Interaction betwen position eigenstates of particle

[maxverywell]

If a (charged) particle is in superposition of two different positions A and B is it interacting with itself by electric forces (and gravitational force)? Is it true that the particle is in both places A and B simultaneously?

 

[alxm]

No, the particles don't interact with themselves. (Causing quite a dilemma when developing quantum field theory!)

Yes, it's true the particle is 'in both places at once'. E.g. if you look at it from the perspective of any other particle, the second particle will interact with the first particle at both point A and B at the same time.

 

[arkajad]

This would lead to a nonlinear Schroedinger equation and this a "no-no".

 

[maxverywell]

No, the particles don't interact with themselves. (Causing quite a dilemma when developing quantum field theory!)

Yes, it's true the particle is 'in both places at once'. E.g. if you look at it from the perspective of any other particle, the second particle will interact with the first particle at both point A and B at the same time.

Thanks for your reply. So if the particle is 'in both places at once' why they don't interact? How QFT dealt with that?

 

[alxm]

So if the particle is 'in both places at once' why they don't interact? How QFT dealt with that?

Well the positional superposition here is 'wave-like' behavior, so it's better to look at it that way; like two crests of a wave, they're not two distinct entities but both part of the same thing.

Now, the problem of why the particle doesn't interact with itself doesn't really hinge on the fact that it can be in several places at once. You have a self-interaction problem even in purely classical terms (it does get more complicated in QFT though). The solution that they came up with is termed 'http://en.wikipedia.org/wiki/Renormalization" '. Basically they 'invented' some counter-terms that canceled out the infinities that came about from self-interaction.

(Paul Dirac was famously very unhappy with this solution, saying "Sensible mathematics involves neglecting a quantity when it turns out to be small - not neglecting it just because it is infinitely great and you do not want it!")