Exploring Foundations of Quantum Mechanics & QFT

[AndreasC]

TL;DR 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.

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 going to 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.

 

[EPR]

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.

 

[Demystifier]

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.

 

[A. Neumaier]

Few particle quantum mechanics is well understood and only the measurement problem is a conundrum; that's 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.

 

[AndreasC]

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.

 

[AndreasC]

Few particle quantum mechaniics is well understood and only the measurement problem is a conundrum; that's 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.

 

[A. Neumaier]

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.

 

[AndreasC]

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.

 

[Demystifier]

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.

 

[AndreasC]

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.

 

[A. Neumaier]

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.

 

[PeroK]

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.

 

[A. Neumaier]

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 learned from relativistic QM. Better start reading a book like Zeh, and then move to Weinberg.

 

[PeroK]

Relativistic QM is poor introductory reading for learning QFT since one must unlearn for QFT almost everything to be learned from relativistic QM.

Perhaps, but it's hard to see what else there is then. It's just all or nothing?

 

[A. Neumaier]

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.

 

[atyy]

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).

 

[A. Neumaier]

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.

 

[AndreasC]

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 going to take the physics course instead of the applied math course.
EDIT: Oh, I just looked at the other posts...

 

[AndreasC]

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.

 

[A. Neumaier]

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.

 

[Demystifier]

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.

 

[AndreasC]

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...

 

[PeroK]

Well then, I more or less know all that stuff...

David Tong's notes are available here, if you want to get started:

https://www.damtp.cam.ac.uk/user/tong/qft/qft.pdf

 

[AndreasC]

David Tong's notes are available here, if you want to get started:

https://www.damtp.cam.ac.uk/user/tong/qft/qft.pdf

Τhanks, I'll check them out!

 

[Demystifier]

You don't need anything from GR; it does not help to understand QFT at all.

Unless you deal with AdS/CFT.

 

[Elias1960]

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.

Wrong. Bohmian mechanics generalizes nicely to interacting relativistic QFT.

The standard reference to Bohmian QFT is

Bohm.D., Hiley, B.J., Kaloyerou, P.N. (1987). An ontological basis for the quantum theory, Phys. Reports 144(6), 321-375

With the field ontology, that means, the fields $q = \{\varphi(x)\} \in Q \cong C^\infty(\mathbb{R}^3)$ defining the configuration, the interaction terms are simply part of the classical potential $V(q)$, something one does not have to care at all.

Of course, one should be aware that QFT is simply not a well-defined theory. The only well-defined theories in the whole game are the regularizations. And even most regularizations make no sense as well-defined quantum theories.

All what matters is that there has to be at least one regularization which is also a well-defined quantum theory. For this purpose, I recommend lattice regularizations on a large cube with periodic boundary conditions. Such a lattice theory has already a finite number of degrees of freedom, and the usual scheme works without problems. (Or, more accurate in the context of the question, with exactly the same problems as non-relativistic QM.)

So, the generalization of dBB to the part of QFT which is mathematically well-defined (which is not the limit of the lattice spacing going to zero) is unproblematic.

If one interprets QFT as an effective field theory, so that it does not have to be well-defined for arbitrary small distances, but only for distances larger than some critical distance, there is no point in considering this limit at all, thus, everything is fine.

If one thinks that the relativistic and gauge symmetries are somehow fundamental, then one has some problem with such lattice approximations, given that they have no relativistic symmetry and allow gauge symmetry only for vector gauge fields. (Once the observable massless gauge fields, QCD and EM, are vector gauge fields, the last is no problem too. The massive gauge fields are non-renormalizable, but as effective field theories they would be fine too, as well as gravity.) But the idea that relativistic symmetry is fundamental is not compatible with dBB theory (as well as with any other realist interpretation because of Bell's theorem) anyway. So, with QFT understood as an effective field theory dBB has no problems.

 

[A. Neumaier]

Wrong. Bohmian mechanics generalizes nicely to interacting relativistic QFT.

The standard reference to Bohmian QFT is

Bohm.D., Hiley, B.J., Kaloyerou, P.N. (1987). An ontological basis for the quantum theory, Phys. Reports 144(6), 321-375

With the field ontology, that means, the fields $q = \{\varphi(x)\} \in Q \cong C^\infty(\mathbb{R}^3)$ defining the configuration, the interaction terms are simply part of the classical potential $V(q)$, something one does not have to care at all.

QED and QCD have no such field, and no such classical potential. The vector potentials figuring in the action are only defined up to gauge transformations.

Moreover, the ontology of the construction you suggest is flatly contradicting the particle ontology of nonrelativistic Bohmian mechanics. Thus your construction is not a generalization of nonrelativistic Bohmian mechanics but a completely different ontology.

 

[Elias1960]

QED and QCD have no such field, and no such classical potential. The vector potentials figuring in the action are only defined up to gauge transformations.

LOL. Except that the EM potentials as well as the most important gauge conditions have been worked out and became part of mainstream EM theory long before QM was developed. And the first time EM was handled by dBB theory was Bohm's original paper part II:

Bohm, D. (1952). A suggested interpretation of the quantum theory in terms of "hidden" variables II, Phys.Rev. 85(2), 180-193

Moreover, the ontology of the construction you suggest is flatly contradicting the particle ontology of nonrelativistic Bohmian mechanics. Thus your construction is not a generalization of nonrelativistic Bohmian mechanics but a completely different ontology.

Bohm, Hiley and Kaloyerou thought differently, and they have the priority here, see the paper I have given. By the way, the very classical configuration space Q is, of course, a generalization of various particular examples of configuration spaces like $\mathbb{R}^{3n}$ for n point particles. A very well-known and I think quite old too, something one can presuppose as well-known by everybody without further mentioning it. I always preferred to present dBB theory as a theory for general configuration spaces, and never thought of this as a nontrivial generalization.

After this, we simply use the configuration space of the field theories. So, that's only the application of a simple, well-known, and straightforward generalization - the configuration space - to the particular case of field theory.

Moreover, this would not really save your claim

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.

Because the main point remains. Your wording "to interacting relativistic QFT" suggests a "from non-interacting relativistic QFT" (else you could have simply written "to relativistic QFT"). And once you look at the established Bohmian version of non-interacting relativistic QFT, either looking at the original paper or at the paper referenced above, adding interactions is not an issue at all. It is simply a replacement of the potential V(q). So, for the Bohmian interpretation it is well-known apart from your own work that it is not an issue at all.

 

[A. Neumaier]

I always preferred to present dBB theory as a theory for general configuration spaces, and never thought of this as a nontrivial generalization.

So in your view, different quantum models with different configuratio spaces have different ontologies. This makes ontology model dependent - very strange for supposed realistic foundations, where there should be only one reality...

 

[Elias1960]

So in your view, different quantum models with different configuratio spaces have different ontologies. This makes ontology model dependent - very strange for supposed realistic foundations, where there should be only one reality...

Of course, each theory, model and so on proposes a different model of reality. What is strange there? Do you think realistic philosophy should present a universal model of reality independent of the particular theories?

I think it is straightforward and obvious: It is the realistic theory which defines what really exists. Of course, among the many theories proposing different ideas about what is real only one will be the true theory. (If we have a chance to identify this true theory correctly is far from clear, it may be impossible - but so what, such is life.)

 

[A. Neumaier]

Of course, each theory, model and so on proposes a different model of reality. What is strange there? Do you think realistic philosophy should present a universal model of reality independent of the particular theories?

I think it is straightforward and obvious: It is the realistic theory which defines what really exists.

This makes sense only if there is only one realistic theory for everything.

To say that according to nonrelativistic Bohmian mechanics, particles really exist but fields don't, but according to relativistic Bohmian mechanics, fields really exist but particles don't, and the same person adhering to both reality views. With such a multiplicity of realities, nothing really exists for this person.

That's why a proper ontology must take a definite stance on which particular view of everything it takes as being real.

 

[Demystifier]

To say that according to nonrelativistic Bohmian mechanics, particles really exist but fields don't, but according to relativistic Bohmian mechanics, fields really exist but particles don't, and the same person adhering to both reality views. With such a multiplicity of realities, nothing really exists for this person.

Ontology is relative to theory, i.e. ontology says what exists according to a given theory. In IBM microscopic ontology is just an auxiliary thinking tool (not an absolute truth) which helps to gain some intuition about quantum processes.

 

[A. Neumaier]

Ontology is relative to theory, i.e. ontology says what exists according to a given theory. In IBM microscopic ontology is just an auxiliary thinking tool (not an absolute truth) which helps to gain some intuition about quantum processes.

But ontology in Bohmian mechanics is also relative to which fundamental configuration space is assumed for the universe. Which is strange since different configuration spaces (N-particles or fields) imply very different notions of what really exists.

An auxiliary thining tool that just helps to gain some intuition about quantum processes is not an ontology but a crutch. Most phycisists do not need such a crutch and still have enough intuition about quantum processes to turn them into technolocical successes.

 

[Elias1960]

This makes sense only if there is only one realistic theory for everything.

No, there can be several, but only one of them can be the true one. And once to find out which is the true one is quite difficult, we can as well live with considering several different candidates.

To say that according to nonrelativistic Bohmian mechanics, particles really exist but fields don't, but according to relativistic Bohmian mechanics, fields really exist but particles don't, and the same person adhering to both reality views. With such a multiplicity of realities, nothing really exists for this person.

No. This person is simply not certain which of the theories is correct.

The police tries to find a murderer. One policeman thinks the murderer is a white man, another thinks it is a black women. The chief is not sure and considers both theories. Does it follow that the murderer does not really exist for the chief?

That's why a proper ontology must take a definite stance on which particular view of everything it takes as being real.

Yes, and every particular theory will take such a definite stance. Different theories take different stances, that's all.

But ontology in Bohmian mechanics is also relative to which fundamental configuration space is assumed for the universe. Which is strange since different configuration spaces (N-particles or fields) imply very different notions of what really exists.

It is natural. Quantum theory is not a particular theory, but a general scheme. And the same holds for its interpretations too. dBB is also a general scheme. In the same way as in classical mechanics the Lagrange formalism or the Hamilton formalism are general schemes. That means, they all can be applied to very different theories about what is real.

And it is quite natural to consider the question which of the two possibilities - field ontology or many particle ontology - is the more plausible candidate for describing reality. I think there are very good arguments in favor of the field ontology.

 

[A. Neumaier]

This person is simply not certain which of the theories is correct.

Which means that what really exists is uncertain (and as you inply, unknowable) . But then the notion of existence is a matter of speculation only (there is no way to decide), and one can as well do without it.