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In depictions of the double-slit experiment that model the photon or electron as a particle, i.e. when attempting to measure which slit the particle passes through, it always shows the particle entering one of the two slits. Why is it that the particle can't hit the space between or outside the slits, i.e. never even make it through? Is it implied that the experiment is just repeated until a particle makes it through, i.e. shows up on the film or detector on the other side?

I see how, modeled as a wave, the wave always makes it through. But the illustrations of particles kind of don't make sense to me. Is it because they are just simplified illustrations?

I realize this sounds like a silly question, but I'm trying to go back and question everything I've taken for granted. (For example, I wondered what if there is some weird, hidden interaction between the ones that didn't make it through and the ones that did?)

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    $\begingroup$ I think you are correct in thinking that the wave interpretation is conditional on the fact that there was no collapse of the wave-function at the slit. Those photons or electrons are being ignored. $\endgroup$ – DWin Nov 26 '18 at 8:24
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    $\begingroup$ Why do score results in sports not include a record of every goal that was attempted but not successful? $\endgroup$ – Shufflepants Nov 26 '18 at 15:44
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    $\begingroup$ @Shufflepants ... because methodology doesn't count in those sports? $\endgroup$ – Andrew Cheong Nov 26 '18 at 15:46
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    $\begingroup$ @Shufflepants often stats like "shots on goal" are recorded. $\endgroup$ – Jon P Nov 27 '18 at 0:27
  • $\begingroup$ @JonP That's why I specified "score results". In the same way, there are likely studies that do make mention of rate of particles failing to pass through the slits. It was just a question aimed at getting the OP to realize why nobody talks about the particles that didn't pass through the slits. $\endgroup$ – Shufflepants Nov 27 '18 at 4:11
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"Is it because they are just simplified illustrations?" you ask. The answer is simply: yes it is because they are simplified illustrations.

Furthermore, not only can the particle hit the barrier outside or between the slits, typically most of the particles do that. Only a small fraction make it through. I say 'typically' because in such experiments we don't normally bother to set up the optics (whether for photons or electrons) so as to restrict illumination to only the two slits and not the surrounding area. But in principle it could be done, and then only a few particles would miss the slits.

It is quite common, in experimental physics in this area, to do what is called 'post-selection'. That is the name for the practice of selecting from your dataset only those outcomes triggered by some signal, such as, in this case, the signal that a dot appeared somewhere on the final screen. Then after that the discussion is really saying not 'this is what happened in every run' but 'of those runs where something made it to the detector, this is what happened'. One can regard the simplified pictures as showing what is understood to have happened for those runs which were singled out by this 'post-selection'.

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  • $\begingroup$ I see, thanks. So, am I correct to imagine that the "which way" information is more like this: a which-way time series, and a when-which-electron-hit-the-back-wall time series, the two of which the experimenters can line up to have which-way information about each particular electron. I'm just trying to make these hypothetical experiments as concrete as possible so I can catch any misconceptions I may have. $\endgroup$ – Andrew Cheong Nov 26 '18 at 16:05
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    $\begingroup$ Yes. Suppose the luminosity is quite low, say 1 photon or electron per second making it through the whole journey to the final detection screen. A which-way detector registers some sort of signal each time a particle goes by, with a different signal for each slit, and we may suppose its response time is fast compared to one second in this example. $\endgroup$ – Andrew Steane Nov 26 '18 at 17:30
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    $\begingroup$ @AndrewSteane: I understand your remark about the "detector with a different signal for each slit", but for someone who is not familiar with quantum physics this leaves out a crucial detail. This set-up alters the outcome! You no longer get the diffraction pattern of the double-slit experiment. Instead, you get a mixture of two single-slot diffraction patterns. This has been experimentally validated. The measurement directly affects the outcome. $\endgroup$ – MSalters Nov 27 '18 at 15:10
  • $\begingroup$ @MSalters It gets weirder than that. You can decide after the fact whether or not you detect which slit the photon comes through. Its called the Quantum Time Eraser or Delayed Choice Eraser. I think it was this video that had the visuals that made it click for me why the interference pattern change happens the way it happens. If not there's a bunch of others and I've seen most of the top 10. $\endgroup$ – Draco18s Nov 28 '18 at 14:17
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If you look up Doctor Quantum on youtube you'll find some (horribly dated) 3D animation videos that DO show the particles that bounce off the space outside the slits. At least initially in the 'marble' demonstration (the first light one also shows illumination on the slit device). They are culled later because of the same reason they've been culled from other examples of the double slit experiment.

And that reason these particles aren't shown is because they are irrelevant: they don't pass through the slits and so are not part of the "what happens when they pass through the slits" experiment.

Its kind of like asking why people under the age of 18 aren't included in election polling data. Surely these people exist!

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  • $\begingroup$ If you checked how people under the age of 18 voted, you may or may not be surprised to learn that none of them voted! $\endgroup$ – Neil Nov 28 '18 at 11:03
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When I performed this experiment the last time, I used a laser, so no single photons were fired, but an endless stream of photons, so to say. Then, the double slit was so positioned that the maximal intensity way measured at the detection screen (with a photometer).

That some photons hit the area between or outside the slits is very likely, as the laser itself has a certain cross-section. Then, the wave-function would collapse or the photons are reflected and therefore not measured.

In theory, if you perform this experiment with one photon, what would you expect? Well, your wave function should include the possibility of a reflected (or not visible / detected) photon with a non-zero probability. Then, an experiment on it would only make sense with many many measurements, to have a reliable statistic for you probability-distribution, so you end up with doing the experiment many times.

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Here is a double slit experiment one electron at a time hitting the screen:

dbls

The quantum mechanical setup is : "electron of given momentum scattering on two slits a fixed distance apart , a fixed width". The screen shows the electrons which go through.

The quantum mechanical solution, i.e. the wavefunction $Ψ$ whose $Ψ^*Ψ$ gives the final probability distribution shown in the last frame, gives the probability for the electron to go through the "barrier of two slits" and hit the screen.

Though the distance between slits is small, if one could place a detector there, or a photo-luminescent material, there will be a probability of detecting the electrons having a probability to hit there. One does not need to confirm this, as the wave nature of the probability is evident in the interference pattern.

But the illustrations of particles kind of don't make sense to me. Is it because they are just simplified illustrations?

It should be clear from the above then, that the electrons are not classical particles, and should not be extrapolated on a two dimensional graph as particles, except as an approximation over large distances where they do not interact.

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    $\begingroup$ This is a fine explanation of what actually happens in the double slit experiment ... but that isn't what the OP asked about. They asked about the explanations shown in the text book if you imagine that electrons or photons are particles. Those explanations only show the particles going through a slit, and the OP doesn't understand why they don't show the particles hitting the barrier. $\endgroup$ – Martin Bonner Nov 26 '18 at 11:19
  • $\begingroup$ @MartinBonner I have not seen such graphs, and if they exist they are misleading. I edited to make this clear. $\endgroup$ – anna v Nov 26 '18 at 15:38
  • $\begingroup$ The diagrams are not misleading. When Young did his original experiment, the predominant theory of light was Newton's corpuscular theory. The diagrams accurately show what such a corpuscular theory would predict (exactly two bright patches, and the rest dark). The fact that this is not what is observed is what overturned the corpuscular theory. Example - second diagram on: people.vcu.edu/~djbromle/color-theory/lecture/6a.html $\endgroup$ – Martin Bonner Nov 26 '18 at 15:50
  • $\begingroup$ @boner he is talking about electrons and present day double slit experiments, as far as I understand the question, not asking about the old light as particles, but present day physics. $\endgroup$ – anna v Nov 26 '18 at 15:56

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