I've recently been learning about Bell's Theorem and test experiments (e.g. as described here) and feel I understand why they imply that we cannot have local hidden variables.

However, I have heard some people say that these experiments also prove the universe is nondeterministic (that the state of the universe at time $t+1$ is not a function of its state at time $t$). I don't see why this is the case -- can't we have nonlocality and also determinism?

What, if any, experiments have we performed that would indicate the universe is nondeterministic?

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    $\begingroup$ "I have heard some people say that these experiments also prove the universe is nondeterministic" Those would be people who take localism as a postulate. I've also met people who take realism as a postulate (and take experiments on Bell's Inequality as implying that the universe is necessarily non-local). $\endgroup$ – dmckee Jan 5 at 19:55
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    $\begingroup$ Well, you could have neither, but I don't know anyone who likes that idea... $\endgroup$ – dmckee Jan 5 at 20:03
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    $\begingroup$ @EliRose Quantum mechanics is a pretty reasonable nondeterministic but local theory that explains the Bell experiment. $\endgroup$ – DanielSank Jan 5 at 20:12
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    $\begingroup$ Beware that "(non)local" is an overloaded word. Quantum field theory is "local" in the sense that it does not accommodate faster-than-light communication, but it is "non-local" in the weaker sense that it allows entanglement. String theory, on the other hand, is "non-local" in the stronger sense -- in fact a better word for string theory might be "alocal": spacetime isn't even well-defined in string theory, except as an approximation. So it's important to be clear about what we mean by "local" in discussions like this. $\endgroup$ – Chiral Anomaly Jan 5 at 20:37
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    $\begingroup$ @EliRose In order to engender a constructive answer, could you perhaps precisely define what you mean by "is nondeterministic" ? That way we don't have answers using various definitions. There's a long philosophical tradition of people talking past each other on these points :) $\endgroup$ – N. Steinle Jan 8 at 22:18

In the 19th century, it was believed that knowing all the coordinates and speeds can fundamentally predict the development of the world. But at the beginning of the 20th century, an uncertainty relation was discovered, which states that the values of speed and coordinates can only be determined with an error. So it is impossible to predict the development of the world. Moreover, quantum mechanics rejects the notion of a trajectory, roughly speaking there is only a cloud of particles and it is possible to predict its movement only with the help of probability theory. This suggests that our universe is not deterministic.

  • $\begingroup$ Not necessarily - in the Heisenberg Picture one can write the trajectory of the free particle. I think the point you mean to make is that measurement in quantum mechanics is probabilistic which you interpret to suggest that the universe is "not deterministic." So in principle, if one had the appropriate wave function then they could predict the "development of the world" in some sense using something like the Wheeler-DeWitt equation en.wikipedia.org/wiki/Wheeler%E2%80%93DeWitt_equation $\endgroup$ – N. Steinle Jan 8 at 22:17
  • $\begingroup$ I would not want to go beyond quantum mechanics using quantum gravity. It seems to me that we need to give a general presentation about quantum mechanics.Knowledge of the wave function predicts the measurement of probability. $\endgroup$ – Evgeniy Yakubovskiy Jan 8 at 23:09

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