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I'm not studying physics, I was just curious that if the electric field created by electron and positron in a dipole follows the same rules as double slit experiment. That is, for example on the midpoint, the field should be the sum of two separate fields, is the field energy 4 times higher than that of the single electron? (2 times higher than the sum of individuals). Does this mean that if another electron is put in between, it is four times likely that it hits a photon?

Then in the mentioned scenario can't we measure which one interacted with the other electron?

If we can't why, and if we can shouldn't the field energy be half? (Is it like: interacting with one + the pair attracting each other = interacting with the other one)

hhoomn
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Static electric fields like those generated by an electron and a positron add together just like the oscillating electric fields associated with light. So for example if the electron and positron are separated by a distance $2d$ then at the point halfway between them the total field is:

$$ E = \frac{ke}{d^2} + \frac{ke}{d^2} = 2\frac{ke}{d^2} $$

The fields add because at the midpoint they point in the same direction:

Dipole

If we had two electrons, as in the lower picture, the fields are equal and opposite so they would sum to zero.

The energy density, i.e. the number of joules per cubic metre, in an electric field is given by:

$$ \rho = \tfrac{1}{2}\epsilon_0 E^2 $$

So the energy density at the midpoint of the dipole is indeed four times the energy density at the same distance $d$ from a single charge. However it isn't clear what you mean by:

Does this mean that if another electron is put in between, it is four times likely that it hits a photon?

I wonder if you are thinking that the field is made up from virtual photons. If so this is a misunderstanding. We calculate the interactions between charges using virtual photons, but they are a computational device and do not really exist.

John Rennie
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  • So the actual interactions that happen are photons, right? So isn't field energy related to either number/probability of interactions or strength of interactions that actually happen (e.g. is it more similar to classical physics)? I think I'm missing some fundamental concept – hhoomn Jan 20 '19 at 20:25
  • @hhoomn So the actual interactions that happen are photons, right? - no. The fundamental concept you're missing is that the interaction is described by quantum field theory. When we calculate the interaction between two electrons using quantum field theory we approximate the interaction as the exchange of virtual photons, but this is a computational device and virtual particles do not actually exist. – John Rennie Jan 21 '19 at 11:07