If an answer is the "most upvoted/accepted answer", or even if it is by someone with the highest reputation among the respondents, it is by no means an indication of the accuracy of the answer. The majority of voters are not experts in QFT, and I would guess that a significant fraction probably didn't even take a formal QFT course.

@PeterKravchuk That's to be expected. What I meant to convey by bringing that up is that general concensus (whether mistaken or not) isn't even the same every time the same question is asked.

The problem with all these statements is that they are mostly operationally vacuous. What does it mean for a virtual particle to "exist" or be "observable"? They "don't exist" and "aren't observable": you can't do the same experiments with them as with on-shell particles. But they "do exist" as contributions to scattering amplitudes and "are observable" as more-or-less concrete signatures in the final expressions. This is all just words, different people will give different meanings to these words, and so you get what you get.

In practice, I would say that people working on QFT just agree on which quantities are observable and how to compute these quantities, and are not generally concerned by the questions you raise.

There is a level of this topic that is philosophical/semantic. Whether or not you count anything that occurs on the quantum field level as existing or if you only consider observables to exist is a choice you can make. Even though I personally think there's a more reasonable choice to make here, not everyone will agree. That being said, there's definitely a level where answers can get misinformative despite the subjectivity by answering in much too absolute and objective terms without defining the context within which that answer applies.

Besides, it's not like you can't define these questions in more concrete ground: If "Do virtual particles exist?" is too vague, you can ask "Do non-particle effects occur on the quantum field level?" (a more rigorous description of what non-particle and quantum field evel mean might be needed, but this is a comment). While the effect itself may not be observable its effects on particles might be. Isn't that the idea behind the Casimir effect after all?

A perspective that may clarify things is that QFT is a theory of quantum fields, not particles. There are many quantum field theories (conformal field theories) that do not have any meaningful notion of particles (either real or virtual). They still exhibit the Casimir effect etc. Virtual particles are just a language which you can use to describe some aspects of some QFTs (sometimes with great success), and real particles are concrete observable aymptotic states of some QFTs, but neither concept is synonymous with QFT.

@PeterKravchuk That is understandable, but a field theory that attempts to explain classically (i.e. anything prior to QFT) particle-like phenomena must be able to recover such particle-like description at the appropriate limit. In that sense, whatever more fundamental description QFT provides that doesn't necessarily behave like a particle (virtual or not) in general, but does in those conditions could be said by extension to be the same concept in this new QFT context, but better explained.

At that point, yes you can discard the particle concept with respect to self-contained analysis of the theory, but the connection to former concepts in former theories is still important for the purposes of communication and establishing that we are still talking about the same universe.

Similarly, if a field theory can explain everything that particles can't in terms of fields, that's great. But if that's the case, I might expect an answer of this sort "This is the quantum-field-based description of the phenomenon that virtual particles attempt to explain, if inadequately". Rather than say that virtual particles don't exist, describe the more fundamental field-based explanation.

I am not sure what former theory are you referring to. Much like GR, QFT is a very concrete mathematical model that happens to describe our reality. QFT is capable of describing real particles, and indeed the "former theory" --- the non-relativistic QM --- is formulated in terms of particles. However, the standard non-relativistic QM does not have virtual particles, and virtual particles appear in QFT. Much like Christoffel symbols do not appear in Newtonian Gravity.

The point of my comment was that while QFT is capable of describing real particles, it would be misguided to try to interpret everything that QFT does in terms of particles (be it real or virtual). You do seem to insist on this interpretation, refering to the Casimir effect as being an effect of virtual particles etc.

"Virtual particles" is just a name for a way of doing calculations, and when this way of doing calculations is reliable, it might have definite signatures in the physical results. You might then say that virtual are "real", whatever that means. When people say that virtual particles do not exist, they mean that they do not appear as physical asymptotic states. Unlike the former, the latter is a definite statement that is unambigous both mathematically and observationally.

My comment was furthermore stressing that even the real particles are only one of the features of the QFT. They appear only as asymptotic states in infinite volume; I am not aware of a useful notion of a one-particle state for an interacting theory in finite volume. QFT is a theory of quantum fields, not of classical fields, and not of particles.