### Parallel but opposite or dual and complementary histories of two different ideas?

**Supersymmetry, a decade ago**

Supersymmetry is now 30 years old. The first supersymmetric field theory in four dimensions - a version of supersymmetric quantum electrodynamics (QED) - was found by Golfand and Likhtman in 1970 and published in 1971. At that time the use of graded algebras in the extension of the Poincaré group was far outside the mainstream of high-energy physics.

Three decades later, it would not be an exaggeration to say that supersymmetry dominates high-energy physics theoretically and has the potential to dominate experimentally as well. In fact, many people believe that it will play the same revolutionary role in the physics of the 21st century as special and general relativity did in the physics of the 20th century.

This belief is based on the aesthetic appeal of the theory, on some indirect evidence and on the fact that there is no theoretical alternative in sight. Since the discovery of supersymmetry, immense theoretical effort has been invested in this field. More than 30,000 theoretical papers have been published and we are about to enter a new stage of direct experimental searches.

The largest-scale experiments in fundamental science are those that are being prepared now at the LHC at CERN, of which one of the primary targets is the experimental discovery of supersymmetry.

The history of supersymmetry is exceptional. In the past, virtually all major conceptual breakthroughs have occurred because physicists were trying to understand some established aspect of nature. In contrast, the discovery of supersymmetry in the early 1970s was a purely intellectual achievement, driven by the logic of theoretical development rather than by the pressure of existing data.

Keith Olive and Misha Shifman, Minnesota

CERN COURIER, Feb 26, 2001

**Spectral noncommutative geometry, right now**

Spectral noncommutative geometry is approximately 25 years old. The first noncommutative model of spacetime - offering a geometric understanding of the Higgs term in the Glashow-Weinberg-Salam Lagrangian - was proposed by A. Connes in 1988 and was further developed and expanded to the Standard Model with J. Lott in 1990. At that time the use of operator algebraic tools to characterize spectrally (and extend much further) Riemannian manifolds was far outside the mainstream of high-energy physics.

Two decades later, it would not be an understatement to say that the now well established tools from spectral noncommutative geometry are still largely ignored by high-energy physics theoreticians more accustomed to highly sophisticated but classical differential geometry of String Theory mathematics. Nevertheless constant progress in the understanding of the spectral version of the Standard Model and its possible extensions give hope to the rise of a genuine spectral noncommutative phenomenology. In fact, one can reasonably expect that it will help to realize in the 21st century a synthesis of quantum physics and general relativity from the 20th century.

This hope is based on the epistemological logic and potential heuristics of the theory, on the direct detection of one Standard Model-like Higgs boson and on the fact that there is no experimental sign of other new fundamental particle at the highest accessible energies from colliders. Since the beginning of spectral noncommutative geometry, important breakthroughs have been done in this field but progress has been slow and difficult. Only 300 theoretical papers have been published but we have in some sense already entered in the first stage of direct experimental investigations.

Among the largest-scale experiments in fundamental science are those that are planned to restart at the LHC at CERN, of which one of the target could be the search for a Z' boson associated to a U(1)_{B-L}extension of the Standard Model gauge group compatible with the parsimonious spectral predictions.

The history of spectral noncommutative geometry is quite original. In the recent past, the more publicized theories have implied lot of physicists trying to extrapolate the quantum knowledge gained from strong interaction to explain the weakness of classical gravitation. In contrast, the development of spectral noncommutative geometry for physics started with the work of a lonely mathematician looking for a conceptual understanding of the Brout-Englert-Higgs mechanism that provides mass to the bosons of the weak interaction.

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