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Various texts (1,2) state that electrons are point particles, but if this is the case then when two electrons collide, one of them knows the others position with exact certainty (treating one as an observer and the other the system). If this ever happens we run into contradictions, mentioned in this post.

This must mean that if a collision between electrons takes place, there must be a non zero scattering cross section of each electron. If this is truely the case, what is that cross section?

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  • $\begingroup$ en.wikipedia.org/wiki/Møller_scattering $\endgroup$
    – G. Smith
    Commented Oct 6, 2020 at 3:22
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    $\begingroup$ when two electrons collide, one of them knows the others position with exact certainty Where did you get that idea? $\endgroup$
    – G. Smith
    Commented Oct 6, 2020 at 3:26
  • $\begingroup$ They don’t have to “collide” to scatter. $\endgroup$
    – G. Smith
    Commented Oct 6, 2020 at 3:42
  • $\begingroup$ @G.Smith I thought the two point particles had to be in contact in a collision. From falsehood anything follows, which led me to believe that one would know exactly where the other was during the collision, since both are point particles. $\endgroup$
    – user400188
    Commented Oct 6, 2020 at 9:36
  • $\begingroup$ @KFGauss if you can provide the cross section and your own brief description of what it means, I'll accept it over the current one. It will be more useful to future people looking up the question. $\endgroup$
    – user400188
    Commented Oct 6, 2020 at 9:39

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Electrons do not literally have to hit each other in a collision - they interact via Coulomb interaction, so that the scattering cross-section may be much bigger than the electron "size".

Update
The exact solution is available in many textbooks, in both quantum and classical cases. Moreover, the problem is quite similar to that of scattering in a gravitational field (although the sign of the potential is different), well understood in classical mechanics.

There is however an important point to bring up in this context: the cross section is by definition the cross-sectional size of the scatterer that it would need to have to case the same effect, if we replaced the actual interaction with contact interaction, implied in the question.

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Electrons are quantum mechanical entities , point particles in the table of elementary particles.

In quantum mechanical frames there are no "collisions", but there are interactions, and interaction crossections can be calculated which are independent on the kinematic frame of reference.

The trajectories of the two electrons cannot be predicted. The predictions of quantum mechanical calculations are probabilistic, i.e. many events have to be studied with the same boundary conditions to test the prediction.Up to the present, the theory is validated.

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  • $\begingroup$ Really nice answer. $\endgroup$
    – Árpád Szendrei
    Commented Oct 6, 2020 at 16:18

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