Quantum Theory: Concepts and Methods

Quantum Theory: Concepts and Methods is a 1993 quantum physics textbook by Asher Peres.

Contents

In his introduction, Peres summarized his goals as follows:

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.

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 theories. (Among its substantial discussion of the failure of hidden variable theories, the book includes a FORTRAN program for testing whether a list of vectors forms a Kochen–Specker configuration.) 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.

Peres downplayed the importance of the uncertainty principle, giving it only a single mention in his index, which points to that same page of the index.

Reception

Physicist Leslie E. Ballentine gave the textbook a positive review, declaring it a good introduction to quantum foundations and ongoing research therein. 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. 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."

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,

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.

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' choice of topics to include in the chapter on measurement, he reserved most of his negativity for the publisher, saying (as Ballentine also did) that they had priced the book beyond the reach of graduate students.

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.

Editions

• Peres, Asher (1993). Quantum Theory: Concepts and Methods. Kluwer. ISBN 0-7923-2549-4. OCLC 28854083.