What is the connection between different interpretations of QM and QFT? Does QFT somehow render the study of QM foundations "pointless"?

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Summary:

I read something confusing about QFT rendering the various QM interpretations obsolete. It sounded weird and suspicious to me but I don't know anything about QFT so I don't really know. I'd appreciate it if someone could explain the connection between QM foundations and QFT.

Main Question or Discussion Point

Hey, applied maths and physics student here. I started wondering recently what the meaning of measurement was in quantum mechanics, and I remembered that I had once heard of the bohmian interpretation which challenged the impression I had so far (which was that hidden variables had been "refuted" or something) so I started researching the subject of foundations. I read some preliminary stuff and general overviews, and I'm also reading Bell's collected papers now, which are really interesting and helpful.

However, as I was reading various stuff online I saw some people say stuff like "it's not certain QFT needs an interpretation and it makes QM interpretations obsolete" and things like that. Now it definitely seemed really weird to me because I thought, OK, so QFT exists for all this time, and yet all these people kept looking into the various interpretations, would they do that if their study was made pointless by QFT? Then again, I started thinking, if QFT is indeed more foundational than QM, shouldn't the discussion be at least modified by its existence? I really don't know anything about QFT beyond the fact that it attempts to merge together QM and relativity, and that it lead to the development of the standard model, and it's gonna be a while before I know enough about it, so I'd really appreciate it if someone knowledgeable on the subject could give a general overview of whether that's true and what the connection between foundations of QM and QFT is.
 
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  • #2
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QFT deals with many particle systems and the measurement problem is less pronounced in such a context FAPP. But there are intricacies which are not obvious unless you are truly an expert. In short, the MP is still there. I am sure someone more knowledgeable will explain in more detail.
 
  • #3
Demystifier
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Quantum theory is a general framework, with many sub-theories such QM, QFT, string theory, loop quantum gravity, etc. The problem of interpretation (the measurement problem, ontology, etc.) is inherent to the quantum theory as a whole. This problem is most easily expressed in QM because it is the simplest of the sub-theories, but the problem is there in other sub-theories as well.
 
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  • #4
A. Neumaier
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Few particle quantum mechanics is well understood and only the measurement problem is a conundrum; thats why it attracts attention. But quantum mechanics is only an approximation to relativistic quantum field theory, hence the foundational problems of the former imply very little about the latter.

Relativistic quantum field theory (the standard model, say) has very different interpretational questions hardly discussed by anyone, since it is too difficult for most, and the experts have more pressing problems to solve.
 
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  • #5
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Quantum theory is a general framework, with many sub-theories such QM, QFT, string theory, loop quantum gravity, etc. The problem of interpretation (the measurement problem, ontology, etc.) is inherent to the quantum theory as a whole. This problem is most easily expressed in QM because it is the simplest of the sub-theories, but the problem is there in other sub-theories as well.
Thank you, that's what I would expect, but I couldn't be sure without asking.
 
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Few particle quantum mechaniics is well understood and only the measurement problem is a conundrum; thats why it attracts attention. But quantum mechanics is only an approximation to relativistic quantum field theory, hence the foundational problems of the former imply very little about the latter.

Relativistic quantum field theory (the standard model, say) has very different interpretational questons hardly discussed by anyone, since it is too difficult for most, and the experts have more pressing problems to solve.
Could you clarify that a bit? Are these interpretational questions somehow connected with those of non relativistic quantum mechanics? For instance the measurement problem. Are you saying that the solutions to the problems of the two frameworks are entirely separate, or at least that discussion for a solution to the QM problems is irrelevant when QFT is there, with its own distinct problems?

Also, could you or anyone else point me to something I could read as a sort of overview of the connections and foundational relationships between different theories of modern physics? Not something that goes in depth into all of them, just something that explains the basic issues posed.
 
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  • #7
A. Neumaier
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Could you clarify that a bit? Are these interpretational questions somehow connected with those of non relativistic quantum mechanics? For instance the measurement problem. Are you saying that the solutions to the problems of the two frameworks are entirely separate, or at least that discussion for a solution to the QM problems is irrelevant when QFT is there, with its own distinct problems?
Both quantum information theory (where the Hilbert space is finite-dimensional) and 2-particle quantum mechanics are nonrelativistic, and most entanglement stuff is expressed in these terms. It ignores the problems of particle creation and annihilation, which require a different mathematical basis, namely relativistic QFT. Thus the mathematical implications of the mathematics of QM are invalid in relativistic QFT.
For example, the concept of interacting particles in relativistic QFT is approximate only, and apart from my own work I don't know any discussion of how this affects interpretation issues. For example, Bohmian mechanics does not generalize to interacting relativistic QFT.
Also, could you or anyone else point me to something I could read as a sort of overview of the connections and foundational relationships between different theories of modern physics? Not something that goes in depth into all of them, just something that explains the basic issues posed.
Usually, foundational studies concentrate on one particular setting for one particular area. The bridge between different theories is treated (on a case by case basis, separate for each pair of theories) by formal limits only, and the interpretations are related by handwaving only.
 
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Both quantum information theory (where the Hilbert space is finite-dimensional) and 2-particle quantum mechanics are nonrelativistic, and most entanglement stuff is expressed in these terms. It ignores the problems of particle creation and annihilation, which require a different mathematical basis, namely relativistic QFT. Thus the mathematical implications of the mathematics of QM are invalid in relativistic QFT.
For example, the concept of interacting particles in relativistic QFT is approximate only, and apart from my own work I don't know any discussion of how this affects interpretation issues. For example, Bohmian mechanics does not generalize to interacting relativistic QFT.

Usually, foundational studies concentrate on one particular setting for one paticular area. The bridge between different theories is treated (on a case by case basis, separate for each pair of theories) by formal limits only, and the interpretations are related by handwaving only.
Alright, so if I am not mistaken what you are saying contradicts Demystifier's claims. I'd like to hear what they'd have to say on this too.
 
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  • #9
Demystifier
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For example, Bohmian mechanics does not generalize to interacting relativistic QFT.
That is definitely not true. There are many papers that propose various ways to generalize BM to interacting relativistic QFT. You would probably object that those proposals are not mathematically rigorous, which might be true, but the same can be objected on standard non-Bohmian interacting relativistic QFT.
 
  • #10
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That is definitely not true. There are many papers that propose various ways to generalize BM to interacting relativistic QFT. You would probably object that those proposals are not mathematically rigorous, which might be true, but the same can be objected on standard non-Bohmian interacting relativistic QFT.
Did I accidentally open some kind of can of worms here? That's what I'm sensing... I don't mind, debates are fun I guess, but I'll probably just sit back and watch instead of saying something uninformed.

Anyways, after I'm done with Bell's papers, I'd like to maybe delve a liiittle bit further into the issue of quantum foundations and also maybe also start looking into QFT a bit (although I think I need to learn GR before that). What do you or anyone else reading this suggest for that? Sorry if it's kind of a general, non specific question.
 
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  • #11
A. Neumaier
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That is definitely not true. There are many papers that propose various ways to generalize BM to interacting relativistic QFT. You would probably object that those proposals are not mathematically rigorous, which might be true, but the same can be objected on standard non-Bohmian interacting relativistic QFT.
There are proposals, but they
  1. do not reproduce standard QED (let alone the standard model), not even nonrigorously,
  2. contradict the standard Bohmian particle setting hence are not generalizations of BM but only analogues.
  3. contradict each other.
 
  • #12
PeroK
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Anyways, after I'm done with Bell's papers, I'd like to maybe delve a liiittle bit further into the issue of quantum foundations and also maybe also start looking into QFT a bit (although I think I need to learn GR before that). What do you or anyone else reading this suggest for that? Sorry if it's kind of a general, non specific question.
In terms of looking at QFT, I guess you mean learn SR? QFT and GR are not integrated yet.

QFT is an advanced and highly mathematical topic. Probably you need some to learn some relativistic QM first.
 
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A. Neumaier
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start looking into QFT a bit (although I think I need to learn GR before that). What do you or anyone else reading this suggest for that?
QFT is an advanced and highly mathematical topic. Probably you need some to learn some relativistic QM first.
Relativistic QM is poor introductory reading for learning QFT since one must unlearn for QFT almost everything to be learnt from relativistic QM. Better start reading a book like Zeh, and then move to Weinberg.
 
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  • #14
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Relativistic QM is poor introductory reading for learning QFT since one must unlearn for QFT almost everything to be learnt from relativistic QM.
Perhaps, but it's hard to see what else there is then. It's just all or nothing?
 
  • #15
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Perhaps, but it's hard to see what else there is then. It's just all or nothing?
No.

Nonrelativistic QFT with second quantization (for example via Linda Reichl's book on statistical physics) plus classical special relativity with the Poincare group pave the way to the latter's irreducible representations with nonnegative mass, which gives the 1-particle spaces and the associated free fields. Then interactions can be introduced by ad hoc rules.
 
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  • #16
atyy
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Alright, so if I am not mistaken what you are saying contradicts Demystifier's claims. I'd like to hear what they'd have to say on this too.
Demystifier is correct. All of QT has the measurement problem, because all of QT uses the Born rule which says "When a measurement is made, an outcome is obtain with probability ...." - so one has to decide "when a measurement is made".

A.Neumaier has a different view because he has his own interpretation which he claims solves the measurement problem (I haven't studied it well enough to understand his proposal).
 
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  • #17
A. Neumaier
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Demystifier is correct. All of QT has the measurement problem, because all of QT uses the Born rule which says "When a measurement is made, an outcome is obtain with probability ...." - so one has to decide "when a measurement is made".
But he is not correct in claiming that Bohmian mechanics generalizes to interacting relativisic QFT including the standard model.
 
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  • #18
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In terms of looking at QFT, I guess you mean learn SR? QFT and GR are not integrated yet.

QFT is an advanced and highly mathematical topic. Probably you need some to learn some relativistic QM first.
Where do I do that? It interests me and I can't really wait until we learn that in my uni because I'm not even sure I'm gonna take the physics course instead of the applied math course.
EDIT: Oh, I just looked at the other posts...
 
  • #19
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In terms of looking at QFT, I guess you mean learn SR? QFT and GR are not integrated yet.
I read somewhere that some mathematical techniques used in GR are useful for QFT and that learning GR also gives you a better overview of the issues still posed. I already know some SR but none of the advanced stuff. Whatever, guess I could download some more advanced SR textbook.
 
  • #20
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I read somewhere that some mathematical techniques used in GR are useful for QFT and that learning GR also gives you a better overview of the issues still posed. I already know some SR but none of the advanced stuff. Whatever, guess I could download some more advanced SR textbook.
From SR you just need the basics including Lorentz transformations and the Poincare group.
You also need to know some classical field theory, including the vector potential of electrodynamics.

You don't need anything from GR; it does not help to understand QFT at all. GR is only needed to understand QFT beyond the standard model, assuming that you know already standard QFT.
 
  • #21
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There are proposals, but they
  1. do not reproduce standard QED (let alone the standard model), not even nonrigorously,
  2. contradict the standard Bohmian particle setting hence are not generalizations of BM but only analogues.
  3. contradict each other.
1. It's not so much about Bohmian interpretation as it is about theories with a fundamental cutoff. Anyway, you and me discussed it a lot and agreed to disagree.

2. and 3. This contradiction is not such a big problem. I would compare it with the fact that "modern" quantum theory of Heisenberg, Schrodinger etc. contradicts old quantum theory (Bohr's model of the hydrogen atom), yet Bohr's model is considered an important step in the development of quantum theory.
 
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  • #22
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From SR you just need the basics including Lorentz transformations and the Poincare group.
You also need to know some classical field theory, including the vector potential of electrodynamics.

You don't need anything from GR; it does not help to understand QFT at all. GR is only needed to understand QFT beyond the standard model, assuming that you know already standard QFT.
Well then, I more or less know all that stuff...
 
  • #25
Demystifier
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You don't need anything from GR; it does not help to understand QFT at all.
Unless you deal with AdS/CFT.
 
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