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You claim that there seem to be quantum jumps and ask why this does not refute non-collapse theories. To answer the question of whether there is evidence that rules out no-collapse theories, you first have to work out what would happen is no collapse took place. So suppose that you have an atom $a$ in an excited state $|e\rangle_a$ that has some half life ...

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The no collapse people would say that if you write down the continuous evolution equations for the actual experimental setup in question that it predicts a perfectly continuous evolution of the wave vector into two parts that don't overlap. For instance a Stern-Gerlach device takes an incoming beam with a spin state and that beam branches into two. So the ...

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You speak of the measurement problem, which as yet has no widely accepted resolution. But a pure quantum state after a measurement is in exactly the same kind of entity as it was before the measurement, namely a new pure quantum state. It's simply that the measurement forces (by whatever as yet less than fully understood mechanism that resolves the ...

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