Do different paths of an electron interfere with each other?

[haael]

Suppose we have a double-slit experiment. A particle, say electron, splits into two paths, then it lands on a screen. An interference pattern appears.

Now, can the two "instances" of the same electron interact, say repell each other?

Imagine this setup: we have an electron beam and a splitter that divides it into 2 beams. If the two beams were projected on a screen, they would interfere, but that is not what we do. Instead we focus the beams and shot them against each other. If they were two "normal" separate beams, the electrons would scatter and produce photons that can be detected. Will the same effect be observed with the beams that come from the splitting?

My wild guess is that a "half" of the wavefunction of the electron travels in each beam. When the "halves" should collide, they will produce a "quarter" of a photon. So, the intensity of light from the entangled beams should be 4 times smaller compared to two colliding independent beams. Is that correct?

 

[DrClaude]

Suppose we have a double-slit experiment. A particle, say electron, splits into two paths, then it lands on a screen. An interference pattern appears.

No, it doesn't. The electron will leave a single point on the screen. Interference can only be visible after many electrons have gone through the slits.

Now, can the two "instances" of the same electron interact, say repell each other?

No. It that was the case, it would already have been observed in actual experiments (which show no difference between charged electrons or uncharged neutrons).