Quantum Theory: Concepts and Methods: Difference between revisions

Revision as of 20:55, 13 December 2020

Revision as of 00:41, 19 February 2022

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<blockquote>The purpose of this book is to clarify the ''conceptual meaning'' of quantum theory, and to explain some of the mathematical methods that it utilizes. This text is not concerned with specialized topics such as atomic structure, or strong or weak interactions, but with the very foundations of the theory. This is not, however, a book on the [[philosophy of science]]. The approach is pragmatic and strictly instrumentalist. This attitude will undoubtedly antagonize some readers, but it has its own logic: quantum phenomena do not occur in a [[Hilbert space]], they occur in a laboratory.{{efn|Preface, p. xi}}</blockquote>

The book is divided into three parts. The first, "Gathering the Tools", introduces quantum mechanics as a theory of "preparations" and "tests", and it develops the mathematical formalism of Hilbert spaces, concluding with the [[spectral theory]] used to understand the quantum mechanics of continuous-valued observables. Part II, "Cryptodeterminism and Quantum Inseparability", focuses on [[Bell's theorem]] and other demonstrations that quantum mechanics is incompatible with [[local hidden-variable theory|local hidden-variable theories]]. (AmongWithin its substantial discussion of the failure of [[Hidden variable theory|hidden variable theories]], the book includes a [[FORTRAN]] program for testing whether a list of [[Euclidean vector|vector]]s forms a [[Kochen–Specker theorem|Kochen–Specker configuration]].{{efn|Section 7-5, "Appendix: Computer test for Kochen–Specker contradiction", p. 209}}) Part III, "Quantum Dynamics and Information", covers the role of [[spacetime]] symmetry in quantum physics, the relation of [[quantum information]] to [[thermodynamics]], [[Semiclassical physics|semiclassical approximation]] methods, [[quantum chaos]], and the treatment of [[measurement in quantum mechanics]].

To generate the figures in his chapter on quantum chaos, including plots in [[phase space]] of chaotic motion, Peres wrote [[PostScript]] code that executed simulations in the printer itself.{{efn|Section 11-7, "Appendix: PostScript code for a map", p. 370}}

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Mermin, Mayer and Baez noted that Peres briefly dismissed the [[many-worlds interpretation]] of quantum mechanics.<ref name="Mermin" /><ref name="Baez"/><ref name="Mayer"/> Peres argued that all varieties of many-worlds interpretations merely shifted the arbitrariness or vagueness of the [[wavefunction collapse]] idea to the question of when "worlds" can be regarded as separate, and that no objective criterion for that separation can actually be formulated.{{efn|Section 12-1, "The ambivalent observer", p. 374}} Moreover, Peres dismissed "spontaneous collapse" models like [[Ghirardi–Rimini–Weber theory]] in the same brief section, designating them "mutations" of quantum mechanics.<ref name="Mermin"/>

Manuel Bächtold analyzed Peres' textbook from a standpoint of [[Pragmatism|philosophical pragmatism]].<ref name="Healey">{{Cite book|chapter-url=https://plato.stanford.edu/entries/quantum-bayesian/|title=[[Stanford Encyclopedia of Philosophy]]|last=Healey|first=Richard|publisher=Metaphysics Research Lab, [[Stanford University]]|year=2016|editor-last=Zalta|editor-first=Edward N.|chapter=Quantum-Bayesian and Pragmatist Views of Quantum Theory}}</ref> [[John Horton Conway|John Conway]] and [[Simon B. Kochen|Simon Kochen]] used a Kochen–Specker configuration from the book in order to prove their [[free will theorem]].<ref>{{Cite journal|last=Conway|first=John|author-link=John Horton Conway|last2=Kochen|first2=Simon|author-link2=Simon B. Kochen|date=2006-11-22|title=The Free Will Theorem|url=http://link.springer.com/10.1007/s10701-006-9068-6|journal=[[Foundations of Physics]]|language=en|volume=36|issue=10|pages=1441–1473|arxiv=quant-ph/0604079|bibcode=2006FoPh...36.1441C|doi=10.1007/s10701-006-9068-6|issn=0015-9018}}</ref> Peres' insistence in his textbook that the classical analogue of a [[quantum state]] is a [[Liouville's theorem (Hamiltonian)|Liouville density function]] was influential in the development of [[QBism]].<ref>{{cite encyclopedia|first1=Christopher A. |last1=Fuchs |first2=Blake C. |last2=Stacey |title=QBism: Quantum Theory as a Hero's Handbook |encyclopedia=Proceedings of the International School of Physics "Enrico Fermi" |editor-first1=E. M. |editor-last1=Rasel |editor-first2=W. P. |editor-last2=Schleich |editor-link2=Wolfgang P. Schleich |editor-first3=S. |editor-last3=Wölk |doi=10.3254/978-1-61499-937-9-133 |arxiv=1612.07308 |year=2019 |volume=197 |issue=Foundations of Quantum Theory |publisher=[[IOS Press]] |isbn=9781614999379 |oclc=1086375617}}</ref>

==Related works==