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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?

Qmechanic
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Peter A
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    Since this nice question is closed, I give an answer here https://physics.stackexchange.com/questions/336112/decoherence-and-youngs-double-slit-experiment – HolgerFiedler Feb 04 '21 at 19:30
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    Also added an answer to the other linked question – BjornW Mar 08 '23 at 09:49
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    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 https://physics.stackexchange.com/questions/336112/decoherence-and-youngs-double-slit-experiment – Bohan Xu Mar 08 '23 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.

Roger V.
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  • This is helpful thank you but I am still struggling. The wave function has to interact with the atoms of the material forming the slit. So, even in an idealised situation, decoherence should spoil the experiment. Where is the flaw in my logic? – Peter A Dec 22 '20 at 10:11
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    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 – Roger V. Dec 22 '20 at 10:15
  • Could you explain a bit more how it is possible to set up an experiment where the material presents close to a true double slit potential and the fact it is made up of atoms is irrelevant? Unfortunately I don't have access to the paper you mention and would probably struggle to understand it. – Peter A Dec 22 '20 at 10:21
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    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. – Roger V. Dec 22 '20 at 10:24
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    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?". – Ruslan Dec 22 '20 at 21:28
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    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? – Peter A Dec 22 '20 at 22:09
  • The experiments reported are those, where one could avoid decoherence - using high quality materials, cryogenic temperatures, etc. In most cases decoherence does spoil the experiment - so I do not quite understand your question anymore. If you talk about the real experiments, than your statement is incorrect, if you mean idealized situation, then I have already explained the difference between a real experiment and a model. – Roger V. Dec 23 '20 at 10:31
  • @Ruslan, I think by now the question needs to be refined - as is it leaves everyone to guess what is being talked about: a two-slit experiment in the books, a specific realization of interferometer, etc. – Roger V. Dec 23 '20 at 10:33
  • Is AB the only instance of double slit experiment with electrons that has actually been conducted? – Ruslan Dec 23 '20 at 13:19
  • @Ruslan I think it is certainly not the case, I gave it as an example that decoherence is an issue in real interferometers, that there is more to it than it seems at a first glance, and that it is actively studied. – Roger V. Dec 23 '20 at 14:52
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    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? – Peter A Dec 23 '20 at 17:38
  • That electrons are absorbed or reflected by a material does not by itself have any effect on coherence and phase. Still, this is a vast subject, and you should ask more specific questions. (If you search here for questions containing words decoherence and dephasing, you can learn quite a bit.) – Roger V. Dec 23 '20 at 18:26
  • Question edited for clarity – Peter A Dec 24 '20 at 09:49
  • Dear Vadim. It is usually frown upon to directly copy-paste identical answers. (The problem is if everybody start to copy-paste identical answers en mass.) – Qmechanic Dec 24 '20 at 10:13