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I have read this question:

What is the reason that Quantum Mechanics is random?

where Puk says in a comment:

I see. I would call both "random", with the degree of "randomness" defined by ψ. But yes, just a matter of semantics.

On a measurement level, is quantum mechanics a deterministic theory or a probability theory?

where Arnold Neumaier says:

On the other hand, it is clear from the laws of physics such a computing device can never be built, and the required knowledge can never be collected since an infinite amount of storage is already needed for representing a single transcendental number numerically. Therefore, in fact, one has to be content with approximations, resulting in a probabilistic prediction only. Thus, in practice, physics is probabilistic.

So based on these, the probabilistic nature of QM is basically just the same as randomness, we can never build a computer that could incorporate all the needed information, and we need to use approximations.

How do we know that certain quantum effects are random?

where CR Drost says:

In a very superficial sense of the term, one which has to do with excluding the possibility of determinism and therefore asking, "is there a way to understand the system as having an initial state which forced it to come to this conclusion," the answer is a qualified "no" he qualification here is the word "global": using some thought experiments (my favorite is a game called Betrayal) one can prove that there are quantum effects which cannot be understood in terms of classical local information In a deeper sense randomness is our way of reasoning about information that we do not know

But this one says more. This says that randomness means there is no way for the system to have a initial state which (because of causality) forces the system to evolve to a certain state. And that basically the world is quantum mechanical and there are quantum effects which cannot be understood in classical sense. This would mean that QM is not just simply random, but there are quantum effects that we do not understand and cannot even explain classically, it is not just simply random, but the underlying nature of the universe is probabilistic, and that is what we can model with mathematics.

Is the universe fundamentally deterministic?

But my question is about randomness meaning unpredictable, that is in some ways excluding causality. I do believe that QM probability does include causality, that is, it is predictable (to some extent).

Question:

  1. Is the probabilistic nature of QM simply just randomness (does it exclude causality)?
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    $\begingroup$ For this question to be answerable, you need to decide on a definition for the words "probabilistic" and "randomness". The answer is entirely dependent on the choice of definition. $\endgroup$ Jun 19, 2020 at 16:03
  • $\begingroup$ @probably_someone thank you correct, for randomness I would use "In the common parlance, randomness is the apparent lack of pattern or predictability in events." $\endgroup$ Jun 19, 2020 at 16:09
  • $\begingroup$ It's not clear what you're asking unless you provide clearly where you see the difference between something being "probabilistic" and something being "random". Whether or not the "nature" of the universe is deterministic or not has already been discussed at physics.stackexchange.com/q/63811/50583 and its linked question. Instead of quoting at length from other questions, please try to focus more on how your question is different from them. $\endgroup$
    – ACuriousMind
    Jun 19, 2020 at 18:32
  • $\begingroup$ @ACuriousMind I did edit, amplifying in my question randomness meaning excluding causality and predictability, and QM including causality, and predictability. Can you please reopen? $\endgroup$ Jun 19, 2020 at 18:40
  • $\begingroup$ I don't see how that is meaningfully different from asking whether QM is deterministic, which I already linked a duplicate for. $\endgroup$
    – ACuriousMind
    Jun 19, 2020 at 18:42

2 Answers 2

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I would say without much hesitation, that physicists are separated in two groups.

The first is those who believe in the intrinsic randomness of nature, part of its laws, a random series that cannot be computed by any algorithm.

The seconds is those who believe the randomness is just a result of our lack of knowledge of the physics at smaller than quantum scales, like hidden variable theories. These could be deterministic (but non-local of course) but we cannot predict the randomness because the system would behave partially chaotically due to our lack of knowledge and measurements of the hidden variables' behavior.

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I would regard probability and randomness as essentially synonymous, but I think that does not answer the real question you are getting at, which has to do with determinacy and indeterminacy. In classical physics, and in classical probability theory, it is assumed that random results arise from unknown quantities or "hidden variables". The universe could be determinate, but it would still be impossible to determine all unknown quantities, and consequently we would only be able to give a probabilistic theory of measurement results. This seems to be Neumaier's point, but it does not explain quantum probability.

There are numerous proofs, starting with von Neumann (whose original proof has been tightened up by numerous authors, such as Jauch and Piron, and Stan Gudder), Kochen and Specker, Bell, who gave two proofs (one of which he did not accept himself although it is perfectly valid and usually accepted as a variant on Kochen-Specker) which demonstrate that quantum predictions cannot be explained by a theory determined by classical hidden variables. Those proofs are rejected by some physicists for much the same reasons that Dingle rejected relativity. I.e. "I can't understand this, so it must be wrong". There is not much point in paying heed to that kind of argument (admittedly qm is far more difficult to understand than relativity).

The conclusion must be that randomness (and hence probability) in qm is a result of a fundamental indeterminacy in nature.

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