- #36
Jano L.
Gold Member
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vanhees71 said:Of course, everything in physics is (asssumed to be) causal...
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the state evolution is causal. The Schrödinger equation is a causal differential equation, as it must be, because it describes a physical dynamical process.
Initial value problem with the Schroedinger equation may have unique solution. As I understand, you call that "causal".
When we calculate the spin wave function this way, we obtain unique result ##\boldsymbol \psi_1## giving probability density in space symmetrical in ##z##.
But this calculated ##\boldsymbol\psi_1## is appropriate only before the measurement of the z coordinate takes place; after the measurement, we know the appropriate pair of wave functions in space is no longer that calculated in the above way. Based on the result of the measurement, the best choice is asymmetric pair where one component carries most of the probability and its density is localized asymmetrically in z.
This new pair of wave functions ##\boldsymbol \psi_2## cannot be obtained from the Schroedinger equation in a "causal" way. It is chosen based on the result of the measurement, which is random, not causal in quantum theory.
Another theory (not quantum theory in the usual sense of this name) may explain this change of the wave functions in a "causal" way (as a result of some evolution equation), but I do not think that is what you meant.
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