From the responses to my comment, it may seem pedantic, but it is the wording that strikes me. "Proof" belongs in a different category than experimental verification [1], as it imply logical consistency, or even an equivalence between the model and the object it attempts to model. So in mathematics, proofs make sense because it is dealing with relationships within a closed axiomatic structure. We haven't discovered the axioms of Nature, and therefore everything we propose, as a law, of nature rests on the relative foundation of our experiments.

I guess what I'm trying to say is that if you are a hardcore empiricist (like Bohr, in a sense, were) reasoning beyond the measurable is not physics. That is why the Copenhagen Interpretation doesen't deal with what the probability distribution of a wave-function actually is, simply that it is a useful construct to represent the possible outcomes of a measurement, until an expectation value is calculated. Perhaps that is also why Wheeler's many-world interpretation got off to a bad start, as it didn't provide any new measurable predictions.

[1] or rather lack of falsification, to adhere to https://en.wikipedia.org/wiki/Falsifiability