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Physics and NecessityRationalist Pursuits from the Cartesian Past to the Quantum Present$
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Olivier Darrigol

Print publication date: 2014

Print ISBN-13: 9780198712886

Published to Oxford Scholarship Online: June 2014

DOI: 10.1093/acprof:oso/9780198712886.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 05 December 2021

Quantum Mechanics

Quantum Mechanics

(p.236) 8 Quantum Mechanics
Physics and Necessity

Olivier Darrigol

Oxford University Press

This chapter is devoted to several attempts at showing the necessity of quantum mechanics. It first examines whether necessity arguments can be extracted from the history of quantum mechanics, both on the matrix-mechanics side and on the wave-mechanics side. It then recounts the stunning mathematical discovery (1979) that the only one-parameter deformation of the Lie algebra of classical Hamiltonian mechanics is the Moyal algebra, which is isomorphic to the algebra of infinitesimal evolutions of quantum mechanics. The chapter goes on with an account of “quantum logic” as an attempt to justify the matrix-density representation of quantum states and the unitary evolution of these states by a natural logic of Yes–No experimental questions. The last section is a discussion of Lucien Hardy’s (2001) and more recent proposals of “natural axioms” for statistical measurement correlations, leading again to the matrix-density formulation of quantum mechanics.

Keywords:   quantum mechanics, deformation quantization, quantum logic, Moyal. Von Neumann, Piron, Hardy, correspondence principle

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