# Quantum mechanics

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1. Dec 13, 2015

### AlexGLSY

Why is Quantum mechanics probabilistic?
what prevents it from being deterministic, like classical mechanics ?(is it the lack of information about the processes and the forces applied at this scale?)

2. Dec 13, 2015

### zonde

If physical process and it's outcome is reproducible you can investigate the process and discover deterministic laws that describe it.
But Quantum mechanics says that at some level it is no possible reproduce the same outcome as you repeat the process. It's called uncertainty principle.

3. Dec 13, 2015

### AlexGLSY

That I know.
But my question is what causes it to be uncertain, is it the lack of information, or, there is enough information and that information implies that the processes at this scale are probabilistic?

Thank you :)

4. Dec 13, 2015

### zonde

Information can help us predict the outcome of process (say if we have entangled particle we can perform the same measurement on it), but no information can help us reproduce the same outcome in the same physical process when it is governed by uncertainty principle.

5. Dec 13, 2015

### Staff: Mentor

Quantum mechanics is inherently probabilistic; QM is a theory about the probabilities of various outcomes. You set up a problem and solve it using QM, and you'll get a bunch of probabilities as the answer.
It is possible that there is some deeper deterministic mechanism underneath it all, and that the probabilistic nature of QM is the result of our lack of information about what's really going on, but....
1) So far, no one has been able to find such a thing. That doesn't mean it doesn't exist, but even if it does exist we can't use it if we haven't discovered it - until then we're stuck with the probabilistic nature of QM.
2) if such a thing does exist, it will have to be at least as weird as QM.

6. Dec 13, 2015

### Staff: Mentor

Well first consider that a deterministic theory is a subset of probabilistic ones - it only has probabilities of zero and one.

So without making an assumption one way or the other lets suppose its probabilistic.

Some general considerations show that QM is one of two reasonable alternatives, the other being standard probability theory:
http://arxiv.org/pdf/quant-ph/0101012.pdf

The determining factor is if you want continuous transformations between pure states. It seems very reasonable because if a system is in a certain state and one second later its in another state it should go through some state in half a second.

Now here is the twist. These is this theorem called Gleason's theroem:
https://en.wikipedia.org/wiki/Gleason's_theorem

It has an interesting corollary - the Kochen Sprecker Theorem:
https://en.wikipedia.org/wiki/Kochenâ€“Specker_theorem

This shows that its impossible to assign only ones and zeroes to quantum states ie determinism is impossible. There is an out - contextuality:
https://en.wikipedia.org/wiki/Quantum_contextuality

But mathematically contextuality is a bit strange.

So here is the situation. If you want reasonable and elegant mathematics then nature is fundamentally probabilistic.

There are outs - but mathematically they dont mesh as well as not assuming them.

Thanks
Bill