Completeness for a single particle

[jk22]

Another argument than EPR that quantum mechanics were not complete by Einstein is the following : suppose a single electron passing through a hole and going further to a spherical detector. Quantum mechanics describes this as a wavefunction fulling the whole space inside the sphere and then collapsing to a single point on the screen.

The question was in this description which process forbids that the wavefunction collapses in two points ? There should be an instantaneous interaction ?

 

[fzero]

Detecting the electron at two points is forbidden by conservation of electric charge. If it were a photon, then it's more complicated, but the detected photons would have to have energies that added up to that of the original photon.

 

[jk22]

For photons It is simply solved by quantum field theory ?

 

[fzero]

For photons It is simply solved by quantum field theory ?

Yes, the typical QM thought experiments ignore self-interactions and assume the particle will only interact with a screens, filters, or the detectors. If you use QFT you can consistently treat all of the other possible interactions at the risk of making things very complicated. But the amplitudes by construction satisfy the ordinary QM rules.