The weird thing would be discontinuities showing up in wave function evolution without putting them there with the potential energy functions. In the few cases where we can get analytical solutions there are no discontinuities that look anything like wave function collapse.
You're whole thesis rests on the fact that this should fall out when we put 6e23 particles together for reasons.
So far we've not managed to simulate 1,000 quantum particles because the curse of dimensionallity means we run out of computers on earth rather quickly. Which makes anything you're saying pointless since we can't ever check it, even if we turned the whole observable universe into a computer.
I hope that you read this with a scientific attitude, i.e., critical, but open to the fact that not only your position is wrong, but also the unproductive enterprise of solving "the measurement problem" is wrong.
What I'm trying to explain to you is that:
1) The wavefunction is only the DESCRIPTION of the underlying phenomena.
2) Within this description everything, and I mean ::everything::, evolves unitarily. No exceptions ever.
3) Whenever you decide to measure, i.e., probe the microscopic system with an object that is not within your quantum description, that is you know that it's huge, but have no details about all the phase/amplitude information you're destined to average/trace over the unknown states. This can be done symbolically (as in my first post here) and shown to always give probabilities in the reduced density matrix. That's always what we're left with in case of a large system outside of our description interacting with a small system within our description.
On the other hand if you put a small quantum system, with another small quantum system (say two particles), there's no need to trace/average/apply the born rule immediately because your description can be complete both in principle and in practice. You can just unitarily evolve the system for as long as you wish/can compute for. However sooner or later you'll want to measure, because ultimately that's what physics is all about - verifying your predictions with experiment - and you go back again to small vs big, because that's the only way we, humans, can perceive this microscopic reality - through probing. The result will be completely analogous to the one before, the only change being that you'll now be able to predict probabilities of a two-particle system.
If you're familiar with electrodynamics it's quite similar there, but here it's brought to another level with the probabilistic interpretation. What are the similarities?
You can have your complete description with the four-potential, about which you know, from the Aharonov-Bohm effect, carries more information than electric/magnetic fields alone although we only measure fields not the electric/magnetic potentials.
The potentials were the side product of the formalism that turned out to have real consequences. Similarly as we learned the importance of the wavefunction/phases in the description, even though we only measure probabilities.
About the curse of dimensionality, the only thing I have to add is, that's true. We have a precise way to describe what is going down there but it's insanely expensive to simulate in all detail. That's still a lot to be happy with in my opinion.
Also, if you feel uneasy with wavefunctions which have the status of descriptions of reality,
go and study classical field theory in which the fields are to be thought of as real physical entities,
go step deeper and you're in quantum field theory in which you deal with descriptions again.
Would a theory in which we deal with "real physical entities" be better than that of "descriptions"?
I'd say, the hell with it. Go with whatever works best, not whatever fits your preconceived notions of reality.
You're whole thesis rests on the fact that this should fall out when we put 6e23 particles together for reasons.
So far we've not managed to simulate 1,000 quantum particles because the curse of dimensionallity means we run out of computers on earth rather quickly. Which makes anything you're saying pointless since we can't ever check it, even if we turned the whole observable universe into a computer.