What I mean by this is, with wave function collapse,--and by extension, collapse between two entangled particles--being nonlocal (instantaneous across space), in what reference frame does the entanglement collapse nonlocally? Does it collapse instantaneously in the reference frame of the creation of the entanglement? Is it nonlocal in the frame of the initial measurement that collapses the state of the system? Is it nonlocal in some other reference frame? Essentially, as quantum entanglement means a correlation between two particle states, when will one state be correlated with the other? Is it when the proper time of each particle is the same? Or when one particle is measured in its reference frame? Or is it something else?
Entanglement implies a certain correlation between some measurements you may perform on the subsystems. The way this correlation is "enforced" is not known but there are two main possibilities:
The wavefunction is a real, physical entity. In this case the collapse is a non-local process. The only way to avoid paradoxes is to reject Einstein's view of relativity and go back to a Newtonian absolute frame of reference. I cannot tell you how to find such a frame, but you may explore the de Broglie-Bohm interpretation where this kind of question is being studied.
The wavefunction as an incomplete, statistical description of the system. It's collapse can be understood as a change of available information/knowledge. In this case nothing non-local needs to happen. If you have two distant boxes, A and B, and you know that there is a coin in one of them but you don't know in each one, the probability of finding the coin in A is 50%. If you look in A and find the coin there, the probability "collapses" to 100% in A and 0% in B.
The answer to your question is that QM is a theory that has been proven experimentally, but the way we interpret it can be different. I am writing about one of these interpretations.
In the present paper, we shall treat quantum superpositions exactly as in the Copenhagen interpretation; not the wave functions but only the probabilities are physical realities.
Contrary to popular belief, the wavefunction is not a physical wave, and there is no physical collapse. The wave function is rather a collection of numbers, our knowledge about a physical system.
Dear Jack, there is no physical phenomenon that could be called the collapse. The collapse of the wave function, as first emphasized by Werner Heisenberg and then many others, is just the event when we learn something about a physical property of a physical system. It is a collection of numbers that summarizes our knowledge about the physical system and that can be used to make predictions.
Now in your case, two entangled particles create a QM system, and these two particles are in some ways indistinguishable, the wavefunction describes them both, they have a common wavefunction.
Thus, there is nothing instantaneous between the two particles, there is no information, no particles traveling between them instantaneously. The wavefuntion describes both particles, their properties, and the probabilities of measuring both particles' certain properties. This is the only way to understand and avoid nonlocality.
When things are measured, one of the outcomes is just realized. To simplify our reasoning, we may forget about the possibilities that will no longer happen because we already know what happened with the first particle. But this step, in which the original overall probabilities for the second particle were replaced by the conditional probabilities that take the known outcome involving the first particle into account, is just a change of our knowledge - not a remote influence of one particle on the other. No information may ever be answered faster than light using entangled particles. Quantum field theory makes it easy to prove that the information cannot spread over spacelike separations - faster than light. An important fact in this reasoning is that the results of the correlated measurements are still random - we can't force the other particle to be measured "up" or "down" (and transmit information in this way) because we don't have this control even over our own particle (not even in principle: there are no hidden variables, the outcome is genuinely random according to the QM-predicted probabilities).