Is there any fundamental demonstration that result of an experiment cannot have been determined before the measurement, yet according to the probabilistic rules of quantum mechanics?
I understand that Bell's theorem demonstrates that the outcome cannot be a result of a deterministic hidden system, but is there any problem that the states are defined by quantum probabilistic rules before the measurement is made?
To be more clear:
I am not trying to question if quantum probability is similar to classical probability. I am indeed questioning in terms of the interpretations of quantum mechanics.
As I understand, the most accepted interpretation is that the collapse of the wave function occurs at the instant of measurement. This raises the problematic of information being apparently transferred at speeds faster than light and so on and the other features of entanglement phenomena.
The violations of Bell's inequality, if I understand it correctly, demonstrate that the properties of the entangled particles being probed (spins for instance) could not result from an intricate classical probability dependent on hidden variables. This is ruled out, clearly, such that the outcome of the measurement is effectively probabilistic in the quantum mechanical sense.
However, I could not find a discussion on whether the definition of the particle properties could have occurred BEFORE the measurement, perhaps at a random moment, yet respecting quantum probabilities.
For example, if we perform two measurements of the properties, one after the other. The first measurement supposedly collapses the wave function and provides a specific set of properties for the entangled particles. The second measurement of the same properties would simply confirm the the first measurement. What if the author of the second measurement didn't know about the first measurement? How one should interpret his/her observation? Is that any difference from the second author thinking that he/she was the first one to measure and interpret that the wave function collapsed at the instant of his/her measurement?
If, from the point of view of the second measurement (without knowledge of the first measurement) the result is identical to thinking that it was the first measurement at all, could we think (with no observable differences) that the wave function collapsed at any time between moment the system was produced and the instant of the measurement?
And if so, even more speculatively: could vacuum fluctuations be the reason for the perturbation and ultimate probabilistic collapse of any wave function, thus decoupling the progress of reality from the observations in a philosophical way?