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I just want to know if the quantum world is random. Or if the randomness is fully explained by measurement error. Or if it is just semantic.

The previous questions are open to interpretation and do not ask if "quantum randomness" is a scientific fact.

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marked as duplicate by John Rennie quantum-mechanics Oct 22 '18 at 11:25

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The Schrödinger equation is a deterministic equation that describes how the probability distribution contained in the wave function changes over time. So for a normalized wave function $\phi$ the probability that the system described by $\psi(t)$ is in state $\phi$ at time $t$ is given by $\bigl | \langle \phi \, | \, \psi(t) \rangle \bigr |^2$. So if you pick \begin{align*} \phi(x) = \begin{cases} \frac{1}{\sqrt{\mathrm{Vol}(\Lambda)}} & x \in \Lambda \\ 0 & x \not\in \Lambda \\ \end{cases} \end{align*} for some volume $\Lambda$, then the above is the probability to find the quantum particle inside the volume $\Lambda$ at time $t$.

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  • $\begingroup$ What definition of 'deterministic' are you using? $\endgroup$ – Avantgarde Oct 22 '18 at 4:34
  • $\begingroup$ The Hamiltonian*, and therefore the Schrödinger equation aka evolution equation, does not depend on a random variable. (* There are cases when you would consider a family of random Schrödinger operators, e. g. to treat disordered systems, and then study properties that the system has with probability 1, for example. But that is a slightly different case.) $\endgroup$ – Max Lein Oct 22 '18 at 4:47
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According to our current understanding of physics, the evolution quantum systems are determined by the Schordinger Equation. The Schrodinger equation is totally deterministic, that is, if you know the state of the system to begin, you can calculate the state of the system at any other time with certainty.

The randomness people usually talk about takes the form of the quantum measurement problem, which is apparently fundamentally random (not due to experimental errors).

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – David Z Oct 22 '18 at 3:59
  • $\begingroup$ @Anti Fa If you want to discuss randomness, then we are really entering the realm of philosophy. (The brother of my PhD advisor, who is a philosopher doing research on randomness, asked my PhD advisor, an expert on statistical mechanics, what randomness is. After my PhD advisor gave his view on the topic, his brother just exclaimed: “I can't believe that after all these years you still don't know what randomness is!”) The topic is covered in a section of a book by Detlef Dürr and Stefan Teufel (e. g. whether randomness is connected to lack of knowledge and the like). $\endgroup$ – Max Lein Oct 22 '18 at 4:07

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