Phonons are a nice tool to simplify the quantum-mechanical description of lattice vibrations by identifying the ladder operator of normal modes as creation operators of a certain quasi-particle. In certain special cases, one could even formulate a certain displacement field $\phi_a(x)$, quantize it according to canonical field-quantization procedures and obtain the very same phonons as the "emergent" particles.
On the other hand, a Weinbergian picture of quantum field theory is that particles do not emerge from fields - on the contrary, fields are a necessary consequence of many-particle dynamics. One could then argue that the observation of single point-particles emerging from QFT-computed interactions is an experimental verification of a "Weinbergian" interpretation of modern particle physics. (Even though a lot of particles we observe are not fundamental, they are in the end composed of elementary particles and the fundamental-particle character extends to them.)
To phrase it differently: one could argue that there is no such physical entity as a fundamental quantum field, the so-called "causal fields" are merely useful operators and the only fundamental entity are many-particle states.
But if a clearly non-fundamental non-particle such as a phonon is experimentally indistinguishable from a "really real" particle, then the term "really real particle" has no physical meaning and there is no way to tell whether it is the field or the particle which is more fundamental. (And here by indistinguishable I mean indistinguishable within the cut-offs imposed by the discrete nature of the vibrating lattice.)
EDIT: To make clearer what I mean by "particle behaviour"; when an electron is flying out of a reaction or entering a double slit experiment we often describe it as a plane wave. Indeed, the electron then interacts with the double slit in a plane-wave-like manner and forms an interference pattern on the screen behind it. But in a single event, we see only a single dot on the screen. This is the usual "wave-function collapse" as described by non-relativistic quantum mechanics. But this very "wave-collapse" situation is implicitly assumed to be a part of QFT applied to particle physics. Hence, the plane waves flying off from a QFT reaction are in fact particle-waves which undergo the very same collapse into a single point upon measurement.
Now consider the phonons. As is, they seem to be true quantized waves, not particle-waves. A naive analysis would say that they do not undergo the "wave-function collapse" and never acquire a particle nature. That is, if we were to send them through a hypothetical double slit, they would form a true interference pattern, not one emerging from dots.
But what does it mean experimentally that they would form a true interference pattern? Is it maybe that any experimental method trying to measure a phonon will in principle not be able to assess the difference between a "particle-wave" and a "true quantum wave"? Or does the phonon plainly behave like a collapsing particle-wave upon measurements analogous to those of the electron?
So the question is:
Does a phonon behave like a point particle?
Is this experimentally verified and how?
Is this somehow self-evident from the lattice many-body Hamiltonian in a way I couldn't see?
