Regarding the quote by Einstein: This turned out to be (partly) wrong. While the wave function can hardly be an object of reality (since its collapse depends on the observer, i.e. is not Lorentz invariant) and is thus rather a descriptive means for us, uncertainty in the quantum sense has nothing to do with a lack of knowledge. Put differently, there is a difference between a physical system being in a superposition of states A and B or being either in state A or state B (but not both of them at the same time). There're various experiments that can distinguish between both.
Just for the sake of anybody reading, your claims about the reality of the wave function are not settled science.
Published in 2012, the PBR theorem[1] suggests with some caveats that 𝛹 must be interpreted physically or modified to make new predictions of which there is no evidence of.
Thanks for the link![1] I should have been more precise.
What is settled science is that the collapse of the wave function happens due to different causes for different observers. Example: Take two detectors A and B and place an apparatus in the middle that emits two entangled photons in opposite directions. In the lab frame, both particles will reach the detectors at the same time, so that both detectors cause the collapse of psi simultaneously. In contrast to that, two observers moving to the left and right respectively will see one of the photons reach its respective detector before the other photon reaches his. Thus, for one observer it's detector A causing the collapse (and B then only receives a disentangled photon) and for the second observer it's the other way around. Hence the causal chain of events is reversed (which is forbidden by special relativity).
Now, the problem here is obviously the collapse of the wave function itself (and the faster-than-light propagation of the disentanglement which, however, is widely accepted). Since we still don't know how the collapse actually works[2], it's likely (and I think assumed by most physicists nowadays) that the non-unitary(!) collapse should be replaced with a different mechanism. (Such as decoherence[3] but there are still a lot of questions remaining.)
So it is in this sense that I say that the wave function (in our formalism today) cannot be an actual part of reality because it only works until a collapse occurs. That doesn't mean, though, that the quantum states themselves (given by the wave function in intermediate times) can't correspond to reality. In fact, as I said myself, quantum uncertainty doesn't have anything to do with a lack of knowledge. That is, the view that quantum states merely represent statistical properties of an underlying state (which a priori might be part of a hidden variable theory) is wrong. While I think this was known before 2012, the PBR theorem gives a very general proof of that.
Let me start with a rather mathematical definition: Unitary operators[1] are invertible operators that preserve the inner product of the Hilbert space they live on. They are used in quantum mechanics to describe the evolution of the state of a physical system. The preservation of the inner product in this context (roughly) translates to the statement that probabilities of measurement outcomes don't change, i.e. that probability is conserved. Invertibility, in turn, means that even though we can only talk about probabilities in quantum mechanics, we do so in a deterministic way. Put differently, if you know the state (= the wave function = the set of probabilities) of a system at a time t1, the state at other times t0 < t1 or t2 > t1 is uniquely determined. That is, using the unitary evolution operator, you can basically go back and forth in time, thus determine what the state of the system will be in the future or what it was in the past. In this sense, quantum mechanics is still a deterministic theory, even though we can't predict measurement outcomes with 100% certainty anymore. (Namely, what we can do is deterministically predict probabilities.)
Now, the problem with the collapse of the wave function (or the measurement process in general) is that it breaks this, i.e. the collapse is non-unitary. Probabilities are changed and the process is neither reversible nor predictable, i.e. entirely non-deterministic. If you have a system in a superposition of states A and B (say with a chance of 50% of measuring A or B, respectively) and you then measure A, then – due to the collapse of the wave function – the state of the system will be A with a probability of 100% directly afterwards. The probability changes and you have no way of knowing anymore what the state was before the measurement. (Nor did you have any idea that you would measure A and not B before actually carrying out the measurement.)
On the one hand, this shouldn't come as a surprise because the fact that "god plays dice", i.e. that systems might be in superpositions of states until they are observed and have to decide, is at the heart of our interpretation of quantum mechanics. On the other hand, this is weird because all the equations governing quantum mechanics are unitary evolution equations, so actually shouldn't allow non-unitarity. The crucial point seems to be that we still haven't nailed down what a measurement actually is and that we use classical terminology to describe it (i.e. we distinguish between the quantum systems and our classical measurement devices). But if our world is entirely quantum, then our instruments should be quantum, too, in particular they should not be able to bring about a non-unitary time evolution. Hence, the question is how the unitary interaction of a small quantum system and a large quantum system (like a measurement device) can lead to an apparent break of unitarity – even though it is actually not. A related question is how classical behavior emerges from quantum behavior for large objects (that is, why is our world entirely classical when the microscopic world actually is not).
Concluding, my reference to the non-unitarity of the collapse of the wave function served to remind the reader that the collapse is not compatible with unitary time evolution and thus explain why, as a concept, it likely (hopefully) won't survive the next revolution in physics.
Sorry for getting back to this so late, but yeah this was great! Again thanks for taking the time to write this. I had no clue it got this weird in quantumland, and it's awfully fascinating.
