Expansion de la physique et consolidation des mathématiques (et réciproquement)

“The trouble with physics” is the title of an interesting and well-informed polemic by Lee Smolin against String Theory and present main stream physics at large. He notices a stagnation in physics, so much promise, so little fulfillment [Sm06, p. 313], a predominance of anti-foundational spirit and contempt for visions, partly related to the mathematization paradigm of the 1970s, according to Smolin: Shut up and calculate. Basically, Smolin may be right. Børge Jessen, the Copenhagen mathematician and close collaborator of Harald Bohr once suggested to distinguish in sciences and mathematics between periods of expansion and periods of consolidation. Clearly physics had a consolidation period in the first half of the 20th century with relativity and quantum mechanics... while, to me, the mathematics of that period is characterized by an almost chaotic expansion in thousands of directions. Following that way of looking, mathematics of the second half of the 20th century is characterized by an enormous consolidation, combining so disparate fields like partial differential equations and topology in index theory, integral geometry and probability in point processes, number theory, statistical mechanics and cryptography, etc. A true period of consolidation for mathematics, while - at least from the outside - one can have the impression that physics ... of the second half of the 20th century were characterized merely by expansion, new measurements, new effects - and almost total absence of consolidation or, at least failures and vanity of all trials in that direction. Indeed, there have been impressive successes in recent physics, in spite of the absence of substantial theoretical progress in physics: perhaps the most spectacular and for applications most important discovery has been the High Temperature Superconducting property of various ceramic materials by Bednorz and Muller - seemingly without mathematical or theoretical efforts but only by systematic combinatorial variation of experiments - in the tradition of the old alchemists, [BeMu87].

The remarkable advances in fluid dynamics, weather prediction, oceanography, climatic modelling are mainly related to new observations and advances in computer power while the equations have been studied long before. Nevertheless, I noticed a turn to theory among young experimental physicists in recent years, partly related to investigating the energy landscapes in material sciences, partly to the re-discovery of the interpretational difficulties of quantum mechanics in recent quantum optics.

Bernhelm Booss-Bavnbek,
Steps towards Quantum Gravity and the practice of science: will the merger of mathematics and physics work? 23 novembre 2009