In an electromagnetic theory class, my professor introduced the concept of "action at a distance in physics". He said that:
If two charges are at some very large distance, and if any one of the charge moves, then the force associated with the charges changes instantaneously. But according to Einstein, no information can travel faster than the speed of light. So photons (the information carriers in electromagnetic force) cannot instantaneously deliver information. So that we associate a field with the two charges and if any charge moves, there is a deformation in that field and this deformation travels with the speed of light and conveys the information.
If the field deformation information cannot travel more than the speed of light, how does the force instantaneously change at very large distances?
Answer
The force does not change instantaneously, the correct way the electromagnetic field of (and thus the force exerted by) a moving electric charge is given by the Liénard-Wiechert potential, where one can see that the effect of the charge does not travel faster than light.
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