To really get a sense of the nature of the wavefunction, let’s go back to the early days of contemporary physics and look at the nature of light. By ‘contemporary’ here I am referring roughly to post-Galilean physics. As far back as Newton and Huygens there was a debate over the nature of light – Newton held the corpuscular (particle) view, which likely stemmed from his work on optics, while Huygens held the wave view. The wave interpretation began to dominate the rhetoric after the implications of Young’s double-slit experiment (1801) were fully realized. It was then that the debate began to center on just what was it that was ‘waving,’ as it were. Maxwell, of course, answered that question by showing that light was merely the fluctuation of an electromagnetic field, though debate about this continued in the form of debate over the aether. Suffice it to say that, once the Michelson-Morley experiment was performed and certainly by the time relativity came along, the consensus was that what was ‘waving’ was an electromagnetic field. (Of course, ironically, in the same year he introduced special relativity, Einstein also explained the corpuscular nature of light that seemed to be suggested by certain experimental results.)
Since it had also become clear that light demonstrated corpuscular behavior as well, the wave-particle duality of light was firmly established. Louis de Broglie then proposed, in his PhD thesis, that all matter possessed this same duality. It took quite awhile for physicists to determine exactly what was ‘waving’ in the case of the particles of matter, but, as QFT seems to indicate, it’s just some other type of field.
But is Young’s double-slit experiment really evidence for the wave nature of light? Passing single photons through the slits one at a time gives a statistical distribution on a detection screen. I’m not sure of the historical roots of this, but I suspect that this is what led to the interpretation of the wavefunction as a probability distribution. Somehow along the way, when this notion was melded with the modern formalism of quantum mechanics, the wavefunction appears to have lost its ontological status.
On the other hand, we know that we get an interference pattern regardless of the wavelength of the light which means we can get interference with radio waves as well. In fact this is easily demonstrated using a pair of broadcasting radio antennas acting in the place of the slits. But most people never discuss “photons” in the context of radio waves because the notion somehow seems difficult to imagine (how big would radio photons be?). (Either they’re there and simply hard to imagine or they’re not there. If it is the latter, at what wavelength does light suddenly ‘rid itself’ of photons?)
Given the fact that, starting with de Broglie and Einstein essentially, photons were just another particle (in this case a massless boson), it made sense to treat the wavefunction of all these particles in the same manner. Given that it took awhile for QFT to really explain many of the other particles and the fact that the probability distribution interpretation seemed to work just fine, it seemed as if wavefunctions no longer needed any ontological status and was divorced from its association with the fluctuating field. But by stripping them of that status we are forgetting the historical origins of the wavefunction as I’ve just outlined and we are forgetting that, in the case of light at least, and really in the case of all particles, something physical – a field – really is fluctuating.
Now, given all of that, it is not particularly clear where the quantum-classical transition comes into play here. People often talk about ‘quantum’ versus ‘classical’ light, i.e. noting that light exhibits both quantum and classical behavior. But, according to Rovelli, Griffiths, and others, the world is entirely quantum and classicity is merely a perception on our part.
Given all of this and assuming for the moment that wavefunction collapse is real and that the act of measurement should cause this (again, just assume this for the moment whether or not you buy it), then shouldn’t the act of listening to the radio collapse the signal wave to a particular, localized state thereby preventing anyone else from listening to it on a different radio?