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From what I've understood from reading different online sources including PSE*, measurements in quantum mechanics are generally argued to be irreversible (at least, when a macroscopic measuring device is used). This irreversibility is usually ascribed to an increase in total entropy (measured system $+$ measuring device) that occurs when the measurement is made. Quoting from the article "Irreversibility and Measurement in Quantum Mechanics" by Douglas M. Snyder:

Bohr (1935) maintained that quantum mechanical measurement also depended on the interaction between a macroscopic measuring instrument and the physical existent measured. He noted that when a macroscopical physical measuring apparatus is used, there is inevitably some loss of information concerning the measured system due to the resulting physical interaction. [...] For Bohr, once the information is lost in the measurement process, the measurement cannot be reversed.

However, this description only accounts for interaction-based measurements. What could we say about interaction-free measurements, then? (See the Wikipedia article for examples). If there is in those cases no physical interaction between the measuring instrument and the existent measured, by which mechanism could irreversibility be explained?

*See, for instance, this related question or this answer.

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dahemar
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    The subject is presumably wrapped up with entanglement. Pun intended, but the comment is serious. – dmckee --- ex-moderator kitten Aug 09 '16 at 21:15
  • @dmckee That's what I suspected... – dahemar Aug 09 '16 at 21:22
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    There are no interaction free measurements. Period. End of story. None of the examples in Wikipedia are even close, even though they show different levels of intellectual failure by their authors. – CuriousOne Aug 10 '16 at 01:14
  • @CuriousOne Could you please explain why do you think so? – dahemar Aug 10 '16 at 04:25
  • Because in all examples ever given the authors are blatantly ignoring that nature doesn't make a distinction between the field that is being measured and the matter that is measuring it, they are the exact same phenomenon. Quantum field theory doesn't have any self-consistency issues of this kind, they are only created by application of classical matter/quantum mechanical field approximations in non-relativistic QM. – CuriousOne Aug 10 '16 at 06:14
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    You cannot make a measurement without some energy exchange because all measurements are interactions. The best you can do is minimise the magnitude of the interaction, a process referred to as weak measurement. – John Rennie Aug 10 '16 at 09:53
  • @JohnRennie weak measurements are distinct from IFMs though. Renninger’s hemispherical detector fails to click, it localizes the particle to the other hemisphere with zero interaction. Not weak, not gentle, zero. With zero energy exchange. – JPattarini Mar 15 '23 at 15:25
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    @CuriousOne It sure seems like plenty of people who do this for a living have issues with interpretation, not just Wiki editors. Vaidman, Renninger, and plenty of others may be wrong, but what’s needed to correct those accounts is a clear explanation of how we should interpret these types of interactions instead. If you can point me toward an account that properly captures this I’d really appreciate it – JPattarini Mar 15 '23 at 15:28
  • Some measurements can actually be undone. I'll try to find the paper that now escapes me. – lcv Jan 21 '24 at 13:08

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So imagine an electron double slit experiment where you find interference patterns build up after sending a large number of electrons through one at a time. You then set up a detector at one of the slits to detect the passing electrons. Even though this only detects about half the electrons you find no interference patterns at all build up. In a Copenhagen type interpretation the measurement of absence at that slit, despite no apparent physical event occurring in the detector, is still an interaction between the measuring device and the superposition of the electron positions that reduces this superposition to being at one slit or the other. To argue this is not an interaction is to presuppose such an interpretation is wrong, which also flies in the face of the evidence that all interference patterns disappear.

Lawrence Davies
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