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Imagine firing one electron at a time at a double slit. Clearly the wave function interacts with the atoms of the material, and presumably many electrons do not pass through. Why does decoherence from these interactions not spoil the experiment?

The question has been asked before, but there is no answer

Edit, to clarify the question: since the electron wave function interacts with the atoms of the material in which the double slit is cut, I naively expect that decoherence would make the system classical, no matter how carefully the experiment is set up. I must be misunderstanding the decoherence mechanism that prevents macroscopic systems being in quantum superpositions. The question is, why doesn't this decoherence spoil the double slit experiment? Can anyone explain why decoherence ensures Schrodinger's cat is alive or dead, but does not ensure the electron goes through one slit or the other?

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    $\begingroup$ Since this nice question is closed, I give an answer here physics.stackexchange.com/questions/336112/… $\endgroup$
    – HolgerFiedler
    Feb 4, 2021 at 19:30
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    $\begingroup$ Also added an answer to the other linked question $\endgroup$
    – BjornW
    Mar 8 at 9:49
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    $\begingroup$ In short: this is because when quantum fluctuation of certain object's observable is "small", one can treat such observable classically so this classical parameter can't decohere the system of interest. A longer and more mathematical version of my answer is in physics.stackexchange.com/questions/336112/… $\endgroup$
    – Bohan Xu
    Mar 8 at 17:23

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One should distinguish the idealized model discussed in textbooks and real interferometers. Decoherence is indeed an issue in many experiments, which is why realizing such interferometers in practice has been challenging.

What is more surprizing, is that some degree of decoherence is present even in the simplest discussions of the two-slit experiment, as not all the particles arrive at the screen - some of them escape in space, while others land on the non-transparent part of the wall with the slits. Thus, the first attempts of literally realizing an Aharonov-Bohm experiment in solid state devices, with the two particle beams confined within two waveguides (arms of a ring) resulted in phase rigidity - AB oscillations with phase either $0$ or $\pi$. To make the phase change continuously, one had to introduce artificially particle losses, as in this paper. Since then the decoherence in AB interferometers was studied extensively, both experimentally and theoretically. There have been even proposals of using controlled decoherence for measurements, as here.

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    $\begingroup$ I think you are missing the nature of idealization here - you are trying to include the interactions which the idealized description deliberately excludes. In other words, you are trying to consider a non-ideal two-slit experiment with dephasing $\endgroup$
    – Roger V.
    Dec 22, 2020 at 10:15
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    $\begingroup$ It is an idealized experiment - a model that exists only on paper, but not in real life. Its point is to capture some essential physics, rather than to provide a detailed description of all physics processes. It is by no means unique to a two-slit experiment - e.g., all the Newtonian mechanics is about an idealized point-like object. $\endgroup$
    – Roger V.
    Dec 22, 2020 at 10:24
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    $\begingroup$ I think the main question here (which your answer doesn't seem to address), as well as in the other thread you have copied this answer to, is "what properties are maximized in the ideal double slit, so as to avoid decoherence?". Or, conversely, "what should be made more-realistic/less-ideal in the double slit to make it necessary to account for decoherence?". $\endgroup$
    – Ruslan
    Dec 22, 2020 at 21:28
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    $\begingroup$ In addition, what I am trying to get at is that the experiment has been performed succesfully many times, so it is not a matter of idealised theory versus reality. The electrons (or their wave function) interact with the atoms in the material, since many don't get through. If so, then why doesn't decoherence break the experiment? The answer must be that I have a misunderstanding of how decoherence works I think. But what is it? $\endgroup$
    – Peter A
    Dec 22, 2020 at 22:09
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    $\begingroup$ Thank you both for the helpful comments. My question is more about decoherence than the double slit experiment specifically. I thought that as soon as the electron interacts with a macro system, in this case the material making the slit apparatus, then decoherence applies and the system becomes classical. Therefore my belief is the experiment can never work because many electrons are absorbed or reflected by the material, and they share the same wave function as those that pass through. The expt has been done many times, so my q is what is my misunderstand of decoherence? $\endgroup$
    – Peter A
    Dec 23, 2020 at 17:38

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