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In physics, action at a distance is the instantaneous interaction of two objects which are separated in space; the term was coined as "spooky action at a distance" by Albert Einstein. Newton's theory of gravity was one of the first theories incorporating this notion. After the advent of special relativity, action-at-a-distance was seen to violate the principle of relativity - if one of the interacting objects were suddenly displaced from its position, the other object would feel its influence instantaneously, whereas the special theory of relativity sets the speed of light as the upper limit to the speed of propagation of an interaction. Attempts to sort out the conflict between Newton's theory with action-at-a-distance, and the principle of relativity in the theory of gravitation led to the theory of general relativity.
Incidentally, there is no problem with Coulomb's law in electrostatics seeming to be a theory with action-at-a-distance - Coulomb's law deals with charges which have always been static, and the completion of Coulomb's law to include moving charges lead to Maxwell's equations, which are fully compatible with special relativity.
Current physical theories incorporate the principle of relativity as one of their basic building blocks, hence ruling out action-at-a-distance. At the same time however, action at a distance appears to be an essential feature of some very fundamental quantum mechanical effects like entanglement and quantum nonlocality. Further understanding of these effects, in order to reconcile them with the principle of relativity, might lead to some new physics.
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