09 GeV...</i></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><i><u>The presence of multiple abelian factors is a peculiar trait of this class of models. The induced kinetic mixing, absorbed in the contribution of the coupling g to the covariant derivative </u></i></div><div style="text-align: center;"><i>D<span style="text-align: justify;"><sub style="text-align: justify;">µ</sub></span> = ∂<span style="text-align: justify;"><sub style="text-align: justify;">µ</sub></span> + ig<span style="text-align: justify;"><sub style="text-align: justify;">1</sub></span>YB<span style="text-align: justify;"><sub style="text-align: justify;">µ</sub></span> + i(<span style="text-decoration: overline;">g</span>Y + g'<span style="text-align: justify;"><sub style="text-align: justify;">1</sub></span> Y<span style="text-align: justify;"><sub style="text-align: justify;">B-L</sub></span>)B'<span style="text-align: justify;"><sub style="text-align: justify;">µ</sub></span> + . . . , (3) </i></div><div style="text-align: justify;"><i><u>may shed light, supported by a precise RG inspection, on the UV embedding that precedes the U(1)’ regime</u> [10–12].</i></div></blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><u>The key for this analysis is in the matching of the low and the high-energy generators basis, used to describe the abelian sector</u>. In our phenomenological survey, adherence with the SM regime suggested the use of the Hypercharge for one of the two U(1). In turn, within the constraints of anomaly cancellation, we chose B-L for the other. The mixing would then provide the component of the Y 0 generator in the Hypercharge direction. From a high-energy perspective is more appropriate to work with the basis that is naturally provided by the embedding of the abelian factors in the unifying group. For example, a Left-Right (LR) symmetric regime SU(2)<span style="text-align: justify;"><span style="text-align: left;"><sub>R</sub></span></span><span style="font-size: x-small;">⊗</span>U(1)<span style="text-align: justify;"><span style="text-align: left;"><sub>B-L</sub></span></span>, which includes U(1)<span style="text-align: justify;"><span style="text-align: left;"><sub>R</sub></span></span><span style="font-size: x-small;">⊗</span>U(1)<span style="text-align: justify;"><span style="text-align: left;"><sub>B-L</sub></span></span>, would select the corresponding YR and Y<span style="text-align: justify;"><sub style="text-align: justify;">B-L</sub></span> set of generators. Close to the energy scale of the LeftRight symmetry breaking, the mixing between the Y<span style="text-align: justify;"><sub style="text-align: justify;">R</sub></span> and Y<span style="text-align: justify;"><sub style="text-align: justify;">B-L</sub></span> is zero, being protected by the overall non-abelian gauge symmetry of SU(2)R. It is possible, with the appropriate normalisation, to match our SM-oriented parameters (g<span style="text-align: justify;"><sub style="text-align: justify;">1</sub></span>, g'<span style="text-align: justify;"><sub style="text-align: justify;">1</sub></span>, <span style="text-decoration: overline;">g</span>) with the ones corresponding to the (candidate) high-energy basis (g<span style="text-align: justify;"><sub style="text-align: justify;">R</sub></span>, g<span style="text-align: justify;"><sub style="text-align: justify;">B-L</sub></span>, <span style="text-decoration: overline;">g</span><span style="text-align: justify;"><sub style="text-align: justify;">R/B-L</sub></span>). Therefore, following the RG evolution of g<span style="text-align: justify;"><sub style="text-align: justify;">R/B-L</sub></span> in terms of g<span style="text-align: justify;"><sub style="text-align: justify;">1</sub></span>, g'<span style="text-align: justify;"><sub style="text-align: justify;">1</sub></span> and <span style="text-decoration: overline;">g</span>, we can recognise, by its zeroing at a given energy, the restoration of a Left-Right symmetry.</i></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><i><u>This analysis can be promptly extended to include thresholds of SO(10) that represent a realistic UV embedding. These involve, in addition to the Left-Right case discussed, a direct breaking of a Pati-Salam (PS) group into our model, and the flipped SU(5) case (fig. 2). Choosing as boundary conditions, for the RG extrapolation, benchmarks points inspired by our phenomenological analysis, the parameter space offers regions that, in case of discovery, would clearly reveal the presence of one of the previous embeddings (fig. 3)</u>.</i></div></blockquote><blockquote class="tr_bq"><a href="https://4.bp.blogspot.com/-_9uwC8xGuKQ/WHZveKQ6cfI/AAAAAAAAB7o/97ctSxtLYRoPBEXCtrY7eMbXYXAnqxYrQCLcB/s1600/GUT1.JPG"><img border="0" src="https://4.bp.blogspot.com/-_9uwC8xGuKQ/WHZveKQ6cfI/AAAAAAAAB7o/97ctSxtLYRoPBEXCtrY7eMbXYXAnqxYrQCLcB/s1600/GUT1.JPG" /></a><br />Figure 2. The SO(10) breaking chart illustrating the chains investigated in this work. The cases for the Flipped SU(5) and Pati-Salam required also additional unification conditions involving the non-abelian gauge sector</blockquote><a href="https://1.bp.blogspot.com/-VP7YrFy23BM/WHZvuu31mlI/AAAAAAAAB7w/fCWsWmhIpHUcd7Z_kKq7Rm1Ov8z50nENACLcB/s1600/GUT2.JPG"><img border="0" src="https://1.bp.blogspot.com/-VP7YrFy23BM/WHZvuu31mlI/AAAAAAAAB7w/fCWsWmhIpHUcd7Z_kKq7Rm1Ov8z50nENACLcB/s640/GUT2.JPG" /></a><br /><blockquote class="tr_bq" style="text-align: justify;"><i> Figure 3. (a) When we consider the stability and perturbativity analysis, the colours refer to the different regions defined by the maximum energy up to which the model is stable and perturbative. The same energy/colour relation is also used for the unification study, referring to regions that fulfil the given unification requirement. (b) Regions with Flipped SU(5) restoration. (c) Regions with LR and PS restoration.</i></blockquote><br /><div style="display: inline !important; text-align: justify;"><blockquote class="tr_bq"><i><u>... The minimal character of this U(1)’ extension of the SM makes particularly efficient the use of vacuum stability and perturbativity as constraining requirements to shape the viable parameter space</u> [13–15]. The vacuum stability is addressed asking for the extended scalar potential to be bounded from below, λ1 > 0 , λ2 > 0 , 4λ1λ2 − λ 2 3 > 0 . (4) Together with the perturbativity requirement it is also challenges the viability of a given unification scenario. If we accept the minimal content of the model, then a coherent extrapolation asks for the maximum scale of stability and perturbativity to be greater than the one realising a successful embedding. By relying on the analysis presented in [7], we may exploit this further constrains. <u>Our final results (fig. 4) give an illustration of how the interplay of the tools presented may enrich the forthcoming collider profiling of specific regions of the parameter space. Moreover, in a possible post-discovery phase, frictions with the measured scenarios would help in outlining the degrees of freedom necessary to recover stability, when a promising unification of the gauge sector is at hand</u>.</i></blockquote></div><div class="separator" style="clear: both; text-align: center;"></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody><tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-5s9TP9YNadA/WHZwOgWOHOI/AAAAAAAAB74/KWZf4sfMi10miYr6Co67gR2BW9690Ho7QCLcB/s1600/GUT3.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="222" src="https://1.bp.blogspot.com/-5s9TP9YNadA/WHZwOgWOHOI/AAAAAAAAB74/KWZf4sfMi10miYr6Co67gR2BW9690Ho7QCLcB/s640/GUT3.JPG" width="640" /></a></td></tr><tr><td class="tr-caption" style="text-align: justify;"><blockquote class="tr_bq"><i><span style="font-size: small;">Figure 4. (a) The effect of the stability requirement to the LR and PS restoration. The similar analysis for the Flipped SU(5) case would result trivially in the surviving only of the case with α = 0.3. Explicit matching of the stability and perturbativity map with the unification regions. Case α = 0.1 (b) and α = 0.3 (c).</span></i></blockquote></td></tr></tbody></table><blockquote class="tr_bq"><div style="text-align: right;"><i><a href="https://arxiv.org/abs/1609.05652" target="_blank"><br />Search for Z', vacuum (in)stability and hints of high-energy structures</a></i></div><div style="text-align: right;"><a href="https://arxiv.org/find/hep-ph/1/au:+Accomando_E/0/1/0/all/0/1">Elena Accomando</a>, <a href="https://arxiv.org/find/hep-ph/1/au:+Coriano_C/0/1/0/all/0/1">Claudio Coriano</a>, <a href="https://arxiv.org/find/hep-ph/1/au:+Rose_L/0/1/0/all/0/1">Luigi Delle Rose</a>, <a href="https://arxiv.org/find/hep-ph/1/au:+Fiaschi_J/0/1/0/all/0/1">Juri Fiaschi</a>, <a href="https://arxiv.org/find/hep-ph/1/au:+Marzo_C/0/1/0/all/0/1">Carlo Marzo</a>, <a href="https://arxiv.org/find/hep-ph/1/au:+Moretti_S/0/1/0/all/0/1">Stefano Moretti</a> (Submitted on 19 Sep 2016)</div></blockquote><br /><br /><b>A final remark</b><br /><div>In Lubos Motl's post to which I referred in the beginning one can read:</div><div><blockquote class="tr_bq" style="text-align: justify;"><i>I think that if there are some ingenious undergraduate seniors at a university anywhere in the world, they have a much harder time to turn into stars than in other periods of the history of physics.</i></blockquote><div style="text-align: justify;">I wish a young student should prove him wrong! In the meantime I propose to the most ingenious graduate ones to challenge their mathematical skills and physical intuition reading the two following fascinating 2016 review articles which seemed to have escaped Lubos radar and most popular science outlets. I encourage them to check the proof or <i><a href="http://www.alainconnes.org/docs/Companion.pdf" target="_blank">first build a “mental picture” oftheir own understanding</a></i> of these research works and construct more and more penetrating mental and practical tools to explore previously hidden aspects of our reality.</div><br /><blockquote class="tr_bq"><a href="https://arxiv.org/abs/1612.08640"><i>The firewall transformation for black holes and some of its implications</i></a> <br /><a href="https://arxiv.org/find/gr-qc/1/au:+Hooft_G/0/1/0/all/0/1">Gerard 't Hooft</a> (Submitted on 27 Dec 2016) </blockquote><blockquote class="tr_bq" style="text-align: justify;"><i><u>A promising strategy for better understanding space and time at the Planck scale, is outlined and further pursued. It is explained in detail, how black hole unitarity demands the existence of transformations that can remove firewalls. This must then be combined with a continuity condition on the horizon, with antipodal identification as an inevitable consequence. The antipodal identification comes with a CPT inversion. We claim to have arrived at 'new physics', but rather than string theory, our 'new physics' concerns new constraints on the topology and the boundary conditions of general coordinate transformations</u>. The resulting theory is conceptually quite non trivial, and more analysis is needed. A strong entanglement between Hawking particles at opposite sides of the black hole is suspected, but questions remain. A few misconceptions concerning black holes, originating from older investigations, are discussed.</i></blockquote><br /><blockquote class="tr_bq"><div style="text-align: justify;"><a href="https://arxiv.org/abs/1606.01189"><i>Quanta of Geometry and Unification</i></a></div><div style="text-align: justify;"><a href="https://arxiv.org/find/hep-th/1/au:+Chamseddine_A/0/1/0/all/0/1">Ali H. Chamseddine</a></div><div style="text-align: justify;">(Submitted on 3 Jun 2016) </div></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><i>This is a tribute to Abdus Salam's memory whose insight and creative thinking set for me a role model to follow. <u>In this contribution I show that the simple requirement of volume quantization in space-time (with Euclidean signature) uniquely determines the geometry to be that of a noncommutative space whose finite part is based on an algebra that leads to Pati-Salam grand unified models. The Standard Model corresponds to a special case where a mathematical constraint (order one condition) is satisfied</u>. This provides evidence that Salam was a visionary who was generations ahead of his time.</i></div></blockquote></div><div><div style="text-align: justify;"><br /></div><br /><br /><br /></div></div>Cédric Bardothttps://plus.google.com/104733107894701960711noreply@blogger.com0tag:blogger.com,1999:blog-3911792794793692366.post-60547033599453148542017-01-11T13:48:00.002+01:002017-01-11T18:22:43.834+01:00How far do we understand the 125 GeV Higgs boson (and its consequences)? A 2017 perspective<div dir="ltr" style="text-align: left;" trbidi="on"><b>From local...</b><br /><blockquote class="tr_bq"><div style="text-align: justify;"><i>Run 1 accumulated striking evidence that the Higgs field is the cause of the screening of the weak interaction at long distances. Indeed, the observation and measurement of the H → ZZ → 4 channel indicate that the Higgs field develops a vacuum expectation value (vev) that is not invariant under the SU(2)L × U(1)Y gauge symmetry of the SM. Furthermore, this vev seems to be the common source of the Z-boson mass and the coupling between the Higgs boson and the Z boson. However, this evidence only addresses the question of how the symmetry of the weak interaction is broken. It does not address the question of why the symmetry is broken or why the Higgs field acquires an expectation value. </i> <i><i><u>The situation is simply summarized in the following tautology</u> :</i></i></div></blockquote><blockquote class="tr_bq"><div style="text-align: center;"><i><i>Why is electroweak symmetry broken?</i></i></div><div style="text-align: center;"><i><i> Because the Higgs potential is unstable at the origin. </i></i></div><i></i><br /><div style="text-align: center;"><i><i>Why is the Higgs potential unstable at the origin? </i></i></div><div style="text-align: center;"><i><i>Because otherwise EW symmetry would not be broken. </i> </i></div><i></i></blockquote><blockquote class="tr_bq"><i></i><br /><div style="text-align: justify;"><i><i><u>The discovery of a Higgs boson allowed first glimpses into a new sector of the microscopic world. Now comes the time of the detailed exploration of this new Higgs sector</u>. And some key questions about the Higgs boson emerge: </i> </i></div><i></i></blockquote><blockquote class="tr_bq"><br /><br /><i>1. Is it the SM Higgs? <br />2. Is it an elementary or a composite particle?<br />3. Is it unique and solitary? Or are there additional states populating the Higgs sector?<br />4. Is it eternal or only temporarily living in a metastable vacuum?<br />5. Is its mass natural following the criteria of Dirac, Wilson or ’t Hooft? <br />6. Is it the first superparticle ever observed? <br />7. Is it really responsible for the masses of all the elementary particles? <br />8. Is it mainly produced by top quarks or by new heavy vector-like particles? <br />9. Is it a portal to a hidden world forming the dark matter component of the Universe? <br />10. Is it at the origin of the matter-antimatter asymmetry? <br />11. Has it driven the primordial inflationary expansion of the Universe?</i> <br /><i></i><br /><div style="text-align: justify;"></div><i></i><i></i></blockquote><blockquote class="tr_bq"><i></i><br /><div style="text-align: justify;"><i><i><u>The answers to these questions will have profound implications on our understanding of the fundamental laws of physics</u>...</i> </i></div><i></i></blockquote><blockquote class="tr_bq"><i></i><br /><div style="text-align: justify;"></div><i></i></blockquote><blockquote class="tr_bq"><div style="text-align: right;"><a href="http://inspirehep.net/record/1467568" target="_blank"><i>Physics of the Brout–Englert–Higgs boson: Theory</i></a></div><div style="text-align: right;"><a href="http://inspirehep.net/author/profile/Grojean%2C%20Christophe?recid=1467568&ln=en">Christophe Grojean</a> (<a href="http://inspirehep.net/search?cc=Institutions&p=institution:%22DESY%22&ln=en">DESY</a> & <a href="http://inspirehep.net/search?cc=Institutions&p=institution:%22Barcelona%2C%20IFAE%22&ln=en">Barcelona, IFAE</a> & <a href="http://inspirehep.net/search?cc=Institutions&p=institution:%22ICREA%2C%20Barcelona%22&ln=en">ICREA, Barcelona</a>)</div></blockquote><br /><br /><b>... to global point of view</b><br /><blockquote class="tr_bq" style="text-align: justify;"><i>The recent discovery of the Higgs boson [1, 2] and the ongoing measurements of its properties [3] are in good agreement with the hypothesis that this particle is a remnant of the Brout-Englert-Higgs mechanism, i.e. the spontaneous breaking of SU(2)L×U(1)Y → U(1)QED.<br /><br />While the precise determination of the Higgs and gauge boson masses, as well as the interactions of the Higgs boson with elementary particles, including itself, will continue to improve our understanding of the scalar potential’s local structure in the vicinity of the vacuum, its global structure, which can possibly explain the nature of electroweak symmetry breaking, is very difficult to probe experimentally.<br /><br />For example, the nature of the Higgs, whether elementary or composite, is still an open question. Even if the Higgs is assumed to be elementary, the shape of its potential remains unknown. It could be of mexican-hat shape as in the Standard Model (SM), or it could be deformed by strong quantum corrections due to virtual effects of additional fields. Were the Higgs boson to be a composite pseudo-Nambu-Goldstone boson of a strongly-coupled sector, one would expect a periodic potential involving trigonometric functions. In all cases, the Higgs mass is fixed by the curvature of the potential at its minimum, and so in the vicinity of the latter the shape of the potential will be similar in all possible models. Nevertheless, deviations are allowed away from the minimum. For example, one could have a barrier at zero temperature between the vacuum and the origin of field-space. Moreover, in composite Higgs models the relation between the Higgs field’s vacuum expectation value (VEV) and the gauge boson masses differs from its SM counterpart, and thus the location of the minimum in field-space may vary.<br /><br />Discriminating between the different possibilities is of fundamental importance for our understanding of nature and, hence, the embedding of the effective Standard Model in an underlying UV theory. This motivates to consider possible observables which could be sensitive to the Higgs potential beyond its minimum. A possible candidate is the energy scale of baryon-number-violating processes. If baryon number is only violated by the anomaly under the weak interactions, then it follows that processes that violate baryon-number are associated with transitions between vacua classified by their weak topological charge. The minimum energy barrier between these vacua thus sets the expected scale of baryon-violating processes, which is an observable that could potentially be probed by experiments, either at colliders [4–9] or cosmic ray and neutrino detectors [10–15]. Getting accurate predictions for the rates of baryon-number-violating interactions is a difficult problem, due to a possible breakdown of the semiclassical expansion used to compute vacuum transitions. After extensive discussion in the literature (see for example [16–24]) the latest estimates point towards rates that could be probed by future experiments [25, 26]; for recent analyses of measurement prospects at colliders, cosmic ray and neutrino detectors, see for example [27–29].</i></blockquote><blockquote class="tr_bq"><div style="text-align: right;"><i><a href="https://arxiv.org/abs/1611.05466" target="_blank">Sphalerons in composite and non-standard Higgs models</a></i></div><div style="text-align: right;"><a href="https://arxiv.org/find/hep-ph/1/au:+Spannowsky_M/0/1/0/all/0/1">Michael Spannowsky</a>, <a href="https://arxiv.org/find/hep-ph/1/au:+Tamarit_C/0/1/0/all/0/1">Carlos Tamarit</a></div><div style="text-align: right;">(Submitted on 16 Nov 2016)</div></blockquote><br /><b>A very personal (thus naive) spectral perspective</b><br />...to go beyond the above tautology<br /><br /><div style="text-align: center;"><i><i>Why is electroweak symmetry broken?</i></i></div><div style="text-align: center;"><div style="text-align: justify;"><blockquote class="tr_bq"><i> </i>Because spacetime geometry has a fine structure or more crudely a "discrete" dimension at the zeptometer scale that the discovery of the Higgs boson makes it possible to uncover provided one understands it through <a href="https://arxiv.org/abs/1008.0985" target="_blank">the spectral noncommutative point of view.</a></blockquote></div><br /><i>Why is the Higgs potential unstable at the origin? </i><br /><blockquote class="tr_bq"><div style="text-align: justify;">This is a consequence of the spectral action principle applied to the proper almost commutative 4D manifold. The latter is a small (but topologically highly nontrivial) extension of our ordinary continuous and commutative geometric model of spacetime while the former is <a href="https://arxiv.org/abs/hep-th/9606001" target="_blank">a stronger hypothesis than the usual</a><a href="https://arxiv.org/abs/hep-th/9606001" target="_blank"> diffeomorphism invariance of the action of general relativity.</a></div></blockquote></div><br />...and propose tentative answers or rather educated guess<br /><blockquote class="tr_bq"><div style="text-align: justify;"><i>1. Is it the SM Higgs? </i>Yes </div></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><i>2. Is it an elementary or a composite particle? </i>It is elementary in <a href="http://www.waltervansuijlekom.nl/wp-content/uploads/2014/12/naw5-2014-15-4-2401.pdf" target="_blank">the spectral model of particle physics</a> compatible with current experiments and observations. </div></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><i>3. Is it unique and solitary? Or are there additional states populating the Higgs sector? </i>There should be more scalars responsible for several gauge symmetry breaking but<a href="https://arxiv.org/abs/1507.08161" target="_blank"> they may be at partial or grand unification energy scales</a> inacessible to terrestrial particle accelerators. <a href="https://arxiv.org/abs/1208.1030" target="_blank">The 125 GeV Higgs boson could be very weakly mixed with (but strongly coupled to) a big brother</a> (<i>"big broson")</i> responsible for the type I seesaw mechanism that gives very low masses to left-handed neutrinos. </div></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><i>4. Is it eternal or only temporarily living in a metastable vacuum? </i><a href="https://arxiv.org/abs/1605.02910" target="_blank">The coupling with the above very massive scalar "big broson" should stabilise the vacuum</a>. </div></blockquote><blockquote class="tr_bq"><i></i><br /><div style="text-align: justify;"><i>5. Is its mass natural following the criteria of Dirac, Wilson or ’t Hooft? </i>This question could be settled once the proper fine structure of spacetime is established and the quantum dynamics of scalars in this <a href="https://arxiv.org/abs/hep-th/0512169" target="_blank">new arena is better understood</a>. </div></blockquote><blockquote class="tr_bq"><i></i><br /><div style="text-align: justify;"><i>6. Is it the first superparticle ever observed? </i>There might be no need for that hypothesis to paraphrase a <a href="http://www.quantumdiaries.org/2011/09/16/there-is-no-need-for-god-as-a-hypothesis/" target="_blank">famous Laplace quote</a>. </div></blockquote><blockquote class="tr_bq"><i></i><br /><div style="text-align: justify;"><i>7. Is it really responsible for the masses of all the elementary particles? </i>There could exist a dilaton scalar ruling all the masses so to speak and responsible for a spontaneous symmetry <a href="https://arxiv.org/abs/1106.3263" target="_blank">breaking of Weyl invariance</a>. </div></blockquote><blockquote class="tr_bq"><i></i><br /><div style="text-align: justify;"><i>8. Is it mainly produced by top quarks or by new heavy vector-like particles? </i>Noncommutative geometry and the spectral action principle provide a conceptual explanation <a href="https://arxiv.org/abs/0706.3690" target="_blank">for the standard model algebra and the number of fundamental fermions by generation</a> so there should be no need for heavy vector-like particles to explain the production rate of Higgs boson at the LHC. </div></blockquote><blockquote class="tr_bq"><i></i><br /><div style="text-align: justify;"><i>9. Is it a portal to a hidden world forming the dark matter component of the Universe? </i>In a metaphorical way the answer could be yes. Indeed, understanding how to accommodate the measured Higgs mass in the spectral noncommutative framework has helped to uncover new mathematical structures to build 4D spin manifolds from <a href="https://arxiv.org/abs/1409.2471" target="_blank">a higher degree Heisenberg commutation relation</a>. This provides new perspectives on the dark component as not composed of unknown particles or fields but mimicking some kind of new quanta of geometry.</div></blockquote><blockquote class="tr_bq"><div style="text-align: justify;"><i>10. Is it at the origin of the matter-antimatter asymmetry</i>? In an indirect way one cold say yes. The phenomenological consequences of the spectral standard model have not been extensively probed but they might be close to the predictions of <a href="https://arxiv.org/abs/1412.4776" target="_blank">a minimal nonsupersymmetric SO(10) model</a> which values of the parameters obtained from the low energy observables yield a baryon assymetry <span style="font-family: "cmr10"; font-size: small;"><span style="font-family: "cmr10"; font-size: small;">in agreement with observations.</span></span></div></blockquote><blockquote class="tr_bq"><i></i><br /><div style="text-align: justify;"><i>11. Has it driven the primordial inflationary expansion of the Universe? </i>This question has not been investigated serioulsy in the most advanced spectral modelisation of spacetime and matter at my knowledge but I think some people responsible for an <a href="https://arxiv.org/abs/1111.0273" target="_blank">interesting extension of the standard model</a> not that far from the spectral one work on this...</div><br /></blockquote><div style="text-align: justify;">The above picture could look like a pretty bleak one for the youngest ingenious physicists engaged for instance in ATLAS and CMS collaborations who cope with data from LHC run 1 and 2. Nevertheless I have no doubt they will make their way exploring unchartered territories with different compasses to guide them and they will improve our knowledge of interactions in the zeptouniverse. Moreover I have only drawn very rough lines and it is not impossible to imagine discovering in <a href="https://arxiv.org/abs/1208.5023" target="_blank">less orthodox</a> or <a href="https://arxiv.org/abs/1509.01606" target="_blank">apparently more contrieved</a> spectral models new right-handed gauge bosons at the LHC ... S<i>ubtle is the Lord</i>! Besides most details are not understandable by myself but I have worked on it here up until now with you, dear reader!<br /><br /><blockquote class="tr_bq"><span class="st"><i>Fortune favors the prepared mind</i>.</span></blockquote></div><div style="text-align: justify;"><blockquote><i>La chance ne sourit qu'aux esprits bien préparés.</i></blockquote><div style="text-align: center;"> Louis Pasteur</div><div style="text-align: center;"></div></div></div>Cédric Bardothttps://plus.google.com/104733107894701960711noreply@blogger.com0