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Classically, charges on a charged sphere is distributed on the surface as to minimize energy (and distribute like charges as far apart as possible). But in QED a single electrons has a probability distribution. Do all of the electrons create a single uniformly distributed probability distribution? Or is each electron independent of all other electrons, interacting in a complex dance of possible paths. And what of the electric field near by? does it have structure due to the point charges or is it smooth, due to the smooth distribution of un-observered electrons?

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  • $\begingroup$ Theoretically you should consider the interference between electrons but sometimes they're weak so you can ignore it. Or just consider the closest ones. $\endgroup$ – Turgon Jul 19 '18 at 8:14
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As far as we understand quantum mechanics, it is meaningless to ask "where" before we've made the measurement. It's nowhere! The particle does not have a "position" until you look at it, and it's wherever the probability distribution says it is likely to be. See here https://www.youtube.com/watch?reload=9&v=0et8kf9YmdE

The best thing science does for us is it informs us when our questions are no longer well-defined. It's like asking what is north of the north pole, or when was there before time? Where was the electron before I measured it's position?

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