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Suppose an electron is created somehow in the universe -- through particle-pair production or what have you. Suppose it is stationary so that electrodynamics (and specifically propagating electromagnetic waves) is unavailable for explanation. Certainly distance charges will feel Coulomb's force, but how quickly?

I'm wondering if, since electromagnetism is manifestly relativistic (Lorentz rather than Galilean invariant) we can use that to always move to a frame where the electron is travelling and then claim that there are in fact EM waves? I don't know.

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    $\begingroup$ "Electrostatics", as the name suggests is "static". Nothing travels in electrostatics, otherwise it wouldn't be electrostatics anymore. Your question is unclear to me. What do you mean by "Suppose it is stationary"? $\endgroup$ – Mo_ Oct 24 '17 at 15:45
  • $\begingroup$ I think you need to look to QM for this. Just because a charge is stationary doesn't mean it can't emit virtual photons. Also a photon does not oscillate spatially, only it's E and B field oscillate. $\endgroup$ – JMLCarter Oct 24 '17 at 15:51
  • $\begingroup$ virtual photons travel at c $\endgroup$ – JMLCarter Oct 24 '17 at 15:54
  • $\begingroup$ Solving Maxwell's equations for charge and current sources yields the retarded potentials as solution. So, if a charge were "created", it's field would propagate at speed $c$. $\endgroup$ – Physicist137 Oct 24 '17 at 15:58
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    $\begingroup$ @Mostafa I mean that the electron and positron just instantaneously created are not moving (I am in their reference frame). Then I'm in the case of electrostatics: no waves. How does the coloumb interaction "reach" distant charges? $\endgroup$ – DPatt Oct 24 '17 at 16:31

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