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If two electron diffraction experiments are conducted under exactly the same conditions and are randomly stopped at the same time, will the results be completely identical? That is, will the diffraction patterns be exactly the same?

What about interference experiments?

Has anyone conducted such a comparative experiment, to investigate whether the diffraction and interference patterns from two identical experiments are completely the same?

UPDATE：

If a stream of two entangled electrons is individually directed toward two equidistant, completely identical diffraction slits (a symmetric diffraction setup), will the resulting patterns be identical or symmetric randomly stopping the experiments?

The resulting patterns will exhibit a form of symmetry due to the entangled nature of the electrons and the symmetry of the experimental setup And No comparative experiments have been carried out, to investigate whether the diffraction and interference patterns from two identical experiments are completely the same，or display form of symmetry at any randomly stopping times ?

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    $\begingroup$ What do you mean by the "diffraction pattern being the same"? The position of the fringes being the same? Or the sequence of point positions appearing in the apparatus? $\endgroup$ Commented Jan 16 at 9:58
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    $\begingroup$ @Ruffolo，both. And I hope there are comparative experiments.and thank You for editing $\endgroup$ Commented Jan 16 at 10:08
  • $\begingroup$ What is the difference between "identical" and "completely identical"? $\endgroup$ Commented Jan 16 at 10:18
  • $\begingroup$ Buildup of random single-electron events to give a diffraction pattern is shown in this paper doi: 10.1119/1.16104. Of course the next experiment would be different, though they do not show that explicitly, if that is what you were wanting. $\endgroup$ Commented Jan 16 at 21:46
  • $\begingroup$ @dharr no,it is not what I want,. I just want two comparative experiments to check if the results are identical at any random times. $\endgroup$ Commented Jan 16 at 23:17

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The whole point of QM is that it is inherently probabilistic, and to achieve comparable results, you need to run the experiment many times. This means that the actual patterns formed by the individual electrons on the screen will never be the same, but on all these patterns, there will be areas where no electron will ever land. These areas will always be the same. If you run the experiment often enough, you will find that it always converges toward the same diffraction pattern. Where exactly the electrons land inside the allowed areas is irrelevant, as long as you can get a clear enough picture of where they won't land.

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  • $\begingroup$ Perfect answer, but one should keep in mind that there are always errors due to the measurement set up as well... So even classical experiments might yield notably (yet small) differences upon repeating. $\endgroup$ Commented Jan 16 at 10:18
  • $\begingroup$ @TobiasFünke Of course. We will never observe the "true" diffraction pattern (or "true" result of any experiment). That is why I deliberately chose vague formulations such as "convetge toward" and "clear enough picture". At the end of the day, physics is all about matching the theoretical approximation with an experimental one, but the match will never be exact. $\endgroup$ Commented Jan 16 at 10:24
  • $\begingroup$ "The whole point of QM is that it is inherently probabilistic, and to achieve comparable results, you need to run the experiment many times. This means that the actual patterns formed by the individual electrons on the screen will never be the same, but on all these patterns, there will be areas where no electron will ever land" I hope there are experiments to supporting the statement $\endgroup$ Commented Jan 16 at 10:41
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    $\begingroup$ @WangAtChicago How do you think this information was obtained in the first place? QM has been around for a century, and is the most rigorously tested physical theory we ever came up with. Electron diffraction has been tested many times. I don't have a link to any papers right now, but it should be simple enough to find by using your internet search engine of choice. $\endgroup$ Commented Jan 16 at 10:52
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$\dots$ will the results be completely identical?
No, as the final result is dependent on a probability function.
Just think of the first electron which passes through an experimental arrangement.
Will it arrive at the same position on detecting "screen" every time the experiment is started?

I assume that there are electron diffraction experiments which have been conducted repeatedly using the same apparatus and it being noted that although the build up of the interference patterns is similar, the patterns are not identical.

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  • $\begingroup$ "No, as the final result is dependent on a probability function." Any comparative experiments supporting the claim? $\endgroup$ Commented Jan 16 at 10:46
  • $\begingroup$ @WangAtChicago the law of large numbers says just do both experiments enough and you'll see their probability function in the data at whatever resolution you have the patience for. E.G., flip a coin enough times and you'll eventually see both sides. If you have lots of patience you may even see it land on edge. $\endgroup$ Commented Jan 17 at 6:24

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