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Electrons have negative charge, and therefore repel each other. That should mean that their position, and momentum probabilities should get skewed away when in the presence of some other electron. I.e. probabilities of them being close together should be very low.

So, if we send in two electrons at a time towards the slits, the probability that they passed through the same slit should be pretty low. Now I have two questions :

$1)$ What happens if we detect the electrons at one of the slits? If we see only one electron enter that slit, then the other electron must either have gone through the other slit, or not gone in. Does interference still occur?

$2)$ Why do electrons interfere anyway. In the two electron case, they should repel each other, and therefore their interference should greatly decrease, right?

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  • $\begingroup$ Your first argument is still stuck in the classical world. Each electron is a wave. Yes, they interact. But why can’t they both go through both slits? Once you assume you can localize one of them you have gone down the wrong path. $\endgroup$
    – Jon Custer
    Commented Aug 8, 2019 at 12:08
  • $\begingroup$ As I've said, the electrons repel each other, so that will affect their relative positions. They should not want to stay near each other. In cases of large number of electrons, the repulsive forces will balance out. In case of single electron, the force does not exist. But in cases with few electrons, there is a net repulsive force which will alter their ordinary probability densities. I am not localizing, but minimizing the probability of both electrons entering one slit, due to repulsion. $\endgroup$
    – Sohan Biswas
    Commented Aug 8, 2019 at 12:26
  • $\begingroup$ You remain fixated on an electron having a specific position. It doesn’t. Thus neither of the two electrons have a specific position. Yet, they do interact. $\endgroup$
    – Jon Custer
    Commented Aug 8, 2019 at 12:32
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    $\begingroup$ Why on Earth is it so hard? Who said anything about specific position? The electrons repel each other. So their position, and momentum probability distributions will be affected. The electrons will have very low probability of appearing close to each other. The probability of finding an electron somewhere will decrease if it is in a position which has a high probability of finding the other electron. Thus, there will be a very low probability of both electrons at the same slit. $\endgroup$
    – Sohan Biswas
    Commented Aug 8, 2019 at 12:50
  • $\begingroup$ I’m sorry you don’t like being told that you can’t have your cake and eat it too. But that is what you are trying to do. $\endgroup$
    – Jon Custer
    Commented Aug 8, 2019 at 13:02

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The interference pattern in the double slit experiment does not result from interactions between electrons.

In fact even if you will send the electrons one by one you are still going to get the interference pattern on the screen.

In quantum mechanics particles like the electrons are described by their wave functions and from the wave function all the information about the particle can be obtained.

One of the things that can be obtained from the wave function is the density probability to find the particle in some point in space which is equal to the squared norm of the particle's wave funcion at that point.

Therefore, the propagation of the particle's wave function in space determined the change of the particle's probability density over space.

The probability density must ensure that the probability to find the particle over all space equals to one.

Because of this it will be higher at some regions of space where it is most likely to find the particle and lower at the rest of space where it is not so likely to find the particle.

When you send an electron through the double slits, its wave function propogate through the slits and interfere with itself in such a way that the density probability to find the electron on the screen will follow the interference pattern.

Meaning that the values of the density probability to find the electron will be the highest on the stripes of the interference pattern on the screen which result with the electrons being measured on the stripes of the interference pattern.

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At the fundamental Planck level, our space consists of a sort of 'matrix' of basic distances which creates potential stress because of entropy (minute variations). Accumulations of potential stress distort space (and d=ct, also time) and distribute ('propagate') potential stress over all of space.

An electron is an accumulation ('mass') of distributing well accepted (observed) negative basic potential stress or 'charge', a fundamental characteristic of our space.

The probability of observing an electron trajectory depends on the potential stress regions the electron meets on its path. In the double-slit-experiment part of the electron may very well pass throught one slit, while another part passes through the other slit, and yet another part doesn't pass through either slit at all.

Two or more electrons, having the same (observed) basic potential stress, will always differ in trajectories at the most basic Planck level (entropy, remember?). In atoms electrons in their trajectories partly pass through one another, pulled inward by the positive basic potential stress at the nucleus, and driven outward by the speed of their distribution. Photons are exchanged. They 'kiss' and 'say goodbye'. Their trajectories change constantly. They fill a region of space with their combined potential stresses, which in normal circumstances shields the potential stress at the nucleus.

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It is a misconception that you are shooting multiple electrons at a time. Actually, you are shooting single electrons at a time.

The dot on the screen means that the electron has interacted with the screen atoms. Now the electron's partial waves travel through both slits and interfere with each other.

When the interference is constructive, you will see a dot. When the interference is destructive, you will not.

The interference pattern shows up because the wavefunction shows the probability distribution of electron's position in space, and because the electron and the slits are entangled. All the electrons you shoot are prepared with the same laserpump. The boundary conditions are the same for all electrons. When you repeat the experiment and shoot another electron, it will have the same probability distribution as all the electrons.

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  • $\begingroup$ You did not answer my question in the slightest. We can very easily send in two-ish electrons at a time by adjusting frequency of the electron gun, or using two guns. The question is why should they interfere when they repel. Their probability distribution will be affected by the repulsion, since they will tend to stay away from each other. In a stream of electrons, the repulsion force on any one electron can balance out, but not when there are very few electrons, like the two electron case. $\endgroup$
    – Sohan Biswas
    Commented Aug 8, 2019 at 11:07

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