The wavefunction that describes the electron is calculated based on the geometry of the experiment and provides a statistical prediction of which screen locations are more probable than others. The wavefunction is a vector field, and so when two of them are superimposed, the vectors at each point are summed. Vector addition is what makes interference patterns emerge when you would expect to see two blobs in the double slit experiment.
"Particles" interact via forces. They do not interfere with each other or themselves. The vector field which predicts probable outcomes of an experiment does interfere, which is simply stating that sometimes the sum of two vectors has a smaller absolute value than the absolute value of either of the vectors.
This doesn't answer your question, its just me being fussy because I'm annoyed that certain popular statements about QM imply incorrect, magical things because of their inaccurate wording.
The wavefunction is formulated with no assumptions about the number of "particles" that are present, on the contrary, it would be much more difficult if particle-particle interactions were considered. It can be normalized to any number you want so it shouldn't be surprising when it works as well for low intensities as for high...
The one assumption that all paradoxical and unintuitive scenarios share is the assertion that there is any such thing as "particles" in the first place. So I would say that the "particle" splitting and taking both paths is an interpretation of the results, as well as the existence of the particle. I know this is not what you wanted to hear. Sorry.
jobermark said:
You mention Feynman, and I think he may be the only person who does not characterize this as having the electron split and interfere with itself.
Instead, he prefers the approach where you combine all possible timelines and let them interact. So it is more like the electron is free to go back and forth freely in time before deciding on its ultimate destination, but all of the forward paths interfere with all of the 'previous' forward paths in this very long 'lifetime' of time-reversals. So when it comes forward again, it needs to avoid the other paths that it 'tried out' and chose not to take, as if there were another electron that *did* choose to take them.
To make the point in an extreme way, he once proposed that there is only one electron in all the universe, but it has gone back in time often enough to be all of the existing electrons we see now. It captures a way of looking at quantum mechanics that is less bizarre than the possibility function with a collapsing wavefront.
I love this idea, since the arrow of time is something that arises from the tendency of thermal systems to maximize disorder purely because all states are equally likely and the number of states of maximum disorder is astronomically large compared to all others, there is no reason for it to apply to a single electron.
But since the wavefunction does not consider particle-particle interactions, and would be different if it did so, how can a model in which the particle reverses direction in time and affects itself, through the electromagnetic force I assume, produce the same predictions?
