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You might be interested in this question or this question (and some others I cannot track down now). The basic problem is this: It is not clear what we exactly mean by "deterministic". If you mean that we can in principle determine the future state of a system solely from initial conditions, then the time evolution given by the Schrödinger equation is ...

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To say the least, they are inseparable. The "indeterminacy" is meant to be a synonym of the "uncertainty" (original in German: Unschärfe oder Unbestimmtheit), e.g. the nonzero values of $\Delta x$ (uncertainty of position) and $\Delta p$ (uncertainty of momentum) that obey $$\Delta x \cdot \Delta p \geq \frac\hbar 2$$ This is a consequence of the nonzero ...

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The most important thing to learn in Chaos Theory is perhaps the idea that deterministic equations lead to unpredictable dynamics. It is not always a matter of having been able to make the measurements practically accurate. Infinitesimal difference in Initial Conditions make the difference between the paths in the phase space diverge exponentially (jargon: ...

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Well, there's three different types of answers I can think of, with regards to what you asked. One case we can have is that there's some systems that are so complicated, that if you change their initial states only slightly, the system changes drastically. This is called chaos. James Gleick's book is a good one for laypeople. Any graduate level mechanics ...

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This is a partial answer based on a quick read of the paper. If somebody would like to post a fuller analysis I'll delete this. Anyhow, the experiment is not defying the uncertainty principle. Instead it's effectively moving the uncertainty around. The uncertainty attached to the whole system is unchanged, but it's possible to measure one aspect of the ...

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So I was wondering when physics takes this approach to this subject matter is it saying that the movement of an atom is actually random or that the details of explaining may be to cumbersome and be approximated with great accuracy just by using these distributions? Depends on the physicist. Some like to think there is fundamental randomness in nature, ...

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The quantum world is really random. There are no local hidden variables.

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There is nothing stopping you from interpreting the Schrodinger equation as rules for a cellular automata, in fact, the Schrodinger equation has the same form as the diffusion equation, but evolving in imaginary time. Let's write down some rules. $$i \hbar \dot \psi = H \psi$$ assuming we have a time independent potential  i \hbar \dot \psi = ...

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