Action at a distance (physics)

In physics, action at a distance is the interaction of two objects which are separated in space, and no hint as to the nature of the mediator of the interaction. Newton's theory of gravity offers no prospect of identifying any mediator of gravitational interaction. Also, gravitation is assumed to act instantaneously, regardless of distance. Newton had shown mathematically that if the gravitational interaction is not instantaneous, angular momentum is not conserved, and Kepler's observations gave strong evidence that in planetary motion angular momentum is conserved. (The mathematical proof is not valid in the case of a non-Euclidean space geometry.)

Another fundamental question, raised by Ernst Mach, was the question of how rotating bodies know how much to bulge at the equator. How do they know their rate of rotation? This, it seems, requires an action-at-a-distance from distant matter, informing the rotating object about the state of the universe. Albert Einstein coined the term Mach's principle for this question.

After the advent of special relativity, instantaneous action-at-a-distance was seen to violate the relativistic upper limit on speed of propagation of interaction - if one of the interacting objects were suddenly displaced from its position, the other object would feel its influence instantaneously.

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. Efforts to develop a theory of interaction between moving charges, electrodynamics, led to the necessity to introduce the concept of a field with physical properties. In the theory of electrodynamics as formulated in Maxwell's equations, interactions between moving charges are mediated by propagating deformations of an electromagnetic field. These deformations propagate with the speed of light. The deformations of the field can carry momentum independently, thus facilitating conservation of angular momentum.

One of the conditions that a relativistic theory of gravitation must meet is to be mediated with a speed that does not exceed lightspeed. It could be seen from the previous success of electrodynamics that the relativistic theory of gravitation would have to use the concept of a field, and Mach's principle may be incorporated. In Einstein's theory of general relativity, this program has been realized. In Einstein's theory of gravitation, gravitational interaction is mediated by deformation of space-time geometry, and all motion is determined by interaction of matter with space-time geometry. Thus, local space-time geometry is informing a rotating body about the rest of the universe. In Newton's theory of motion, space acts on objects, but is not acted upon. In Einstein's theory of motion, matter acts upon space-time geometry, deforming it, and space-time geometry acts upon matter.

Current physical theories incorporate the upper limit on propagation of interaction as one of their basic building blocks, hence ruling out instantaneous action-at-a-distance. At the same time however, instantaneous action at a distance appears to be an essential feature of some very fundamental quantum mechanical effects like entanglement and quantum nonlocality. For these implications of quantum mechanics, Einstein coined the term "spooky action at a distance".

The question of whether this 'spooky action' at a distance constitutes a violation of the relativistic upper limit on the propagation of interaction is not straightforward. According to the laws of quantum mechanics, entanglement cannot be employed for relaying information from one place to another.