Quantum Theory: Concepts and Methods: Difference between revisions

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'''''Quantum Theory: Concepts and Methods''''' is a 1993 [[quantum physics]] textbook by Israeli physicist [[Asher Peres]].

==Contents==

In his preface, Peres summarized his goals as follows:

:<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]]. (Among 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 approximation]] methods, [[quantum chaos]], and the treatment of [[measurement in quantum mechanics]].

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Physicist Leslie E. Ballentine gave the textbook a positive review, declaring it a good introduction to [[quantum foundations]] and ongoing research therein.<ref name="Ballentine">{{Cite journal|last=Ballentine|first=Leslie E.|date=March 1995|title=none|url=|journal=[[American Journal of Physics]]|language=en|volume=63|issue=3|pages=285–286|doi=10.1119/1.17946|issn=0002-9505 }}</ref> [[John C. Baez]] also gave the book a positive assessment, calling it "clear-headed" and finding that it contained "a lot of gems that I hadn't seen", such as the [[Wigner–Araki–Yanase theorem]].<ref name="Baez">{{Cite web|url=http://math.ucr.edu/home/baez/week33.html|title=week33|last=Baez|first=John C.|authorlink=John C. Baez|date=1994-05-10|website=[[This Week's Finds in Mathematical Physics]]|url-status=live|archive-url=|archive-date=|access-date=2020-04-10}}</ref> [[Michael Nielsen]] wrote of the textbook, "Revelation! Suddenly, all the key results of 30 years of work (several of those results due to Asher) were distilled into beautiful and simple explanations."<ref>{{cite web|last=Nielsen|first=Michael A.|author-link=Michael Nielsen|title=Asher Peres|url=http://michaelnielsen.org/blog/asher-peres/|date=2005-01-05|website=michaelnielsen.org|access-date=2018-02-21}}</ref> Nielsen and [[Isaac Chuang]] said in their own influential textbook that Peres' was "superb", providing "an extremely clear exposition of elementary quantum mechanics" as well as an "extensive discussion of the Bell inequalities and related results".<ref>{{Cite book|last=Nielsen|first=Michael A.|title=Quantum Computation and Quantum Information: 10th Anniversary Edition|last2=Chuang|first2=Isaac L.|date=2010-12-09|publisher=[[Cambridge University Press]]|isbn=9781107002173|___location=|pages=118|language=en|oclc=844974180|author-link=Michael Nielsen|author-link2=Isaac Chuang}}</ref>

[[N. David Mermin]] wrote that Peres had bridged the "textual gap" between conceptually-oriented books, aimed at understanding what quantum physics implies about the nature of the world, and more practical books intended to teach how to apply quantum mechanics. Mermin found the book praiseworthy, noting that he had "only a few complaints". He wrote,:

:<blockquote>Peres is careless in discriminating among the various kinds of assumptions one needs to prove the impossibility of a no-hidden-variables theory that reproduces the statistical predictions of quantum mechanics. I would guess that this is because even though he is a master practitioner of this particular art form, deep in his heart he is so firmly convinced that hidden variables cannot capture the essence of quantum mechanics, that he is simply not interested in precisely what you need to assume to ''prove'' that they cannot.<ref name="Mermin">{{Cite journal|last=Mermin|first=N. David|author-link=N. David Mermin|date=1997-03-01|title=none|journal=[[Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics]]|language=en|volume=28|issue=1|pages=131–135|doi=10.1016/S1355-2198(97)85538-4|issn=1355-2198 |bibcode=1997SHPMP..28..131M }}</ref></blockquote>

Mermin called the book "a treasure trove of novel perspectives on quantum mechanics" and said that Peres' choice of topics is "a catalogue of common omissions" from other approaches.<ref name="Mermin"/>

[[Meinhard E. Mayer]] declared that he would "recommend it to anyone teaching or studying quantum mechanics", finding Part II the most interesting of the book. While he noted some disappointment with Peres' selection of topics to include in the chapter on [[measurement in quantum mechanics|measurement]], he reserved most of his negativity for the publisher, saying (as Ballentine also did<ref name="Ballentine"/>) that they had priced the book beyond the reach of graduate students.:

:<blockquote>Such pricing practices are not justified when one considers that many publishers provide very little copyediting or typesetting any more, as is obvious from the "[[TeX]]"-ish look of most books published recently, this one included.<ref name="Mayer">{{Cite journal|last=Mayer|first=Meinhard E.|author-link=Meinhard E. Mayer|date=2008-01-11|title=none |journal=[[Physics Today]]|language=en|volume=47|issue=12|pages=65|doi=10.1063/1.2808757|issn=0031-9228}}</ref></blockquote>

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"/>