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Let $S$ be a quantum system and let $D$ be a detector. Suppose that $D+S$ does not interact with the environment. Now when $D$ makes a measurement of $S$, the wave function of $S$ collapses. Therefore, the wave function of $S$ does not follow a unitary evolution, so it follows that it does not satisfy the Schrödinger equation during the measurement process.

But the combined system $D+S$ also has a wavefunction. On the one hand, you could argue that the wavefunction of $S$ is a part of this system, so since this wavefunction collapses, the wavefunction of $D+S$ can not satisfy the Schrödinger equation during the measurement process. On the other hand, $D+S$ is a closed system so it should satisfy the Schrödinger equation. How can this be resolved?

Tobias Fünke
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Riemann
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    Note that in general you cannot associate a wave function to a subsystem (entanglement), but only a mixed density operator. – Tobias Fünke Jan 15 '23 at 12:41
  • If that is true, how can we then ever speak about wavefunction collapse? Because wavefunction collapse means that a system is measured, but that means that the system is a subsystem of [system+detector]. So whenever there is wavefunction collapse, we can actually not say that there is a wavefunction at all? – Riemann Jan 15 '23 at 12:42
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    I don't understand. Considering projective measurements, suppose your state is described by a (possibly mixed) density operator; then the post measurement state is given by the Lüders rule. So even if you don't consider subsystems etc., the notion of measurement in a mixed state is defined. – Tobias Fünke Jan 15 '23 at 13:16
  • https://physics.stackexchange.com/questions/33437/is-quantum-entanglement-functionally-equivalent-to-a-measurement – Alex K Jan 15 '23 at 13:49
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    This is just the paradox of Wigner's friend. You keep asking questions where you assume "wavefunction collapse" is something that explicitly happens in quantum mechanics and you keep getting answers saying "it depends on your interpretation". What are you hoping to achieve by this series of questions? – ACuriousMind Jan 15 '23 at 13:52
  • It’s all coming down to the question when the curious thing happens that in some interpretations is called ‘wavefunction collapse’ and on other interpretations ‘branching of the multiverse’ and in other interpretations ‘a measurement’. This phenomenon happens under certain circumstances, but there should be a simple objective criterion independent from the interpretation. – Riemann Jan 15 '23 at 14:21
  • An example of such a criterion would be ‘when at least five particles form a structure that is able to do this complex action and that is able to store information in this specific way, and when this structure interacts with another particle in this specific way, then and only then a measurement occurs, or whatever you want to call it’ – Riemann Jan 15 '23 at 14:23
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    How do you get something like the concept of entropy if everything is microscopically reversible? Because entropy, as well as the collapse (that is related a non-unitary evolution), arise when you have elements that are not included in your description. If everything is in the wave function (good luck.. useless scheme) then there is no collapse. Collapse, as stated here ( ) is a black box for when you only model the few degrees of freedom pertaining to the – Quillo Jan 15 '23 at 15:17
  • @Quillo so it seems the answer to this question is yes? – Riemann Jan 15 '23 at 15:24
  • @Riemann it's not unreasonable to say that the whole Universe follows unitary evolution (leaving out, just to be conservative, the black-hole "paradox"). However, the only value of such a statement is just philosophical consolation: you can calculate nothing out of it. I believe that the answer is "obviously YES". – Quillo Jan 15 '23 at 15:33

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