Feynman Path Integral - All Possible Paths - Relativity Conflict?

[lovatto]

Hello

I have not familiarised myself with the mathematics etc I merely have the conceptual idea that, for example, with the two slit experiement and electron is permitted to take "all possible paths" from the electron gun to the detector screen.

The thought occurred (and as will all thoughts like this it will have obviously occurred to everyone else, I am only after an explanation, I am not claiming to have found a flaw etc)that not all paths are permitted.

An electron is fired at t0 and hits the screen at t1. There is obviously a finite number of permitable paths as the time limit imposes constraints, in that it can't have gone to the andromeda galaxy and back to the screen as there is simply not enough time for the electron to propagate that distance.

Can somebody point out how this is reconciled in the path integral formulation, or whether this exposes a fundamental misunderstanding on my part?

 

[bahamagreen]

I believe the formulation occurs in a four dimensional space/time which has some supporting features for this kind of thing.
The concept of "distance" in space/time is different, it includes time and the speed of light (both squared) subtracted from the sums of squares of the usual three space dimensions, all under the radical.

I'm probably mangling this explanation, but it is something like this means that the idea of space distance alone becomes zero between any two event points and time is treated as an imaginary number so the electron is free to travel "paths" through space/time forward and backward.

While I am mangling things, this raises another question... if one electron can truly take all paths, do we need to have more than one electron? With sufficient paths forward and backward in time and covering all possible paths might it only take a single electron to account for all observations and suggest a reason why they all look alike? Sort of like using a single straw to weave a basket; it might look like a lot of individual straws until you notice how it was made...