Does the various interpretation of quantum mechanics have any impact on how we interpret quantum field theory?

Question

Does the various interpretation of quantum mechanics have any impact on how we interpret quantum field theory? Or can QFT be considered as one of the interpretation of QM, I mean the later case as in QM is weird because the fuller theory, QFT picture is not taken into account, once we see the experiments in QM in light of QFT, the mysteries goes away.

Please focus more on the first question, eg. Does many world interpretation of QM mean that in QFT each particle's existence as part of the excitation of the field is realized in one of the universe, thus literally, anything that can happen happens?

Or if you have your favourite QM interpretation, welcome to apply it to QM, does it make sense to even do that? Eg. Can Bohm's interpretation survive the transition to QFT?

Ok, thanks for the answers so far, maybe a more clear question is this. Now from what I have learned from popular physics, QFT says space always have fields and when you put energy in them, the particles pop up as excitations. This seems very much independent of any interpretation of quantum mechanics. Or is this way of understanding QFT fundamentally Copenhagen or would other kinds of interpertation eg. Transactional interpretation give us very different underlying picture of QFT?

Answer 1

I'm curious about the same questions myself and have been slowly making my way through "Interpreting Quantum Theories," by Laura Ruetsche. This is a surprisingly technical text both philosophically and mathematically but I believe it addresses your questions.

In short, and from my understanding so far (which might be incorrect), she argues that the violation of the Stone-von Neumann theorem for quantum theories with infinite degrees of freedom introduces a wrench into several interpretations' programs. This violation implies a lack of a singular Hilbert Space in which all quantum states "live in." Thus several popular interpretations run into the problem of requiring an ontologically preferred Hilbert Space over many possible, inequivalent choices. I am not aware of any QFT-versions of these interpretations that handle this problem either by moving the interpretation's ontology from the Hilbert Space to the C*-algebra it represents, or by handling this difficulty straight-on.

Full Disclosure, I am no expert in this field by any means so perhaps I'm misrepresenting her argument or there is some flaw in her approach beyond my awareness. Regardless I recommend checking out the text yourself keeping your questions in mind.

Answer 2

The question is a mixture of a few different questions. This answer tries to help sort them out.

(First, here's a note about language. The name "quantum mechanics" is sometimes used as a synonym for the general principles of quantum theory, and it is sometimes used to refer to a non-relativistic special case. Both languages are fine, as long as it's clear which language is being used. The following answer uses the name "quantum theory" for the general principles and "non-relativistic quantum mechanics" for the special case.)

Do the various interpretations of quantum mechanics have any impact on how we interpret quantum field theory? Or can QFT be considered as one of the interpretations of QM ...

Quantum field theory (QFT) and non-relativistic quantum mechanics (QM) both respect the general principles of quantum theory. QFT might help clarify exactly what the "measurement problem" is, simply because QFT is more accurate and comprehensive, but it certainly doesn't resolve the measurement problem at all, and it isn't a new interpretation. The issue of interpreting quantum theory is the same in QFT as it is in non-relativistic QM. Those mysteries don't go away.

Can Bohm's interpretation survive the transition to QFT?

If by "Bohm's interpretation" you mean Bohmian mechanics (also called pilot-wave theory), then it is not an interpretation of quantum theory at all. It is an entirely different theory, one that tries to work as well as quantum theory does. But, although I have seen occasional claims, I have not seen any extension of that idea to anything that works as well as QFT.

Now from what I have learned from popular physics, QFT says space always has fields and when you put energy in them, the particles pop up as excitations. This seems very much independent of any interpretation of quantum mechanics.

Like you suggested, the occurrence of particles in QFT is independent of any interpretation of quantum theory. In contrast to non-relativistic QM, QFT is formulated in terms of fields, not particles. In QFT, particles are predicted rather than assumed, even though the most common computational methods (involving Feynman diagrams, etc) can make it look like particles are being assumed. The subject of particles in QFT is an interesting one, but it is independent of any interpretation of quantum theory.

Answer 3

QFT uses the free particle solutions of the quantum mechanical equations as a field, with an operator field acting on them. I would call it a meta-level of quantum mechanics.

Its success in modeling and predicting data is based on the use of Feynman diagrams that can be described using QFT, allowing the study of many particle systems, which the simple potential problem solutions cannot address.

In this sense I would not call it an interpretation, it is a higher level formulation using the same theoretical basis.

Does many world interpretation of QM mean that in QFT each particle's existence as part of the excitation of the field is realized in one of the universe, thus literally, anything that can happen happens?

You have to define "happens" . For an experimentalist, "happens" means an experiment can be performed to validate the model. As by itself the use of "interpretation" means that there is no difference in measurable consequences the question is moot because it is not a prediction that can be measured and validated or falsified.