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

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.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.

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.You're confusing the Schrodingerpicturewith the Schrodingerequation. 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.

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.

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:As for the Schrodingerpicturein QFT, itisused, 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.

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

(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?Soon after the invention of quantum field theory, its Schrödinger representation was also known, and it has been mentioned since in some text books [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].

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

So, again, all one can learn from history, from the real development of science, would be:Which such restriction follow from your Bohmian field ontology? I don't know any that would have guided quantum field theory development.

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.