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I am new here and I am studying the philosophical implications of Quantum Mechanics. I read somewhere that QM and determinism are mutually exclusive and that QM involve a number of philosophers to think that nature is probabilistic. Is this true? And what are the theories or physical laws (in QM)that state that nature is probabilistic? In other words, where is the modal aspect in QM?

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    QM, as a mathematical formalism, and determinism are not mutually exclusive, the standard (Copenhagen) interpretation of QM (and many others) and determinism are mutually exclusive. What suggests indeterminism is that, unlike classical physics, quantum mechanics only predicts distributions of outcomes. There are deterministic interpretations of QM, e.g. Bohmian mechanics, although they are, arguably, "artificial" because the deterministic hidden variables are undetectable. Many consider even the Many Worlds interpretation "deterministic", although it is a quaint kind of determinism – Conifold Apr 11 at 18:44
  • Thanks @Conifold. I am ignorant on the theme and I just started with it. For this reason, Could you clarify me why QM as mathematical formalism and determinism are not mutually exclusive? Are you saying that the mathematical equations and formulas of QM express a certain kind of determinism?Thanks for the help. – Patrick Apr 11 at 20:29
  • Moreover, are the mathematical formalism of QM and determinism never mutually exclusive? @Conifold – Patrick Apr 11 at 20:32
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    Mathematical formalism (with some minimal interpretation relating numbers to meter readings) expresses nothing by itself, so it can not exclude anything philosophical. Abstract generalizations, like realism, determinism, materialism (or lack thereof) require postulates way beyond the formalism. Some weaker relations can be argued, like "suggests" indeterminism, or makes it "more plausible", the way classical mechanics made determinism more plausible (because it made unique predictions for any initial values), see QM vs determinism thread. – Conifold Apr 11 at 20:43
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The basic formula of QM in its most simple form is Schrödinger's equation. That's a linear differential equation like other differential equations from classical Newtonian mechanics or Maxwell's electrodynamics.

The distinctiveness of the Schrödinger equation: The equation describes in a deterministic way the time development of a probability.

According to the Copenhagen interpretation QM is a complete theory. Hence in QM we cannot do better than deriving a probability for the outcome of our experiments. And there is no other theory which derives more precise predictions than QM - also Bohm's theory does not.

I consider a good introduction to the Copenhagen interpretation - without any mathematical formalism - the book

"Werner Heisenberg: Physics and Philosophy".

Heisenberg is one of the founders of QM.

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