ペレス量子論の概念と手法―先端研究へのアプローチ 単行本 – 2001/9
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(1) Gathering the Tools - Hilbert Space, Linear Operators, Spectral Theory (roughly one hundred pages). We read:
" the new feature introduced by quantum theory is that the probabilistic nature of the outcome of a measurement is inherent." (page 56).
(2) Crypto-determinism and inseparability, Bell's theorem, Gleason's theorem (all couched within exposition of one- hundred pages). Read: " there is no escape from nonlocality, it is the entire universe which is an indivisible, nonlocal entity." (page 173).
(3) Quantum dynamics and information, Wigner & symmetry, thermodynamics and measurement. Read: " By analogy with the classical formalism, we shall assume that the evolution of a quantum state is given by the unitary transformation satisfying the group property." (page 239). This last part (part three) is a feast for those inclined to peruse this marvelous resource. A few words from Asher Peres:
(1) " Quantum theory is nothing more than a set of rules whereby physicists compute probabilities..." (page 18).
(2) " Amplitudes, not probabilities, are fundamental...from which the probabilities are derived." (page 43).
(3) "...analogy is admittedly vague...must ultimately break down." (page 298, referring to the so-called correspondence principle). A brief table presents the relationship between Dirac's bra-ket scheme and complex vectors. (page 78). Excellent pedagogy. I highlight words from Chapter Twelve: Measurement of Time:
" time is not a dynamical variable" and "...there is no time operator." Time was mentioned, too, earlier in the book:
" The asymmetry between past and future is fundamental in the axiomatic development of quantum theory."(page 12). We read: " in quantum theory frequency means energy" (an issue too often neglected !).
There is an interesting discussion of Fock space (pages 136-145). One of the few texts introducing Wigner's functions which "may give a qualitative feeling of the approximate location of a quantum system in phase space." (page 314).
Read: " the notion of truth and falsehood acquire new meanings in the logic of quantum phenomena." (page 288),
The bibliography includes Max Born, The Mechanics Of The Atom: "a remarkable book, one of the best sources for canonical transformations, action-angle variables and Hamilton-Jacobi theory." (see page 22, this is an accurate assessment of Born's book !).
Concluding: this advanced textbook should be part and parcel of the education of every student and instructor.
Highly recommended !
If you are interested to know quantum theory as it is genuinely practiced, in the laboratory, and its standard Copenhagen Interpretation, then this is the book. In this book quantum theory is unfolded as it actually works, and not lending itself to Deepak Chopraik charlatanism. Quantum Theory is conceived as a set of rules for calculating the probabilities of atomic and subatomic phenomena; that is it and no more and no less. It is a highly professional and practical version of the theory.
This book does an incredible at presenting quantum theory from a perspective with the *fewest* assumptions. For anyone interested in foundational/interpretational questions, this is essential. That being said, it can be a challenging read even for a researcher in physics. Aspects of the Hilbert Space formalism that are usually suppressed under a simpler undergraduate presentation (eg. Griffiths or Liboff) or the standard graduate presentation (eg. Sakurai) are brought to the forefront. By largely abandoning Dirac notation, the reader is forced to think more about the operational approach to quantum mechanics, not simply how to calculate quantum probabilities. The exercises aren't exceptionally difficult, are practical, and well chosen.
Once the foundation is set, the book proceeds to cover those topics of quantum theory that have had the greatest philosophical and conceptual impact since the theory's conception. Peres devotes a great deal of the book to issues such as EPR and Bell's inequalities. He continues by introducing contextuality and the Kochen-Specker theorem; KS is nearly as important a result as Bell's inequalities, but isn't mentioned in most introductory presentations of QM.
After committing the book to various other frequently uncovered topics (see the book's contents) he even goes on to talk about quantum information and the measurement process.
I'll summarize with this: for the reader who is interested in learning about quantum mechanics and not simply learning how to be a quantum mechanic, this is, hands down, the single best book. After reading, your insights are bound to run far deeper than ever before.
I am not a physicist nor a mathematician, just someone who is scientifically inclined with a deep interest in quantum theory and this book is a very valuable addition to my library. I highly recommend it. the author in my opinion literally guides you through an excellent exploration of the subject matter.