The reason I ask the question is that, as discussed e.g. in the context of this post of mine, there is a semiclassical treatment of the photodetection process in which a photodetector responds to a classical electromagnetic field (where the notion of a photon doesn't make sense) in the typical way that is considered as heralding photons appearing in the detector. But this is obviously not the case.

Thus the question arises where similar discrete detection events that are usually considered as showing the detection of particles can also be interpreted as responses of a quantum detector to a classical external field.

The most interesting class of such detection events (apart from photon counters) are tracks in a bubble chamber (or their modern analogues, wire detectors).

In the case of massive particles like an electron, I'd say you can measure the charge over mass ratio by applying an external magnetic field or you measure, e.g., the energy loss in the detector material, which is characteristic for this ratio. Perhaps you find something more concrete when googling for particle ID.

In case of photons it's not very easy to make sure to detect only one photon. The oldfashioned treatment a la Einstein's paper of 1905 is very misleading, because indeed it's fully explanable with semiclassical modern quantum mechanics, semiclassical meaning here that the electromagnetic field is treated as a classical field and the bound electrons in the material quantized and then using first-order time-dependent perturbation theory, as detailed in my Insights article

To be sure to have only precisely one photon one way is to use parametric downconversion to create a polarization-entangled photon pair and detect one of the photons as a "trigger". Then you know that you have one and only one other photon.

Do they interpret, e.g. the traces in a bubble chamber after calculating expectations from the SM, or the other way round? I'm asking because I wonder how spins are 'detected'.

I think all those thousands of people at CERN think that they work at a particle collider, and talk about particles all the time. Nevertheless, it is still possible that the wave picture or QFT could be more accurate than the particle picture (QM, or whatever you call it.) I think other posters have made the point that the particle picture is at least pretty good FAPP. Therefore I think it should be acknowledged that the claim that particles do not exist can only be true (if it is) in a highly technical manner of speaking and not in the ordinary meaning of the terms. This should not be interpreted to depreciate a very technical wave based explanation, particularly if it is in some way more accurate or more precise than the particle based explanation. However, there should be some proof that it is a true rival theory, not just a rival terminology.

Now you've got me wondering whether the analysis in Mandel & Wolf for the flat 2D detector case could be extended to a 2nd order analysis for a 3D detector.

After all, ionization chambers can detect both gamma rays and alpha/beta rays, so why should the latter be fundamentally different in terms of particle-vs-wave-vs-field?

There are many reasons electrons are considered particles rather than field. Going back to Millikan's measurements, oil drop was found to have only electric charge that is multiple of elementary charge ##e##. If electron was a field, one would expect the electric charge of the oil drop to be distributed continuously, not in multiples of ##e##.

There are two rival theories: Interacting quantum field theory, where electrons are fields and particles exist only asymptotically (since Fock space is essentially an asymptotic concept), and quantum mechanics, where electrons are particles with ghostlike properties. They are considered to be compatible, but the relation between the two (via the S-matrix) is only very thinly discussed in the literature.

In quantum field theory it is impossible to speak of a sequence of single electrons moving from a source to a detector, while in quantum mechanics this is the standard picture. Thus there is something to be reconciled.

My question is whether there is actual proof that electrons (and other particles) in quantum mechanics really exist, or whether - similar to nonexistent photons detected by a photodetector coupled to an external classical electromagnetic field - they are just ghosts manifesting themselves only through the discrete responses of macroscopic quantum detectors to an electron fields.

People also talk about photons all the time, although this is a very fleeting (and - as the semiclassical treatment of the photoeffect shows - much more questionable) concept.

Having good terminology that captures what ''really'' happens is important, I think, though not as important as having it right in the formal treatment that decides upon what can be predicted and how well.

Well, that's also an interpretation as is the particle picture. Of course, by definition within relativistic QFT a particle is an asymptotic-free Fock state of definite occupation number 1, and as you write yourself in the first postings of this thread the appearance of tracks in a medium is well-understood since the early days of modern quantum theory (see the there cited paper by Mott).

If you are very precise you can argue that in an detector like a cloud or wire chamber you don't observe electrons but in-medium quasi-particles ;-)).

Yes, but I had asked for a sequence of electrons (many, well-separated in time). There is no asymptotic picture for these, only for a single electron!

So the sequence of electrons only makes sense if you take the S-matrix from QFT and interpret the sequence of electrons in QM! Which is of course the conventional procedure but nevertheless very strange, if one thinks that QFT should be able to describe the source, the particles and the detector by a single (complicated) state of the quantum fields involved.

Well, perhaps there's some way to understand the tracks of an electron in a cloud chamber using quantum electrodynamics (in the medium). What we really see are of course droplets condensing due to ionization. So one would have to calculate the condensation probability density given a single electron in the chamber.

For a single electron, this can probably be made to work similar to Mott's analysis.

But again the problem is how to model a train of electrons in a single beam on the QFT level, which (given a single state) describes the dynamics of fields everywhere in space-time - rather than on the QM level, which (given a single state) describes what happens under temporal repetition (''identical preparation'') of the same situation.

That's also an interesting question. As far as I know from talks of accelerator physics, they treat the particles in the accelerators as classical particles. This works obviously very well. I guess, in a first approximation you can just use magnetohydrodynamics or the Vlasov equation to describe the beams in an accelerator on a continuum level. Then the argument would be that you can approximate the Kadanoff-Baym equation with a Boltzmann-Vlasov equation very well.

You can model such a sequence with suitable wave packets. If the sequence is finite (but as long as you want), the usual approach of non-interacting initial and final states with interaction in between works nicely.

I don't get the point of the discussion. In principle, it is possible to work with quantum field theory everywhere. It is also possible to use general relativity for an inclined slope problem. It is just needlessly complicated.

In particle accelerators, particles are treated as classical objects. You need some input from quantum mechanics, e.g. the power and spectrum of synchrotron radiation, but once you have those inputs you can use classical trajectories of the accelerated particles. Classical thermodynamics with time- and space-dependent external fields.

In the collision process itself, QFT is unavoidable.

After the collision, the description is (nearly) classical again: you have particles flying in different directions. Decoherence happens so quickly with every interaction that quantum effects are not relevant here. If particles decay, the actual decay process needs QFT again, but only to determine the lifetime, branching fractions, angular distributions and so on, not for the propagation of the initial or final particle. Mixing is a bit special, because you need some quantum mechanics in flight, but again you can cover that as effect based on the classical flight time.

I was going to leave this thread alone, but to me it sounds like angels and pinheads. Of course particles have tracks and of course they exist, at least in the sense that they can be counted. On the theoretical side, anything I can care about can be calculated and compared with theory. So if this isn't completely mathematically rigorous, I don't much care. It's not the first time in my life I have done a calculation that wasn't perfectly rigorous, and I don't expect it to be the last.

Often one can indeed do the latter. But both the Kadanoff-Baym equations and the Boltzmann-Vlasov equations are field theories in phase space, not particle theories.
Instead of particles one has only phase space densities. Thus talking about particles seems to be simply a left-over from the 19th century when Boltzmann derived his equation from a classical particle picture.