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Hi! I've been having this pestering question about the double slit experiment stuck for too long in my head and it's quite annoying, could use some help.

SO. If you had an electron gun that sent only 1 electron through the slit/hole at a time. Then you had a detector on the other side to know where the wave collapsed, so where the electron landed.

You knew where the electron WAS (through the slit/hole), and based on where it collapsed we can retroactively calculate the direction/momentum of when it WAS PREVIOUSLY in the hole.

Does the Heisenberg uncertainty principle allow for retroactive calculations of both position and momentum as long as it's not observed at the same time? (here it would be observed at different times, with a calculation to send it back). or is this also not allowed? if not, what am I misunderstanding?

thank you!

Oop
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  • If your electron gun sends an electron through a specific slit, it's a single slit experiment, not a double slit experiment. – John Doty Jan 07 '23 at 00:17
  • Consider signal processing instead of physics: the uncertainty principle says I can't measure time and frequency with high accuracy at the same time. Can I retroactively calculate both? – user253751 Jan 07 '23 at 00:19
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    You cannot infer which slit the electron went through based on where you detect the electron on the screen, assuming both slits were open and you didn't do anything to measure the electron when it passed through the slits. – Andrew Jan 07 '23 at 01:44

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By the defining statement of he Heisenberg Uncertainty Principle (HUP) :

The position and momentum of a particle cannot be simultaneously measured with arbitrarily high precision.

Note "simultaneously " means "at the same time".

The HUP can be derived from a given quantum field theory.

If one could design a double slit experiment with very high experimental accuracy measurements there is no constraint from the HUP

To elaborate on Andrew's comment have a look on the experiment one electron at a time

singlelectrdbl

The experiment is: an electron scattering off double slits of specific width of the slits and specific distance between the slits. The interference will appear only when the momentum of the electrons in the beam has a wavelength of the order of the distance between the slits. This is a a very small number $λ=h/p$. See this question here for numbers .. IMO it is not possible to have an experiment because from the detected point of interaction of the electron to accurately point back to an individual slit with a geometric ray, the experimental errors are too large.

anna v
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