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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).

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    $\begingroup$ Bell's inequalities, which have been experimentally tested show that there is no local hidden variable theory that can reproduce the results of quantum mechanics (modulo some small loopholes). What this means is that a classical theory in the normal sense simply cannot reproduce quantum mechanics. Whether or not the classical theory is chaotic is irrelevant. There has to be something strange going on. The mainstream view is that the "something" is that the world is quantum, and not deterministic. $\endgroup$
    – Andrew
    Jul 1 at 20:50
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    $\begingroup$ I recognize there is a mainstream view. However, a few prominent physicists believe things are not inherently random at the core. I am simply asking for what is possible given current experimental observations. $\endgroup$ Jul 1 at 20:53
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    $\begingroup$ Chaos is not a solution to the problem, because chaos is a feature of classical mechanics. Classical mechanics is not able to reproduce the results of Bell's inequality tests. To explain observations while avoiding standard quantum mechanics, you have to change classical mechanics in a deep way, such as making it nonlocal (which is hard to jive with special relativity because in special relativity nonlocality implies acausal transfer of information, meaning you can kill your grandfather), or by appealing to superdeterminism. $\endgroup$
    – Andrew
    Jul 1 at 20:57
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    $\begingroup$ I do like your above comment, but I guess I would like some more specific rigorous reasons for that. Also appreciate the link. $\endgroup$ Jul 1 at 21:00
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    $\begingroup$ Bell's inequalities are the rigorous statement. Both the mathematical proof and experimental tests are described in the wikipedia article about Bell's inequalities I linked above. $\endgroup$
    – Andrew
    Jul 1 at 21:01

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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.

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  • $\begingroup$ Is it true that chaos cannot produced biased distributions?? If you could add more explanation to your answer that would be helpful. $\endgroup$ Jul 11 at 18:35
  • $\begingroup$ a specialist in chaos should answer that. It is a different question., $\endgroup$
    – anna v
    Jul 11 at 19:10
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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 $\vert -;y\rangle$.

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  • $\begingroup$ @CarlosGauss Not sure I follow. There is no interpretation here; the interpretation comes after, in explaining the (possibly apparent) randomness, not in the factual observation that the outcomes are 50/50. $\endgroup$ Jul 2 at 3:08
  • $\begingroup$ @CarlosGauss I am not suggesting an explanation to this randomness (real or apparent), just claiming it is random inasmuch as identical preparation and perfect measurement do not lead to identical outcomes (hence independence on initial conditions). $\endgroup$ Jul 2 at 9:53
  • $\begingroup$ @CarlosGauss I edited my answer to hopefully remove some confusion. $\endgroup$ Jul 2 at 10:02
  • $\begingroup$ I see, thanks, I am sorry about the confusion, I erased my comment $\endgroup$ Jul 2 at 11:28
  • $\begingroup$ I guess my comment is that perhaps the initial states of all the atoms in the measurement apparatus, and the initial state of all the fields (including perhaps gravitational) could not be exactly reproduced in practice, and hence the apparent randomness. These are the “initial conditions” I was referring to. $\endgroup$ Jul 11 at 18:32

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