We first explore the role of (non-) determinism in various modeling frameworks and zoom in on two of them: Markov processes and quantum mechanics. A close and precise alignment of these two frameworks shows that quantum mechanics contains an embedded Markov process. The well-known Bell experiment is used to show that quantum mechanics is probabilistic and hence non-deterministic. We show that the established model for the Bell experiment, based on four observables, is wrong and leads to an apparent contradiction. An appropriate probability model, based on two observables and two detector settings, avoids this paradox. We also offer a proof that there cannot exist a so-called hidden variable that makes our probability measure separable, in agreement with Bell’s main finding. Finally, we speculate whether at some deeper level there may exist a deterministic theory for quantum mechanics.

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Is Quantum Mechanics Deterministic or Non-deterministic?

  • Kees van Hee,
  • Kees van Berkel

摘要

We first explore the role of (non-) determinism in various modeling frameworks and zoom in on two of them: Markov processes and quantum mechanics. A close and precise alignment of these two frameworks shows that quantum mechanics contains an embedded Markov process. The well-known Bell experiment is used to show that quantum mechanics is probabilistic and hence non-deterministic. We show that the established model for the Bell experiment, based on four observables, is wrong and leads to an apparent contradiction. An appropriate probability model, based on two observables and two detector settings, avoids this paradox. We also offer a proof that there cannot exist a so-called hidden variable that makes our probability measure separable, in agreement with Bell’s main finding. Finally, we speculate whether at some deeper level there may exist a deterministic theory for quantum mechanics.