Olivier DARRIGOL

Abstract : In its most common formulations, quantum mechanics begins with shockingly counterintuitive concepts and highly abstract mathematical objects such as operators in Hilbert space. Since the early years of quantum mechanics, there have been several attempts to reconstruct it from more natural assumptions.

The purpose of this talk is to outline three outstanding examples of such reconstructions. The first is based on continuous deformation of the classical algebra of infinitesimal evolutions (Jacques Vey, André Lichnerowicz, and Simone Gutt); the second on the basic logic of Yes-No experimental questions (John von Neumann and Constantin Piron); the third on natural axioms for the probabilities of measurement outcomes (Lucien Hardy), partly justified by correspondence arguments.

These reconstructions may help to understand the contents of the theory, they may prepare future generalizations, or they may shed new light on quantum paradoxes and interpretation problems. Regarding this last point, it will for instance be shown that one of the oddest consequences of quantum mechanics, the EPR correlations, can be derived from very simple and natural assumptions on spin measurements.