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In this figure from Wikipedia, we know that electron's wavefunction collapse at screen F, causing an interference pattern. Does it mean that in this case when the wavefront arrives at the screen, the screen does something similar as a 'measurement' to cause the wavefunction to collapse? If so, why wouldn't the electron's wavefunction collapse at screen S2 which will produce no interference pattern at the screen F, since the wavefront first arrives at the screen between slits B and C?

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  • $\begingroup$ My standard comment: there is no such thing as collapse. $\endgroup$
    – my2cts
    Jan 21 '20 at 10:28
  • $\begingroup$ The wave function is a mathematical description of the wave associated with the electron. It exists on a piece of paper or in the mind of an observer. When the electron goes from a free traveling entity to one that has been captured, a different description must be used. $\endgroup$
    – R.W. Bird
    Jan 21 '20 at 20:05
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This is an insightful question. Actually, the comment by @my2cts is right on the mark.

"Wave function collapse" really doesn't happen. Instead, the microscopic quantum state (location of photon's impact on the screen, which is quantum mechanically indeterminate) gets correlated to a macroscopic state (your perception of the location of the photon's impact on the screen). Your perception state, too, is quantum mechanically indeterminate. What you see is one randomly selected location out of the entire range of possible locations (with the randomness weighted according to the squared amplitude of the wavefunction at each location). If the wavefunction of the whole system is expanded to include you, there will be an infinite number of yous, each seeing the photon apparently hitting a different location on the screen.

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    $\begingroup$ Well, in this picture the collapse corresponds to picking out the version of you that sees a particular realization of the experiment. We've simply shifted the focus to a later stage, nothing changed. $\endgroup$
    – Ruslan
    Jan 21 '20 at 15:13
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As you can see from the comments, wavefunction collapse is just one of the interpretations (Coppenhagen) in QM, actually a very interesting one.

Now to your question, why does the electron's wavefunction not collapse at the first screen?

The answer is the two little slits. As the wave reaches the first screen, you say that the wavefront reaches the screen first between the slits. This implies that you think of the wave as propagating in the displayed fashion.

In reality, the electron as it propagates, a QM object, its trajectory is undefined. It takes all possible paths. Yes QM is a tricky beast and it is very unintuitive to imagine.

What really happens is that the electron as it propagates, reaches the first screen and continues to propagate through the slits, that is why there is no decoherence with the environment, that would cause the electron's superposition to reduce to an eigenstate, with a certain eigenvalue (the position of the electron on the screen).

The photons do not have a well defined trajectory. The diagram shows them as if they were little balls travelling along a well defined path, however the photons are delocalised and don't have a specific position or direction of motion. The photon is basically a fuzzy sphere expanding away from the source and overlapping both slits. That's why it goes through both slits. The photon position is only well defined when we interact with it and collapse its wave function. This interaction would normally be with the detector.

Shooting a single photon through a double slit

What confuses you is that you try to imagine the wave as reaching the part of the screen between the slits first, then decohere, and cause the collapse of the wavefunction. What really happens is that the electron takes all paths and finds a way through the slits. Yes it is very hard to understand how the wave takes all the paths, and knows not to collapse because there are two slits to go through. This is QM.

The most intuitive way of looking at interference that I have encountered is Feynmann's Path Integral Formulation. Loosely speaking, if you have a photon (or anything, really) in location A and want to work out its chance of moving to B, you imagine it taking every possible path between the two at the same time.

How two photons interfere in a double slit experiment

When the electron reaches the second screen, it does not find any slits to propagate through, and finally interacts with the screen, leaving a dot on the screen. That is what you call the collapse of the wavefunction. Its position becomes localized.

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  • $\begingroup$ Thanks for the answer. I asked this question because this may be a way to test Bohm Mechanics. So in your answer, the electron is taking every possible path at the same time and finds a way through the slits. Does that mean, that if I shoot N electrons one at a time to the slits, the final screen will detect N electrons and no electrons are found at screen S2? Because in Bohm Mechanics the N electrons are taken to be in an ensemble with different initial conditions, even the electrons reached the final screen displays interference pattern, there will be electrons didn't go through the slits. $\endgroup$
    – Winniebear
    Jan 22 '20 at 0:19
  • $\begingroup$ @Winniebear you are correct, no electrons are detected at S2. I actually asked a question about this, and each and every electron that was shot, will leave a dot on F. physics.stackexchange.com/questions/506916/… $\endgroup$ Jan 22 '20 at 4:36

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