system
Given the following post, respond as if you're commenting on Reddit:
human
Double slit experiment with electrons using detectors

My understanding of the standard electron double-slit experiment is as follows:

If you fire electrons at the correct momentum at a pair of slits, the electrons hit the screen in the distribution of an interference pattern. i.e. each electron hitting the screen at a position with a given probability which follows a wave-like distribution.

What's really odd is that this probability function is even obeyed if we send one electron through at a time. The explanation I've heard for this is that the electron actually travels through both slits and interferes with itself. 

My question is whether this can be detected. Since electrons in motion produce a magnetic field, we could stick a field detector in each of the double slits. We could then work out which slit the electron went through.

What happens here? Is the magnetic field detected half of what we expect of a electron moving with that momentum?
gpt
If you detect which slit the electron goes through, you collapse the wavefunction so that its position is defined at that point, so no wavefunction 'goes through' the other slit and there's nothing to interfere with. Instead, you see a simple ballistic pattern, without interference.

To say that another way, measuring which slit it goes through forces it to choose. We can't detect bits of wavefunction, only actual electrons, because the detector either detects nothing (the wavefunction didn't collapse to have the electron here) or an electron (the wavefunction did collapse to an electron here). Once we know which slit it does through, the interference of wavefunction through the other slit is negligible, even if you use an interpretation that says these paths are possible.