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Quantum What's wrong with the Messiah "Quantum Mechanics" textbook?

  1. Jun 14, 2018 #1
    Hi.

    I bought Messiah's "Quantum Mechanics" because it was at an excelent price from Dover. But, even though it was considered a Bible of quantum mechanics until recently, people consider it outdated now. Is it no longer comprehensive? I intend to read on relativistic quantum mechanics and quantum field theory from other books anyway.

    So, what are the handicaps of using this book to go deeper into QM? And if you only had Messiah's QM, would you pay more to get your recomended book?

    Thanks.
     
  2. jcsd
  3. Jun 14, 2018 #2

    George Jones

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    Quantum entanglement, which I think is an essential component of any treatment of modern quantum theory, is largely (possibly completely) absent. The Einstein-Podolsky-Rosen effect predates Messiah, but, at a quick glance, I don't see it in Messiah.

    Other modern application of entanglement:
    no cloning theorem (1970, 1982);
    quantum teleportation (theory, 1993; experiment 1997);
    quantum computing.

    These days, this stuff is so important theoretically and experimentally, that it is a necessity to include quantum entanglement and at least some of its applications
     
  4. Jun 15, 2018 #3
    Hi.

    Susskind's "Quantum Mechanics: The Theoretical Minimum", has about 25% (86 pages) of his book dedicated to quantum entanglement. If I start with Susskind and then move to Messiah, do you think I would end up with a solid and broad understanding of QM?

    Thanks.
     
  5. Jun 15, 2018 #4
    My interest in quantum theory is mostly on amateur level, so forgive my ignorance, but are there many cases where entanglement is important outside the quantum communications and building quantum computers? What I mean is that, if I was doing computations on response of solid-state, or molecular systems, I would be using a lot of the QM machinery. In some cases one could even probably single out bits of the system that are entangled. But surely, this would do very little to help in computing the ground-state energy (for example).

    My question is therefore, should one consider entanglement, in the way you characterized it (teleportation etc), and integral part of QM, or should it be a more specialized sub-branch of quantum optics, such as squeezed states, Schrodinger cat states etc.? Of course one can consider entanglement outside the quantum optics, and it is important, but are there not many parts of QM which are also important? The one that comes to mind immediately is path-integral formulation of QM (which is probably also not in Messiah :-)).

    Please do not regard this as attack on your message, I sincerly just want to understand better.
     
  6. Jun 15, 2018 #5

    Demystifier

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    If you do that, then your knowledge of entanglement will be at a somewhat lower level than that of more traditional topics in QM.
     
  7. Jun 15, 2018 #6
    Hmm, I see. So I guess my question goes back to the most basic: what QM book should I read to get a comprehensive understanding of non relativistic QM? The goal is not to read an exaustive encyclopedic treatmen of QM. But I'd like to read a book containing everything a theoretical physicist should know about non relativistic QM. Is (Susskind)+(Messiah) good enough, or would you guys recomend another route?
     
  8. Jun 15, 2018 #7

    atyy

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    Messiah is excellent. One of its strengths is that it discusses interpretation correctly. It includes entanglement the old fashioned way, in which basis vectors for the Hilbert space of two particles are direct products of the basis vectors for each particle. This old fashioned knowledge was enough for Einstein, Podolsky and Rosen to write their famous EPR paper, and for Schroedinger to write his paper on entangelement. So you will be fine to start. However, I used Messiah only as a supplementary text. My own favourites are Landau and Lifshitz (very good on interpretation), French and Taylor (quick and easy), Griffiths (slow and easy), Shankar (lots of detailed explanation), Nielsen and Chuang (great overview of the formalism in its most modern form).

    What is missing in Messiah is the 1964 development by Bell showing that entanglement in quantum mechanics means that no local hidden variable theory can reproduce the results of quantum mechanics. However, after Messiah you should be able to pick that up easily by reading things like:
    http://www.drchinese.com/Bells_Theorem.htm
    http://drchinese.com/David/Bell_Theorem_Easy_Math.htm
    https://arxiv.org/abs/1303.3081

    However, being trained the old fashioned way, I still believe these topics which are now in modern textbooks are not as important as knowing how to calculate atomic and molecular spectra, chemical bonding, physical and electrical properties of materials etc. Bell himself said something like it was the fact that quantum mechanics explained so many things, that he was pretty sure that quantum mechanics would hold and that his inequality would be violated at spacelike separation. Schroedinger did not agree, but I believe his statements came earlier, before all the triumphs of quantum field theory, whereas Bell made important contributions to quantum field theory.
     
    Last edited: Jun 15, 2018
  9. Jun 17, 2018 #8

    kith

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    I agree with almost everything what atyy said. I'd like to add that I consider Messiah to be well-suited for self-study because he gives a lot of details.

    What you should know, however, is that he takes the approach of starting with wave mechanics first and only introduces the full mathematical machinery later on. If you are not a physicist, this may help to build intuition but it is a slower path to the conceptual heart of QM. Sakurai for example takes the complementary approach: he doesn't start with waves but with the most quantum-mechanical system there is (a spin 1/2-particle) and uses the full mathematics from the beginning. (But because he also barely covers wave mechanics later on, I wouldn't recommend him as a first text for self-study).
     
    Last edited: Jun 17, 2018
  10. Jun 17, 2018 #9

    kith

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    Thanks for the pointer! Indeed, he gives a very nice discussion.

    But there's one subtlety which I don't think is compatible with what we know today. About the possibility of hidden variables, he writes in chapter IV §16: "The wave function would not represent the objective state of the system under study; rather it would be a mathematical object containing the totality of information which one possesses on an incompletely known system." This combination of a purely statistical nature of the wave function with hidden variables seems to be in conflict with the PBR theorem to me.
     
  11. Jun 17, 2018 #10

    atyy

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    That's a very interesting point. Let's consider Bohmian Mechanics. In one frame of reference, the true absolute frame, the wave function is real. However, since the wave function in one frame (including state reduction) cannot be unitarily related to the wave function in another frame, doesn't that mean that except for the the wave function in the true absolute frame, the wave functions in all other frames cannot be real?

    That is my "counterexample" to PBR. But I am not sure if the counterexample if right. If the counterexample if right, then presumably there is some assumption in PBR that is a little too strong. PBR does make the assumption called "preparation independence", but I'm not sure if this is the same assumption violated by my Bohmian Mechanics example.
     
  12. Jun 18, 2018 #11

    Demystifier

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    @atyy The PBR theorem is about non-relativistic QM. As far as I know, there is no relativistic version of PBR theorem. But I wouldn't be surprised if one would find a theorem according to which reality of wave function in the PBR sense is incompatible with relativity. And that would not be very surprising since we already know that reality (in the Bell sense) is incompatible with locality.
     
  13. Jun 18, 2018 #12

    atyy

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    @Demystifier, would my comments make sense assuming only Galilean relativity?
     
  14. Jun 18, 2018 #13

    Demystifier

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    I'm afraid not, because wave function does not depend on the Galilean frame. Or more precisely, depends in a trivial way, so that they are all physically equivalent.
     
  15. Jun 19, 2018 at 11:28 AM #14

    atyy

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    @Demystifier, why doesn't PBR work for relativistic quantum theory?
     
  16. Jun 19, 2018 at 4:11 PM #15

    Demystifier

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    I think the main problem is not PBR as such. The main problem is how to define quantum state in a relativistic invariant form. In practical relativistic QFT one avoids this problem by turning attention to relativistic invariant S-matrix, but for PBR one must turn attention back to the state itself, at a finite time.
     
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