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

[FourEyedRaven]

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 But, even though it was considered a Bible of quantum mechanics until recently, people consider it outdated now.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.

 

[George Jones]

So, what are the handicaps of using this book to go deeper into QM?

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

 

[FourEyedRaven]

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.

 

[vsv86]

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

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 sincerely just want to understand better.

 

[Demystifier]

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?

If you do that, then your knowledge of entanglement will be at a somewhat lower level than that of more traditional topics in QM.

 

[FourEyedRaven]

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 recommend another route?

 

[atyy]

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.

 

[kith]

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).

 

[kith]

Messiah is excellent. One of its strengths is that it discusses interpretation correctly.

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.

 

[atyy]

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.

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.

 

[Demystifier]

@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.

 

[atyy]

@Demystifier, would my comments make sense assuming only Galilean relativity?

 

[Demystifier]

@Demystifier, would my comments make sense assuming only Galilean relativity?

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.

 

[atyy]

@Demystifier, why doesn't PBR work for relativistic quantum theory?

 

[Demystifier]

@Demystifier, why doesn't PBR work for relativistic quantum theory?

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.

 

[zmth]

Don't need to be concerned with the more recent and advanced subjects like entanglement at this time as you will be kind of 'left in the woods'. It is more important to have a good mathematical functions of the basics like very good understanding of eigenfunctions, eigenvalues, spin, electron antisymmetry etc. and even group theory in general before moving on to things such as entanglement. Messiah is a good text. Also I liked the classics such as by L. Schiff,Rojansky , Pauling and Wilson etc.and possibly Bohm for hidden variables. All in all probably my favorite is by Schiff. You really need to have a very good understanding of all those as things such as entanglement in itself assumes you know very well the basics and if you go to hurriedly into entanglement you will not really understand it either.

 

[FourEyedRaven]

If I were to complement Messiah with these two books, would it compensate the missing entanglement parts from Messiah?

"Foundations of Quantum Mechanics", by Norsen
https://www.amazon.com/dp/3319658662/?tag=pfamazon01-20

"The Physics of Quantum Information", by Bouwmeester, Ekert, and Zeilinger
https://www.amazon.com/dp/3540667784/?tag=pfamazon01-20

Norsen is about interpretations of QM and covers entanglement and Bell's theorem. The other book is about the physics of quantum information, cryptography, teleportation, and computation. Since I want to learn interpretation of QM and quantum information anyway, maybe these two books are enough to compensate?

 

[yucheng]

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.

Hi atyy. Other than Messiah, are there other textbooks that discuss such practical calculations? Or if one is interested in these topics, it would be better to delve into books on quantum chemistry? Thanks!

 

[yucheng]

Messiah is excellent. One of its strengths is that it discusses interpretation correctly.

Are there books that do not discuss interpretation correctly?

 

[bob012345]

If I were to complement Messiah with these two books, would it compensate the missing entanglement parts from Messiah?

"Foundations of Quantum Mechanics", by Norsen
https://www.amazon.com/dp/3319658662/?tag=pfamazon01-20

"The Physics of Quantum Information", by Bouwmeester, Ekert, and Zeilinger
https://www.amazon.com/dp/3540667784/?tag=pfamazon01-20

Norsen is about interpretations of QM and covers entanglement and Bell's theorem. The other book is about the physics of quantum information, cryptography, teleportation, and computation. Since I want to learn interpretation of QM and quantum information anyway, maybe these two books are enough to compensate?

If you are a serious student as it seems you are, I don't see how you can go wrong if you choose these two books (which I have no knowledge of at all) because whether they are the absolute 'best' choices or not, your study will eventually cover more and more questions and other resources to fill in any gaps.

Essentially, in my view, if you study them then they are good books for you to start with.

 

[vanhees71]

Are there books that do not discuss interpretation correctly?

"Interpretation" is highly overrated. First learn the no-nonsense physics. You can bother with so-called "philosophy" after retirement .

 

[andresB]

There is almost nothing wrong with Messiah. Quite often when people ask a question in the forums I just open Messiah and the answer is there.

Having said that, (1) the last chapters on relativistic QM are probably too outdated, and it's better to go for a modern treatment of QFT, (2) the book would have benefited from a much larger set of problems with a wider level of difficulty.

 

[dextercioby]

@andresB. Yes, but even the last chapter on relativistic QM is worth reading. I do not have it handy right now, but I recall being written at the end of the '50s, when the x4=ict was still the norm in relativity and qft texts. Messiah used +---- metric which makes it in line with most books on QFT nowadays (notable exception Weinberg). The first to use the +---- metric in a comprehensive QFT text were Schweber and Bethe in their 1955 "The theory of mesons" (if I remember the name correctly) which evolved into Schweber's masterpiece on QFT in 1961. So in a good condition, this book I think it is still worth buying.

 

[yucheng]

"Interpretation" is highly overrated. First learn the no-nonsense physics. You can bother with so-called "philosophy" after retirement .

I had the that suspicion that skipping the chapter on "Interpretations" in Messiah is worthwhile $: )$ but still I'll need the statistical interpretation part.

 

[vanhees71]

Indeed, but that's all you need (and don't take the "collapse postulate" too seriously).

 

[Demystifier]

You can bother with so-called "philosophy" after retirement .

Like you?

Philosophy of physics is too important to be left to philosophers and the retired.

 

[vanhees71]

My philosophy is to fight philosophy of physics ;-).

 

[Lord Jestocost]

To my mind, physics is indeed in no need for philosophy. I think, however, that it is a general psychological fact that our beliefs often precede and dominate our rational arguments. Even physicists are not free of that. Anthony J. Leggett puts the value of philosophy for physicists in a nutshell ( (PDF) An Interview with Sir Anthony Leggett - ResearchGate ):

“Yes, it was very useful. In some sense, all of it was useful and particularly useful was the philosophy part. I think that if you go through a course of analytical philosophy – I’m very conscious that philosophy means different things in different parts of the world – but in the Anglo-Saxon tradition, a degree in philosophy is very highly analytical, and if you go through it you do became much more conscious of the implicit assumptions that you’re making in your work. I do feel that one benefit I had from this is that – more than a lot of my colleagues in physics who hadn’t had this kind experience – I’m conscious of the implicit assumptions I’m making.” [in bold by LJ]