Interaction betwen position eigenstates of particle

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Discussion Overview

The discussion revolves around the interaction of a charged particle in a superposition of two different positions, A and B. Participants explore the implications of this superposition on self-interaction through electric and gravitational forces, as well as the challenges it presents in quantum field theory (QFT).

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants propose that a charged particle in superposition of positions A and B does not interact with itself, which raises questions in the context of quantum field theory.
  • Others argue that the particle can be considered to be 'in both places at once', suggesting that another particle would interact with it at both positions simultaneously.
  • A participant mentions that this scenario could lead to a nonlinear Schrödinger equation, which is problematic.
  • There is a discussion about the wave-like behavior of the particle in superposition, comparing it to the crests of a wave, indicating that they are not distinct entities but part of the same phenomenon.
  • One participant notes that the issue of self-interaction exists even in classical terms and becomes more complex in QFT, mentioning the concept of renormalization as a solution to infinities arising from self-interaction.
  • A historical perspective is provided with a reference to Paul Dirac's dissatisfaction with the renormalization approach, emphasizing the philosophical implications of neglecting infinities in mathematics.

Areas of Agreement / Disagreement

Participants generally disagree on whether particles interact with themselves in superposition. While some assert that they do not, others maintain that interactions occur at multiple points. The discussion remains unresolved regarding the implications of these viewpoints in quantum field theory.

Contextual Notes

The discussion highlights limitations in understanding self-interaction in quantum mechanics and QFT, particularly regarding the assumptions about superposition and the mathematical treatment of infinities.

maxverywell
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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?
 
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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.
 
This would lead to a nonlinear Schroedinger equation and this a "no-no".
 
alxm said:
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?
 
maxverywell said:
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!")
 
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