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

• I
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.

weirdoguy and PeroK
A. Neumaier
2019 Award
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.

PeterDonis
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
2019 Award
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....

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
2019 Award
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
Gold Member
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
2019 Award
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.

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
2019 Award
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.

Last edited:
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.
No. It is simply the same situation as with physical theories in general. The really true theory about everything is yet unknown. Together with this theory, it is also unknown what really exists. Potentially we may fail to identify the really true theory about everything. And, as a consequence, we will also fail to identify what really exists. (This is not unknowable, that would be too strong, but we can never be certain that we have identified the correct one if we have identified such a candidate for this.)

But this does not mean that it is speculation only. The theory of what really exists is part of the theory of everything, which is a physical theory which makes testable predictions.

Can one live with theories which are not realistic? As long as they make predictions, one can. If the predictions made are supported by empirical evidence, one can live with astrology too. But realistic theories have some some additional structure, the ontology, and some restrictions following from this, say, the evolution equations for really existing things should be well-defined and should not depend on things which do not really exist. Such restrictions for realistic theories are useful as guides for theory development. Compare this with the Lagrange formalism. Can classical theories survive without a Lagrange formalism? Certainly. Many theories don't have a Lagrange formalism. But if there exists a possibility, one will not simply ignore this, but prefer the variant which has a Lagrange formalism. Same here. We can live with theories which are not realistic, like Copenhagen QT. But if there is a realistic interpretation, we will prefer it.

A. Neumaier
2019 Award
what really exists. (This is not unknowable
How would you objectively decide whether you know?
But this does not mean that it is speculation only. The theory of what really exists is part of the theory of everything, which is a physical theory which makes testable predictions.
What are the testable predictions of your Bohmian field ontology? Testable is only the part that is in the QFT books, and that has nothing to do with Bohmian mechanics.
But realistic theories have some some additional structure, the ontology, and some restrictions following from this [...] Such restrictions for realistic theories are useful as guides for theory development.
Which such restriction follow from your Bohmian field ontology? I don't know any that would have guided quantum field theory development.

Demystifier
Gold Member
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.
I agree. Most physicists don't need the Bohmian crutch. But all physicists need some crutch, i.e. they need some more-or-less intuitive interpretation to have in mind because, in reality, no human physicist is a shut-up-and-calculate machine. So all physicists need a crutch, while physicists who construct various interpretations in general, and versions of Bohmian mechanics in particular, are crutch designers. Most physicists are satisfied with their old crutch and are not interested in learning how to use new ones, but those who learn how to use some new crutch (Bohmian or otherwise) would never change it for the old ones.

Last edited:
PeterDonis
Mentor
2019 Award
The theory of what really exists is part of the theory of everything, which is a physical theory which makes testable predictions.
I don't see how you can make this claim without knowing the theory of everything, which nobody does.

How would you objectively decide whether you know?
I would not, I do not even plan to. Because I have some basic education in philosophy (scientific methodology) which tells me that we cannot verify our theories. We can only falsify them. Everything else (simplicity, predictive power, beauty, compatibility with principles like causality, realisms, and so on) may be useful as guiding my choices, but cannot be decisive. So I know that I cannot objectively find out if the theory I actually prefer is true.
What are the testable predictions of your Bohmian field ontology? Testable is only the part that is in the QFT books, and that has nothing to do with Bohmian mechanics.
No, it is also part of Bohmian mechanics. All the quantum predictions follow from Bohmian mechanics too.
Which such restriction follow from your Bohmian field ontology? I don't know any that would have guided quantum field theory development.
Of course, once the community which developed the SM has not been guided by BFT, but thoroughly ignored it, it would be very strange if the QFT development would have been nonetheless guided by BFT principles.

What would have plausibly changed if BFT would have been accepted much earlier? Once there is a real configuration space trajectory ##q(t)\in Q##, the average velocity which is part of the continuity equation
$$\partial_t \rho + \nabla (\rho \vec{v}) = 0$$
which follows from the Schroedinger equation is something really causally influencing q. Once this requires FTL causal influences, one would have started to care about the possibility of some hidden preferred frame, without waiting many years for Bell's theorem and then even more years for all the experiments and even then not accepting the straightforward consequence (and rejecting realism and causality and embracing ... like many worlds). What would have been reached in this direction is, of course, unclear.

But the effective field theory paradigm could have been reached easier. To consider the cutoff at some critical length as a sort of approximation for a real more fundamental theory which really cuts higher momentum has the problem that such a cutoff does not have Lorentz symmetry. So to accept this would require to give up relativistic dreams.

I don't see how you can make this claim without knowing the theory of everything, which nobody does.
If the theory of everything does not make empirical predictions, nobody will accept it as a physical theory, even less as a theory of everything. (Or at least I hope so, the history of string theory suggests that this may be not the case.) And that it defines an ontology follows from realism. Else, realism would be wrong. In the context of my answer, realism was presupposed.

A. Neumaier
2019 Award
No, it is also part of Bohmian mechanics. All the quantum predictions follow from Bohmian mechanics too.
But all these predictions guided theorists without any need of Bohmian mechanics. So there is no additional guiding available from maintaining a Bohmian view. Occam's razor therefore does away with it.

Once there is a real configuration space trajectory ##q(t)\in Q##, the average velocity which is part of the continuity equation
$$\partial_t \rho + \nabla (\rho \vec{v}) = 0$$
which follows from the Schroedinger equation
But the Schrödinger equation plays no role in relativistic QFT. It is replaced by the representation theory of the Poincare group.
Once this requires FTL causal influences, one would have started to care about the possibility of some hidden preferred frame, without waiting many years for Bell's theorem
But Bell's theorem assumes a preferred frame rather than deriving it. And theorists and experimenters were looking for evidence for preferred frames without any prodding from Bohmian mechnaics. You are full of wishful thinking about the latter's importance.
But the effective field theory paradigm could have been reached easier. To consider the cutoff at some critical length as a sort of approximation for a real more fundamental theory which really cuts higher momentum has the problem that such a cutoff does not have Lorentz symmetry. So to accept this would require to give up relativistic dreams.
Hardly anyone is willing to give up the relativistic paradigm. Effective field theories work quite well within the relativistic paradigm, producing covariant effective fields from covariant underlying fields.

Last edited:
PeterDonis
Mentor
2019 Award
In the context of my answer, realism was presupposed.
Then you are just arguing in a circle. You can't assume realism and then use that to argue that the theory of everything must be a realist theory.

EPR
EPR
If realism failed at the micro scale, what 'ontology' could anyone expect from a non-realist TOE?

Then you are just arguing in a circle. You can't assume realism and then use that to argue that the theory of everything must be a realist theory.
It was not intended to argue in this direction. The intention was only to explain what realists think. They think that there will be one true theory of everything, and this theory will be realistic, and so this theory will define the true ontology of the universe. All the various different incomplete and with large probability simply wrong theories we have today naturally given only incomplete and with large probability wrong theories about what it the true ontology of the world.

These are simply trivialities about what realists think, but it seemed necessary to describe them given that quite strange statement
This makes ontology model dependent - very strange for supposed realistic foundations, where there should be only one reality....
If realism failed at the micro scale, what 'ontology' could anyone expect from a non-realist TOE?
Of course, none. Even if it does not fail (a failure would require that there is no viable realistic theory/interpretation able to compete with the non-realistic theories, which is actually not the case) one cannot expect the definition of any ontology from a non-realist TOE.
But all these predictions guided theorists without any need of Bohmian mechanics. So there is no additional guiding available from maintaining a Bohmian view. Occam's razor therefore does away with it.
You don't know, and cannot know, the progress which could have been reached now if theorists after 1952 would have been guided by the Bohmian view. It could have been much larger than what has been reached now. So we have here a quite strange application of Occam's razor: Cut away all research directions which have never been seriously tried, given that we don't know the results they could have reached if seriously tried.
But the Schrödinger equation plays no role in relativistic QFT. It is replaced by the representation theory of the Poincare group.
Yes. So we have already identified one direction of research which was seriously harmed by the relativistic paradigm. What could have been reached by the development of the Schroedinger picture for QFT? We cannot know. (And according to your version of Occam's razor, we will never know, because research direction which have not given yet much because they were not tried yet have to be rejected forever.)
But Bell's theorem assumes a preferred frame rather than deriving it.
?????????????
What is assumed in the many variants of Bell-like theorems is always Einstein causality. Then, together with Einstein causality
1.) The EPR criterion of reality, thus, an extremely weak notion of realism.
or
2.) Causality in a version containing Reichenbach's principle of common cause
or recently
3.) Nothing but the objective Bayesian interpretation of probability as the logic of plausible reasoning.

You have to reject them all, not (1) and not (2) and not (3), or, alternatively, you have to return to a preferred frame. So, it is a consequence of the violation of the Bell inequalities. And only one of the possible consequences, you can, as well, conclude that not (1) and not (2) and not (3) holds.
You are full of wishful thinking about the latter's importance.
No. I know very well that it was not at all important in the development of what we have now. The result is what has to be expected - no progress at all on the fundamental front, all the real progress restricted to more of the same (SM for QED) based on better particle accelerators, and some progress reached by Bell and his followers after seeing, accidentally, the impossible done by Bohm.
Hardly anyone is willing to give up the relativistic paradigm. Effective field theories work quite well within the relativistic paradigm, producing covariant effective fields from cova[r]iant underlying fields.
I agree. You can, without doubt, cut away all what is in conflict with the relativistic paradigm (which is not something related with experiment, but the metaphysical "there is no preferred frame" hypothesis) and the remains will work nicely too. They will give much less - but so what, your version of Occam's razor makes sure that we will never try what could have been reached following these research direction.

As a consequence, we can hardly expect any progress on the fundamental front. But so what, the SM and GR work fine, the unsolved problems (which will never be solved) will motivate grants going to relativists forever, and Neumaier's razor protects them from competition.

weirdoguy
PeterDonis
Mentor
2019 Award
The intention was only to explain what realists think.
Then your statements should be prefixed with something like "this is what realists think: ..." or "realists believe that...". Stating it the way you did makes it seem like you think it's simply a fact that any interpretation or viewpoint must account for.

PeterDonis
Mentor
2019 Award
What could have been reached by the development of the Schroedinger picture for QFT?
You're confusing the Schrodinger picture with the Schrodinger equation. The latter is what @A. Neumaier referred to and is obviously non-relativistic. Its relativistic counterpart, the Klein-Gordon equation, was actually discovered first AFAIK, so it doesn't seem appropriate to say it was somehow neglected.

As for the Schrodinger picture in QFT, it is used, though not as much as other methods. See, for example, the work of Symanzik. So we do know what "could have been reached" using it: it's whatever has been done with it up to now.

A. Neumaier
PeterDonis
Mentor
2019 Award
the relativistic paradigm (which is not something related with experiment, but the metaphysical "there is no preferred frame" hypothesis)
No, the "relativistic paradigm" is the belief that Lorentz invariance is fundamental, so our fundamental theories should reflect that. "No preferred frame" is just the simple observation that we have no evidence for one, so there's no need to include one in our theories.

PeterDonis
Mentor
2019 Award
They will give much less - but so what, your version of Occam's razor makes sure that we will never try what could have been reached following these research direction.

As a consequence, we can hardly expect any progress on the fundamental front. But so what, the SM and GR work fine, the unsolved problems (which will never be solved) will motivate grants going to relativists forever, and Neumaier's razor protects them from competition.
The issue of how grants for scientific research are given or how particular directions of research are decided is way off topic for both this thread and this forum. We have a forum for STEM Career Guidance where topics like the grant and funding process can be discussed.

A. Neumaier
2019 Award
What could have been reached by the development of the Schroedinger picture for QFT? We cannot know.
Coleman, Jackiw and others used the Schroedinger picture for QFT to study solitonic degrees of freedom and instantons - without any input from Bohmian mechanics.

On the other hand, what did the Bohmian's do to develop this picture? Nothing at all. They just say that they have a realistic Schrödinger equation interpretation, and leave the rest to others, just as before. They are content to iterate their mantra that there is no need for them to do such work, as you did:
No, it is also part of Bohmian mechanics. All the quantum predictions follow from Bohmian mechanics too.
and Demystifier did:
in IBM (instrumental Bohmian mechanics) electrons, photons etc. do not have trajectories. Only fundamental particles have trajectories. But we still can't observe those fundamental particles (we would need a stronger particle collider for that), so in practice we don't need to worry about details of those fundamental particles and their Bohmian trajectories. In practice we can use the standard instrumental QM/QFT, while Bohmian mechanics can be used for a conceptual explanation of those instrumental rules.
Thus we know that Bohmian mechanics (around almost as long as renormalized QED) has no innovative potential in QFT.