Quantum mechanics: Myths and facts

  • #26
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I don't think that i d/dp is a position operator for massive relativistic particles.

Isn't there a problem because the states live on a mass hyberboloid in spacetime?
True, because of the measure dp/E(p) ; E(p) = sqrt(p^2 + m^2), id/dp is not hermitian. This is corrected by
id/dp - i/2 p/(p^2 + m^2) = 1/2 (id/dp + conjugate(i d/dp ) ).

Cheers,

Careful
 
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  • #27
Demystifier
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What's missing in the Physicist's approach to group theory for definition of particle states, that's necessary, and apparently neglected by Weinberg?
Well, I think that there is something missing. See Sec. VIII.C in my "myths and facts" paper. Essentially, it is not clear how to reproduce the (experimentally confirmed) probabilistic interpretation of nonrelativistic first quantization in the configuration space.
 
  • #28
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Well, I think that there is something missing. See Sec. VIII.C in my "myths and facts" paper. Essentially, it is not clear how to reproduce the (experimentally confirmed) probabilistic interpretation of nonrelativistic first quantization in the configuration space.

Experiments never confirm a theory, the latter can only pass experimental test.
 
  • #29
reilly
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QFT is simply a form of ordinary QM that is particularly conducive to problems in which numbers of particles are dynamical variables. Hence the usual apparatus of the probability interpretation is immediately available for QFT. Simple minded? Perhaps, but that approach seems to work just fine, as is discussed in countless books and papers. To suggest that the consensus approach, of 70-80 years, to many-body problems is based on an incorrect interpretation of number operators requires a very detailed and logically presented, blow-by-blow demonstration of why, and why it's important.

Also, it seems to me that many issues of a field-oriented QFT can be handled nicely by coherent states, which form a nice bridge between fields and Fock Space particles.

I can't figure out the connection between your 'interpretation claim" and group theory. As Weinberg demonstrates the group theory stuff is about as controversial as Angular Momentum theory -- clever but very standard.

You may be right, but ......
Regards,
Reilly Atkinson
 
  • #30
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QFT is simply a form of ordinary QM that is particularly conducive to problems in which numbers of particles are dynamical variables. Hence the usual apparatus of the probability interpretation is immediately available for QFT. Simple minded? Perhaps, but that approach seems to work just fine, as is discussed in countless books and papers. To suggest that the consensus approach, of 70-80 years, to many-body problems is based on an incorrect interpretation of number operators requires a very detailed and logically presented, blow-by-blow demonstration of why, and why it's important.

Also, it seems to me that many issues of a field-oriented QFT can be handled nicely by coherent states, which form a nice bridge between fields and Fock Space particles.

I can't figure out the connection between your 'interpretation claim" and group theory. As Weinberg demonstrates the group theory stuff is about as controversial as Angular Momentum theory -- clever but very standard.

You may be right, but ......
Regards,
Reilly Atkinson
The ``interpretation claim'' is very simple : in particle physics, you look for unitary representations of groups on Hilbert spaces HILB. Now, this is only meaningful when the real multiparticle dynamics is indeed given by a well defined, densly defined, symmetric operator on HILB (in either you have to take the multiparticle wave as well as the Schroedinger equation as adequate). Nobody says that you need to interpret angular momentum in this way (in either as a unitary operator on HILB), I can speak as well about angular momentum in Einstein Cartan and MacDowell Mansouri theory (classical field theories) without any need for tensor product representations (only the defining representation is used here). Moreover, there is no miracle happening as to why QFT gives very accurate answers : (a) the classical theory does it already for you (that is, first quantized matter and classical gauge fields) (b) QFT is a ``linear approximation´´ which should work fine (given periodic boundary conditions for fields) given that radiative corrections are usually small anyway. Therefore, to maintain that the only reason not to touch it is its experimental accuracy, despite of problems from the theory side (it is not a theory yet), seems like putting your head in quicksand.

Likewise, I could say that QFT received many criticisms from distinguished scientists (including nobels), that it was the concensus for at least 2000 years that the earth was the center of the universe etc.... (so lets not make ``social'' comments, they are usually worthless anyway). So, you see what can happen to very standard things ; Weinberg starts from the assumption that multi particle QM is fine, something which I argued only to be true in certain circumstances.

And of course I am right ; actually if you really want to study something interesting you might listen better to Zbyszek : after many years of thought about unifying GR and QM, I arrived at pretty similar (albeit not exactly the same) conclusions.

Careful
 
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  • #31
reilly
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Careful -- If you are right, then write a paper for Phys Rev. If you are right, then a revolution in particle physics will certainly take place. By the way, you'll have to show that your notions lead to solid numbers for the anomolous magnetic moment of the electron, the Lamb Shift, and all the other QED computations. And, you will need to bring something new to the table, otherwise why bother to change -- unless your approach leads to simpler ways to compute, or other benefits.

As many have demonstrated, including me in my doctoral thesis, radiative corrections need not be small.

There are many reasons to be wary of QFT, but so far it is still the best game in town. If you can do better, let us see better.
Regards,
Reilly Atkinson
 
  • #32
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A common understanding of quantum mechanics (QM) among students and practical users is often plagued by a number of "myths", that is, widely accepted claims on which there is not really a general consensus among experts in foundations of QM. These myths include wave-particle duality, time-energy uncertainty relation, fundamental randomness, the absence of measurement-independent reality, locality of QM, nonlocality of QM, the existence of well-defined relativistic QM, the claims that quantum field theory (QFT) solves the problems of relativistic QM or that QFT is a theory of particles, as well as myths on black-hole entropy. The fact is that the existence of various theoretical and interpretational ambiguities underlying these myths does not yet allow us to accept them as proven facts. In
http://arxiv.org/abs/quant-ph/0609163
I review the main arguments and counterarguments lying behind these myths and conclude that QM is still a not-yet-completely-understood theory open to further fundamental research.
If someone is interested, now a revised version accepted for publication is also available. :smile:
 
  • #33
DrChinese
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If someone is interested, now a revised version accepted for publication is also available. :smile:
Demystifier,

That is a very cool paper! You are really covering a lot of ground.

Would I be wrong to assume that you lean a bit towards the Bohmian side?

-DrC
 
  • #34
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If someone is interested, now a revised version accepted for publication is also available. :smile:
I am new to this forum, so thanks for reposting to the topic to put it back on the radar.

I glanced at the body of your paper... and, it is more interesting than I had thought. (So, there is the danger of your abstract summary; as soon as I hit your words "these myths include" and then you list almost everything, it seemed it could not be a serious paper. Just a note, not a criticism.)

But, I'll set aside some time to read it and post any question/comments here.
 
  • #35
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Ok, had the chance to look it over, but not read all of it. A few short comments (I'm short on time):

1. In general, nicely done! Your points seem valid.

2. I think this type of broadly conclusive analysis is worthwhile, but

3. You're going to get "beat up", because

4. You are covering too much important territory at once.

I realize that the length of the paper is necessary to prove your point. But, the shorter the paper, the better (the more people who will read it.)

Solutions: Perhaps break it into multiple papers in a related series? Or, expand it into a book?

Good luck. Keep at it.

PS: there are a few typos remaining.
 
  • #36
Demystifier
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Demystifier,

That is a very cool paper! You are really covering a lot of ground.

Would I be wrong to assume that you lean a bit towards the Bohmian side?

-DrC
You would not be wrong. In fact, I am a Bohmian.
 
  • #37
Demystifier
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4. You are covering too much important territory at once.

I realize that the length of the paper is necessary to prove your point. But, the shorter the paper, the better (the more people who will read it.)

Solutions: Perhaps break it into multiple papers in a related series? Or, expand it into a book?

PS: there are a few typos remaining.
Well, a number of short papers discussing different aspects of QM already exists. I wanted to do something new. Perhaps one day I will write a book, but at the moment it is too early for that. In addition, the number of downloads is already quite big, much bigger than that of related shorter papers. Thus, it seems that the paper is read a lot, despite its length (or maybe just because of its length, which makes it look more serious).

Can you point where these typos are? :smile:
 
  • #38
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(So, there is the danger of your abstract summary; as soon as I hit your words "these myths include" and then you list almost everything, it seemed it could not be a serious paper. Just a note, not a criticism.)
The paper was aimed to be a sort of supplement to standard textbooks, to cover the points that are usually omitted in them. That is why it includes "almost everything".
 

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