Stephen Hawking : a quantum Prometheus

The mortal shadow and the eternal flame

R.I.P dear Stephen Hawking or @StepHawking1 and congratulation for your work @Steven_Hawking. Pass on our greetings to Sadi Carnot, Max Planck, Albert Einstein and our other #ScienceHeroes. Don't hesitate to give us a node through next #EventHorizonTelescope #BlackHoles images!

Sur la scène du théâtre quantique, Stéphane a tiré sa révérence. Nous pleurons l’ombre évanouie qui se projetait sur le décors classique mais gardons à l’esprit que sa flamme est toujours présente, seulement plus évanescente à nos yeux de mortels. En attendant qu’émerge de la poussière d’orchestre une symphonie véritable, je me réjouis d’entendre déjà, quelque part dans les coulisses, le chant spectral d’un chœur qui résonne et diffuse peut-être à sa manière la même lumière que Hawking a volé pour nous à l’Obscur.

An English translation (provided by a tentative increased intelligence experienced in the French anagrams of Jacques Perry-Salkow and Etienne Klein)

On the stage of quantum theater, Stephen has left his role. We mourn the faded shadow projected on the classical scenery but keep in mind that its flame is still present, only more evanescent to our mortal eyes. While waiting for a real symphony to emerge from superstring theory, I am already glad to hear, somewhere in backstage, the spectral song of a choir that resonates and may diffuse in its own way the same kind of light as Hawking stole for us from Darkness.  

Food for thought

Hawking’s 1974 discovery [1] that black holes evaporate ushered in a new era in black hole physics. In particular, this was the beginning of concrete applications of quantum mechanics in the context of black holes. But more importantly, the discovery of Hawking evaporation has raised a sharp problem whose resolution probably requires a better understanding of Planck scale physics, and which therefore may serve as a guide (or at least a constraint) in our attempts to understand such physics. This problem is the information problem.

Quantum Mechanics of Black Holes
Authors: Steven B. Giddings (Submitted on 16 Dec 1994)

A Glow of Enlightenment through closed eyelids?

Ideas of quantum information theory and entanglement have played an increasingly important role in quantum field theory and string theory in recent years... Many important developments are cited and summarized in the recent review article [1].  

The present notes are not an overall introduction to this subject. The goal here is more narrow: to make accessible some of the mathematical ideas that underlie some of these developments and which are present in the existing literature but not always so easy to extract. In the process, we will also make contact with some of the older literature on axiomatic and algebraic quantum field theory… 

In section 2, we describe the Reeh-Schlieder theorem... which demonstrates that in quantum field theory, all field variables in any one region of spacetime are entangled with variables in other regions. Actually, the entanglement of spatially adjacent field modes is so strong that entanglement entropy between adjoining spacetime regions in quantum field theory is not just large but ultraviolet divergent...  

An important tool in dealing with entanglement when it is a property of the algebras and not just the states is provided by Tomita-Takesaki theory, which we introduce in section 2. It has been used in a number of recent developments, including an attempt to see behind the horizon of a black hole [9], a proof of the quantum null energy condition [10], and too many others to properly cite here...  

The essence of the matter is that in quantum field theory, the divergence in the entanglement entropy is not a property of the states but of the algebras … These algebras are not the familiar Type I von Neumann algebras which can act irreducibly in a Hilbert space. Instead they are more exotic algebras with the property that the structure of the algebra has the divergence in the entanglement entropy built in. In this section, we explain barely enough about von Neumann algebras to indicate how that comes about. 

Notes on Some Entanglement Properties of Quantum Field Theory

Authors: Edward Witten

(Submitted on 13 Mar 2018 (v1), last revised 15 Mar 2018 (this version, v2))

Personal explicit comments 

I let young physicists enjoy their own close encounters of the third type or rather rendez-vous with von Neumann algebra of type III reading E. Witten who holds the candle and enlighten us brilliantly as usual in the forefront of the quantum theatre arxiv.org/abs/1803.04993.

Last but not least remark : there is a blind spot in every eye even Witten’s one … Thus I would suggest to my most brilliant highschool senior student to find some inspiration for  quantum time in the experience gained by the mathematician who contributed quite significantly in understanding von Neumann algebras, watching for instance http://www.youtube.com/watch?v=ODAngTW8deg.

He's alive!

Stephen Hawking's flame that has enlightened us on quantum gravity is alive indeed but the subtitle of this paragraph is a wink to Jester's comeback in his Resonaances blog.

Waiting for new resonances at LHC, I am already delighted that my recent wish on twitter has been already partly fullfilled :-)

All the best to #HighEnergyPhysics contributors (or could I say #QuantumSpacetime spectroscopists?) from #CERN. May next spring brings us bud burst of unexpected resonances (and new posts @Resonaances ;-) thanks to them!

— cédric bardot (@bardot_cedric) 10 mars 2018

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/Last edit : March 17th 2018 (adding some content from the Witten's Notes)