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Action at a distance is the concept in physics that an object's motion can be affected by another object without the two being in physical contact; that is, it is the concept of the non-local interaction of objects that are separated in space. Coulomb's law and Newton's law of universal gravitation are based on action at a distance.
A theory that includes the principle of locality is said to be a "local theory". This is an alternative to the concept of instantaneous, or "non-local" action at a distance. Locality evolved out of the field theories of classical physics.
Forces and Fields has eleven chapters. The first ten chapters consist of 5 or more sections. The eleventh, 2 sections. These chapters are titled The Logical Status of Theories, The Primitive Analogies, Mechanism in Greek Science, The Greek Inheritance, The Corpuscular Philosophy, The Theory of Gravitation, Action at a Distance, The Field Theories, The theory of Relativity, Modern Physics, and ...
The energy function in the action principles is not the total energy (conserved in an isolated system), but the Lagrangian, the difference between kinetic and potential energy. The kinetic energy combines the energy of motion for all the objects in the system; the potential energy depends upon the instantaneous position of the objects and ...
Maxwell's theory, restated using vector calculus, is the classical theory of electromagnetism, suitable for most technological purposes. The constant speed of light in vacuum (customarily denoted with a lowercase letter c) can be derived from Maxwell's equations, which are consistent with the theory of special relativity.
Unlike instantaneous action at a distance theories of the early 1800s these "direct interaction" theories are based on interaction propagation at the speed of light. They differ from the classical field theory in three ways 1) no independent field is postulated; 2) the point charges do not act upon themselves; 3) the equations are time symmetric.
In such universes Mach's principle can be stated as the distribution of matter and field energy-momentum (and possibly other information) at a particular moment in the universe determines the inertial frame at each point in the universe (where "a particular moment in the universe" refers to a chosen Cauchy surface).
In Einstein's theory, energy and momentum distort spacetime in their vicinity, and other particles move in trajectories determined by the geometry of spacetime. This allowed a description of the motions of light and mass that was consistent with all available observations.