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To my knowledge it is quite widely accepted in the scientific community that at the quantum level physics is not deterministic, only probabilistic. I know that there were some efforts to find some hidden variables at play that could make quantum physics deterministic. However after Bell's experiment was performed, the chance that hidden variable is at play was diminished. Therefore we often hear that quantum world is truly random.

However even if hidden variables are not at play, I wonder whether we should accept this view that quantum effects are truly random. Why? I will give you an analogy: Let's say we have a pseudo-random function that generates numbers. The numbers it generates seem to be random even though they are not. If we only see the numbers it generates, it is impossible to find some hidden variables at play. Could the same be true about quantum randomness? Maybe at the beginning of the universe there was some "function"/mechanism by which the universe would behave. However this mechanism is pseudo-random and therefore we are not able to find any hidden variables at play even though the mechanism is at the roots deterministic.

I wonder whether my reasoning is correct and therefore even if there are no hidden variables at play, we shouldn't rule out the chance that quantum world is at the roots deterministic given that there is a chance that some pseudo-random mechanism is at play and this mechanism cannot be determined from a pure observation of the nature? Or does Bell's experiment rules out even this kind of determinism which is inherently hidden from us?

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    $\begingroup$ A pseudo-random number generator is a hidden variable: the hidden variable is the internal state used to generate the next "random" number. $\endgroup$ Commented May 10, 2021 at 15:31
  • $\begingroup$ As I understand, there could be super-determinism, which is not ruled out by Bell experiments. Inline Link $\endgroup$
    – aystack
    Commented Aug 13, 2021 at 9:55

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But you are describing the role of the wavefunction. , I have always thought that $Ψ$ , which is completely determined by the solutions of the quantum mechanical equation for the boundary conditions of the specific problem as completely deterministic. For example the hydrogen wavefunction are completely determined.

It is the wavefunction that gives the weight to create non randomness in the probability distribution, the measurable $Ψ^*Ψ$. It has the role of your

pseudo-random mechanism

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    $\begingroup$ Sean Carrol makes the point that quantum mechanics is deterministic in the Many Worlds interpretation. Every outcome happens every time. We are just aware of one outcome. [What is the Many Worlds Interpretation]{youtube.com/watch?v=t_xqNDII--Q} $\endgroup$
    – mmesser314
    Commented May 10, 2021 at 15:04
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    $\begingroup$ Where is the empirical evidence for many worlds? If you can't experimentally demonstrate evidence for such a model, you have to take that model on faith, which is religion, not science. $\endgroup$ Commented May 10, 2021 at 19:12
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The point of hidden variables is so the system can evolve over time in a definite manner. Essentially, if you knew all the hidden variables and had a powerful enough computer, you could calculate the future states of the system. As such, hidden variables are required for quantum physics to be deterministic, if there is only one world. If the Many Worlds interpretation were correct though, all possibilities would occur, each in its own world. As such, quantum physics would have no hidden variables, be deterministic, and unpredictable. I'd also like to mention that dynamic local hidden variables haven't been ruled out, see Classical electrodynamics can violate Bell’s inequalities.

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There is no way the world could be deterministic.

A deterministic universe is a logical impossibility as there is no method for determining the contents of such universe. Random evolution is not possible and neither is intelligent creation. Both possibilities are denied by determinism.

Therefore determinism is only a theoretical construct, a simplified model of reality.

There is no need to fear true randomness. It is the only scientific alternative to religion.

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