I Is Quantum Field Theory Redefining the Foundations of Quantum Mechanics?

[Elias1960]

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.

Sorry, I thought this was clear from the context of the discussion.

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.

Agreement about the first sentence. I disagree about the second part. The observation would be "no empirical evidence for a preferred frame", the conclusion would be "no need for a preferred frame", both would essentially differ from "no preferred frame" because the central point of the latter is an explicit rejection of theories with a preferred frame even if they are viable. As we would do if we, following sentence 1, think that relativistic symmetry is fundamental instead of emergent in some large distance approximation.

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.

I disagree here. The Klein-Gordon equation can be misunderstood as a "relativistic counterpart" of the Schroedinger equation only for the irrelevant one-particle case.

The Schroedinger equation is simply the evolution equation of the state in the configuration space representation of the Schroedinger picture. It becomes a functional equation if used in QFT. If we regularize it, say, by using a lattice approximation, we have a Schroedinger equation in QFT too, even if the original field equation is relativistic.

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.

Strange logic. If some guy, famous for quite a lot of other things like the Callan-Symanzik equation and Euclidean field theory, has written 1981 a paper where he shows not much more than that it exists:

We show here that in renormalizable models, the Schrödinger wave functional exists to all orders in perturbation theory, and give what we believe to be strong arguments that the Schrödinger functional differential operator that appears in the Schrödinger equation does so as well
Symanzik, K. (1981). Schrödinger representation and Casimir effect in renormalizable quantum field theory. Nucl. Phys. B 190 [FS3], 1-44

and where he refers to the use of it before 1981 as

Soon after the invention of quantum field theory, its Schrödinger representation was also known, and it has been mentioned since in some textbooks [1]. Calculations, however, were first done in the interaction representation, which is formally related to the Schrödinger representation by a change of basis. Later, covariant four-dimensional formalisms (S-matrix calculus, Green functions, and in particular functional integrals) were used almost exclusively. Even more than the interaction representation, which preserves a certain conceptual role in scattering theory, the Schrödinger representation fell into disrepute, the more so since it seems to have been considered to be non-renormalizable, as the interaction representation indeed is [2, 3].

(so that we can be quite sure that his work before 1981 does not give much too - he would not have forgotten it, so that all what remains would be the few papers up to his death 1983, all of them without indication in the title that they are somehow related with the Schrödinger picture), we already know all what could have been reached by this method?

Ok, there may be other scientists who have used it. But even if that would be 5 or 10 or so, this would be a small minority thing, and if they failed, it would not prove that the method could not have been reached more. Because out of principle there is no way of knowing this if only a few outsiders have tried it. We can be sufficiently sure that string theory failed given the large amount of resources invested into string theory, but even in this case one cannot be certain that all what string theory could reach has been reached.

This type of argument started with Neumaier's statement

Which such restriction follow from your Bohmian field ontology? I don't know any that would have guided quantum field theory development.

So, again, all one can learn from history, from the real development of science, would be:
1.) A failure of what has been actually used by the mainstream to solve problems they tried to solve, as an argument against what used by the mainstream. This failure (QG, TOE) is quite obvious.
2.) A failure of alternative approaches if they would have rejected the use of methods which have actually been used and which have actually reached some success. There is no such rejection of QM/QFT methods related to the Bohmian approach, so this does not work.
3.) Some successes of outsiders who refused to follow the mainstream but have reached something. This exists, Bell's inequality and all what followed.

We can certainly not learn from history anything about the scientific results which could have been reached by alternative paradigms which have not been used by the mainstream, but were restricted to a few outsiders.

 

[PeterDonis]

the central point of the latter is an explicit rejection of theories with a preferred frame even if they are viable

In other words, part of your definition of "the relativistic paradigm" is "not working on preferred frame theories". That seems more like a question for the people (if there are any) who are working on preferred frame theories: do they consider themselves to be working in "the relativistic paradigm" or not? I don't really have a preference either way as far as terminology is concerned.

we have a Schroedinger equation in QFT too, even if the original field equation is relativistic

The whole point of Symanzik's work that you so blithely dismiss was to show that the Schrodinger equation in QFT is relativistic, in the sense of being Lorentz invariant, even though the Lorentz invariance is not manifest.

In any case, if you think the "Schrodinger picture", or any other line of research for that matter, is somehow not fully explored, the thing for you to do is to go explore it, not to complain about it here.

 

[PeterDonis]

what did the Bohmian's do to develop this picture? Nothing at all.

We can certainly not learn from history anything about the scientific results which could have been reached by alternative paradigms which have not been used by the mainstream, but were restricted to a few outsiders.

As already noted, arguments about which interpretation, or line of research, or whatever, did or did not help to "develop" something, or whether or not we have "learned from history" are off topic.

This type of argument started with Neumaier's statement

And it ends right now. Any further posts from anyone either dismissing a particular line of research, or complaining that a particular line of research has not gotten enough attention, are off topic and will be summarily deleted. Please keep to the thread topic, which is supposed to be simple factual information about what different QM interpretations say about QFT.

 

[Demystifier]

Thus we know that Bohmian mechanics (around almost as long as renormalized QED) has no innovative potential in QFT.

Does thermal interpretation has innovative potential in QFT?

 

[A. Neumaier]

Does the thermal interpretation have innovative potential in QFT?

I didn't claim that, and I don't know. It is likely to have impact on the future relation between QM and QFT.

Why do you ask? @Elias60 was talking about the potential impact of Bohmian mechanics on QFT, and I had commented that history proved this impact to be nonexistent.

 

[Demystifier]

I didn't claim that, and I don't know. It is likely to have impact on the future relation between QM and QFT.

Why do you ask? @Elias60 was talking about the potential impact of Bohmian mechanics on QFT, and I had commented that history proved this impact to be nonexistent.

I think that any interpretation has a potential impact, as long as the interpretation helps someone to get intuitive understanding. It does not need to be explicit in final research papers, because they are usually written in a form that does not depend on interpretation. But the interpretation is hidden in a thinking process that eventually resulted in the research paper.

For instance, in my paper http://de.arxiv.org/abs/1505.04088 I never mention Bohmian mechanics, but my intuition in this paper was significantly influenced by my IBM way of thinking.

 

[Elias1960]

In other words, part of your definition of "the relativistic paradigm" is "not working on preferred frame theories".

Yes.

The whole point of Symanzik's work that you so blithely dismiss was to show that the Schrodinger equation in QFT is relativistic, in the sense of being Lorentz invariant, even though the Lorentz invariance is not manifest.

I blithely dismiss it? I quoted what was claimed, without questioning this claim.
Then, let's see: "relativistic" not found at all, "Lorentz" found once, in the following remark:

For most of our considerations, a plane $\partial \Gamma$ is sufficient, and then, for calculations, dimensional regularization is the most convenient: $3 - \varepsilon$ space dimensions (Re $\varepsilon > 0$), one (euclidean or minkowskian) time dimension. This is as effective as introducing a lattice in space while keeping time continuous, but by itself does not break Lorentz invariance such that renormalization of the speed of light is not needed.

Does not look like the whole point of the paper, which the author himself describes as "We show here that in renormalizable models, the Schrödinger wave functional exists to all orders in perturbation theory".
In any case, the question what Symanzik has reached seems off-topic too, as well as what Coleman and Jackiw have reached here:

Coleman, Jackiw and others used the Schroedinger picture for QFT to study solitonic degrees of freedom and instantons - without any input from Bohmian mechanics.

So, let's concentrate on what follows from BM for QFT.

First of all, the BFT approach itself has to be based on a Schrödinger picture of QFT. If it would not exist, that would be bad news for BFT.

Then, it had to identify the correct choice for the configuration space. Different choices would define different, competing lines of development of BFT. So, if (for whatever reasons) the approach based on particle ontology (favored by Duerr et al) fails, those working with the field ontology would not be impressed at all, they would be even happy that their preference for the field ontology appears preferable. (But this choice may differ for bosons and fermions.)

Then, it has to look at the Schrödinger equation. Is it of the type which allows a dBB interpretation? This appears unproblematic. Beyond this, everything else is unproblematic.

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:

That's a misinterpretation. The dBB approach does not lead to any restrictions in the use of mathematical methods developed by quantum theory. So, Bohmians will be happy about any progress reached with methods which do not rely on Bohmian trajectories too. They can be used as they are, there is no need to modify them or to reinvent them in some Bohmian version. Once the QM formalism can be derived from BM, all what can be reached based on the QM formalism can be reached using BM too.

This differs from the relativistic paradigm. This paradigm rejects those things which are not manifestly (fundamentally) Lorentz-covariant. So they are acceptable only as mathematical tools, only as long as there is no connection to reality.

To illustrate this, let's look at the role of regularizations. To get rid of the infinities in QFT, one has to regularize it. The usual way is to cut large momentum values. But "large momentum values" is nothing Lorentz-invariant. So, straightforward regularizations are theories which are not Lorentz-covariant. Sometimes one can circumvent this problem and find a regularization which is Lorentz-covariant. Say, one adds some large massive particles, and then invents such interactions with them that all the problematic terms are cancelled. But this are exceptions, not the rule. The most straightforward and simple way to regularize a field theory, a spatial lattice regularization, is obviously not Lorentz-covariant.

Once they are not covariant, they are, from the point of view of the relativistic paradigm, not even candidates for fundamental theories. Their only reasonable role is that of a dirty mathematical tool which allows to compute some intermediate results. These cannot be the final results - one has to consider some limit, which leads to some relativistic, Lorentz-covariant theory, else these intermediate results are worthless, and their agreement with observation is nothing but an unexplained accident.

If we restrict ourselves here to lattice regularization, this Lorentz-covariant limit can be reached only in the continuous limit of the lattice distance to zero. Unfortunately, even for renormalizable theories this limit either does not exist at all (Landau poles) or would be trivial (the interaction becomes zero). But, even if they were very uncomfortable with not having a really well-defined (and started research programs like algebraic QFT to solve these problems) this situation was more or less accepted: One could at least compute relations between the observables which had well-defined limits. Unfortunately, important fields (the gravitational field, and massive gauge fields) did not fit into this scheme. While there was found a way to handle massive gauge fields, there was not found a way to handle gravity.

So, the restrictions imposed by the relativistic paradigm created some problems with the quantization of gravity.

In a BM approach, there would not be any objection against the regularized theories. Any assumption that the theory has to be Lorentz covariant at the fundamental level is foreign to BM and with Bell's theorem it is known that one needs a preferred frame in BM. Instead, one would even require a regularization which reduces the degrees of freedom to a finite number, like lattice regularizations on a large cube do (instead of other regularization procedures like dimensional regularization, where it would be unclear if one could do any BM in the regularized theory). After this, there would be no BM-internal point to consider a continuous limit of that lattice theory. In particular, a lattice regularization of GR would be acceptable, and it would work for large distances (greater than Planck length) without any problems.

The approach which is now accepted by the mainstream is Wilsonian effective field theory: All the SM fields, as well as the field-theoretic version of GR, are only effective field theories. That means, there is some critical length, and below that critical length these theories have to be replaced by unknown different, more fundamental theories. The length is usually assumed to be the Planck length, but in principle it could be a different one.

Aside: Of course, Wilson had nothing to do with BM. At least AFAIK. But behind the Wilsonian approach there is an even more evil paradigm - the ether: There are sufficient similarities between classical condensed matter theories and the field theories of fundamental physics. Let's use these similarities by applying the methods used in one part shamelessly in the other part too. As a result, Wilson was able to apply renormalization techniques developed in fundamental physics for the SM in condensed matter theory and to reach quite nontrivial results there about phase transitions.

In the other direction, the empirical success was less obvious. But if one starts with some fundamental theory at Planck length, where all the imaginable terms would be of the same order, one finds that in the large distance limit the non-renormalizable terms are suppressed much more that renormalizable terms, so that this leads to the quite general prediction that we will observe renormalizable theories, except in the case where none exists, where the leading term will be a heavily suppressed (much weaker) non-renormalizable one. Which is gravity, which is indeed much weaker. So we have here also a qualitative but correct empirical prediction.

 

[DrChinese]

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...

Yes. Some in the QFT camp* tend to believe that it solves many foundational issues. On the other hand, I think they mostly remain in one form or another, although perhaps they get moved. Following Bell (as an example): QFT MUST be either non-local or non-realistic (or both). And personally, I don't see that double slit interference is any better explained, nor entanglement swapping between particles that have never interacted.

If we are holding the bag on these, then we are still deep in the swamp. Which is why this subforum exists in the first place. * With no objections to anything about QFT itself. And not intending to cast any dispersion on anyone.

 

[AndreasC]

Oh god I just now realized how many new posts there are... For some reason I stopped getting notifications. And I don't even understand half of them lol.

 

[AndreasC]

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.

OK, so as I've said I don't really know anything about any of this, however if I got what you're trying to say right and aren't misinterpreting you, I don't really agree with that proposal. Sure, results common between other interpretations and the Bohmian interpretation alone won't help you decide the Bohmian one is preferable or whatever (by virtue of them being common), but there isn't really any Occam's razor rule that tells you you must ditch the Bohmian picture because it wasn't involved in the development of QFT. I feel like many people abuse Occam's razor, it's a broad and in many cases ambiguous principle that only helps you filter out unnecessarily convoluted explanations. From what I've seen so far I wouldn't say there is something that sets BM apart as particularly unrealistic or unnecessarily convoluted without any merit compared to others, so I don't think Occam's razor is a good fit here. Maybe you think it is unrealistic and unnecessarily convoluted or whatever (and it may well be, I don't know enough to have an opinion) but that's a separate issue from QFT being developed without it.

Also sorry if my posts are a bit confusing or messy sometimes, English is not my first language.

 

[A. Neumaier]

If we restrict ourselves here to lattice regularization

This restriction is quite artificial. In particular, you cannot apply it to the standard model. Nobody working on the standard model is using this noncovariant regularization scheme. It is useful only in nonrelativistic QFT and partially in QCD. Even in QCD, there is lots of work done in covariant regularrizations.

many people abuse Occam's razor

... just like one can use an ordinary razor to murder someone ...

From what I've seen so far I wouldn't say there is something that sets BM apart as particularly unrealistic or unnecessarily convoluted

Well, from a mathematical point of view it is very unnatural and convoluted. It ditches not only relativity but also symplectic geometry (by dropping the symmetry between position and momentum) - both principles that lead to a huge amount of theoretical and practical insight into physics. If Bohmian mechanics were fundamental it would be surprising why these tools should have a place in the theory at all.

 

[Elias1960]

This restriction is quite artificial. In particular, you cannot apply it to the standard model. Nobody working on the standard model is using this noncovariant regularization scheme. It is useful only in nonrelativistic QFT and partially in QCD. Even in QCD, there is lots of work done in covariant regularrizations.

You cannot apply? Sorry, no, you can apply. There would be simply no point of doing it if all what you want is to shut up and calculate. Please, just accept that for doing different things different technical means are appropriate. If it is easier to compute integrals with dimensional regularization, fine, let's use dimensional regularization if we want to compute those integrals. But if we want to understand why all this can be done on a certain mathematically well-defined base, then the simplest choice if a lattice regularization on a large cube, which gives you a finite-dimensional theory.

And if all you want is to shut up and calculate, minimal QM is fine, and the measurement problem or Schroedinger's cat is simply irrelevant. If you, instead, want an interpretation which does not give rubbish if applied to Schroedinger's cat, then it is better to have a continuous trajectory $q(t)\in Q$. Given that the Schroedinger equation gives you a continuity equation for $|\psi(q)|^2$, this is not a problem at all. But with such a continuous trajectory you can describe the collapse by using the Schroedinger equation for the system and the measurement device, and then use the visible trajectory of the measurement device to compute the resulting effective wave function of the system.
$$\psi_{eff}(q_{sys}) = \psi_{full}(q_{sys}, q_{dev}(t)).$$

Well, from a mathematical point of view it is very unnatural and convoluted. It ditches not only relativity but also symplectic geometry (by dropping the symmetry between position and momentum) - both principles that lead to a huge amount of theoretical and practical insight into physics. If Bohmian mechanics were fundamental it would be surprising why these tools should have a place in the theory at all.

Very simple - once you can derive them starting from the theory, they have a place there. Mathematics is full of such surprises.

As someone who knows particle theory you should be aware how useful approximate symmetries are - even once they, as approximate symmetries, have no fundamental status at all, they can give as well huge amounts of theoretical and practical insights into physics, not? The question if some symmetry is useful has nothing to do with if it is fundamental or only emergent.