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The wavefunction of a particle evolves with time in a manner strictly defined by the Schrodinger equation and the local environment. The wavefunction can become very complicated (e.g. a photon trapped in an odd-shaped box) and thus contain a lot of information about the local environment. When the particle is 'detected', the wavefunction collapses and it seems like almost all that information disappears (e.g. 'detection' might be just a single atom that is moved to an excited state and recoils - which can be very simply described) .

There seems no doubt the wavefunction can contain lot of information. This could be revealed by taking series of repetitive measurements and mapping out the wavefunction and figuring out the details of the environment that caused it to take that particular shape. This information is lost when the wavefunction collapses. But isn't loss of information akin to a decrease of entropy?

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  • $\begingroup$ What does it really mean for a wavefunction to collapse? In the 1D box, what information fully describes the particle? If a wavefunction collapses, is it not the superposition of states which collapse into the detected state? When we track which particle went through which slit of a double slit experiment, have we really lost information in the collapse of the superposition? / $\endgroup$
    – bleuofblue
    Commented Mar 22, 2022 at 7:14

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Information appears to disappear when a quantum system collapses. If a quantum system A ("the system") becomes entangled with another quantum system B ("the environment") then the state of the combined system A+B is no longer a product of their individual states - this is known as decoherence. If we only know the state of A alone we appear to have lost information about A - this is what we call "wave function collapse". Since every observation or measurement of A involves entangling A with the wider environment, then wave function collapse is a consequence of every measurement. If we could examine the state of A+B i.e. the combined state of A and its entire environment then we would find that information has not actually been lost, but has dissipated into the environment - but this is not a practical proposition, not least because we ourselves are part of that wider environment.

This is analogous to how energy appears to be lost from a dissipative system that has friction. If we could accurately measure the energy of the system and its environment we would find that the "lost" energy has been dissipated and appears in the environment as heat energy.

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  • $\begingroup$ couldn't the measurement just be a single atom getting excited? There doesn't seem to be a lot of information involved in that case. $\endgroup$
    – Roger Wood
    Commented Mar 22, 2022 at 23:25

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