Chaos is sensitivity to initial conditions. Could the randomness in quantum mechanics simply be a manifestation of chaos?? The initial conditions would be both the initial state of a particle, and perhaps initial conditions of the measurement device at the time of measurement, and in the fields present at the particle location at the time of measurement. Roger Penrose believes gravity plays a role in the collapse of the wavefunction, so gravity could be included here (in factoring in of initial conditions).
My two cents of the euro, you ask:
Is randomness in the collapse of the wavefunction in quantum mechanics simply a manifestation of chaos, and not inherently random at all?
Do an experiment with a dice.After 1000 throws there is a distribution with the number of times the six faces came up. If it you get a flat probability distribution you decide on true randomness of classical mechanics probable motions on the dice. If you see a biased distribution, you attribute it to a weighted dice.
The experiments at the quantum level do not show, cannot be modeled with classical mechanics statistical distributions. We attribute the bias to quantum mechanics which by now is an elaborate mathematical model , that fits the distributions and, important , predicts correctly new ones. And the collapse is not random in the theory, it is biased with the wavefunction distribution ($Ψ^*Ψ$)
My point is that the "collapse" is biased, not random according to mainstream theory. Chaos would produce random distributions, but the data, crossections and decays directly connected to the probability distribution are not random.
No. Even if one can reproduce exactly the initial state and the measurements are ideal (thus even if the initial conditions are exactly identical) the outcomes can be randomly different.
Thus, even if multiple copies of a system are exactly prepared so the initial state is the spin-up state along $+\hat z$ $\vert +;z\rangle$ (exactly same initial conditions on all copies) and the copies are fed in identical copies of a perfect apparatus designed to measure the $\hat y$ component of spin, the outcome of any one measurement would have 50/50 chance of being either $\vert +;y\rangle$ or $\vert -;y\rangle$.