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I am sorry for the title, which seems to be into the philosophical discussions about reality going random in quantum scale. My aim is to approach the question in a definite and most reasonable, though basic way. Is quantum mechanics deterministic, if the equations allow to predict quantum state? The answer is: yes. Is this correct?

I cannot imagine how this cannot be correct and it is weird that there is so much internet discussion about this, doing so much harm to basic perception of physical reality. Wikipedia states what can help understand the doubts:

The Schrödinger equation, applied to the aforementioned example of the free particle, predicts that the center of a wave packet will move through space at a constant velocity (like a classical particle with no forces acting on it). However, the wave packet will also spread out as time progresses, which means that the position becomes more uncertain with time. This also has the effect of turning a position eigenstate (which can be thought of as an infinitely sharp wave packet) into a broadened wave packet that no longer represents a (definite, certain) position eigenstate.[30]

However, the fact that some part of the system behaves in a particular way - a spread in this case - doesn't mean that it isn't deterministic. It just means that we do not have direct grasp on the particle in the equations, however it behaves predictibly, i.e. deterministically, because.. its evolution is predictable. Is this correct?

Adam Kaminsky
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This is really just a semantic distinction.

If by "deterministic" you mean "given any set of initial conditions, we can accurately predict the value we will measure for spin" then the answer is no, quantum mechanics is not deterministic.

If by "deterministic" you mean "given any set of initial conditions, we can accurately predict the probability with which we will measure a given value for spin" then the answer is yes, quantum mechanics is deterministic.

Izzhov
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  • You are probably aware about few problems with the answers. In the second version, you pass in the word "measure". It changes things. In first version, what is contained in it is the confusion about determinism and ability to predict, and the fact that the matter can still work in strict mechanical (deterministic) way. So one could also see confusion about the term "quantum mechanics" referring both to theory and to physical reality. – Adam Kaminsky Feb 06 '15 at 20:00
  • Actually, I used the word "measure" in both definitions. A definition of determinism that has nothing to do with our ability to observe the world is both meaningless and useless. As for your second point, you're completely right. Hence why the distinction is semantic. – Izzhov Feb 06 '15 at 20:14
  • Is in your opinion possible, that a mechanism works in a random way and still is being accessible for prediction through deterministic equations like those of Schrodinger? This of course comes down to what random means. It means: inconsistency. Compare this to a compiler running on a computer, that has corrupted memory. So, in your opinion, is quantum mechanics implemented over a corrupted base that has its states freely interfered with, creating the wave behavior? Because only then it would be what is indeterminism. – Adam Kaminsky Feb 06 '15 at 21:01