Principle of locality

---

In physics, the principle of locality states that an object is influenced directly only by its immediate surroundings. 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. The idea is that for a cause at one point to have an effect at another point, something in the space between those points must mediate the action. To exert an influence, something, such as a wave or particle, must travel through the space between the two points, carrying the influence.

The special theory of relativity limits the maximum speed at which causal influence can travel to the speed of light, . Therefore, the principle of locality implies that an event at one point cannot cause a truly simultaneous result at another point. An event at point cannot cause a result at point in a time less than , where is the distance between the points and is the speed of light in vacuum.${\displaystyle c}$${\displaystyle A}$${\displaystyle B}$${\displaystyle T=D/c}$${\displaystyle D}$${\displaystyle c}$

The principle of locality plays a critical role in one of the central results of quantum mechanics. In 1935 Albert Einstein, Boris Podolsky, and Nathan Rosen, with their EPR paradox thought experiment, raised the possibility that quantum mechanics might not be a complete theory. They described two systems physically separated after interacting; this pair would be called entangled in modern terminology. They reasoned that without additions, now called hidden variables, quantum mechanics would predict illogical relationships between the physically separated measurements. In 1964 John Stewart Bell formulated Bell's theorem, an inequality which, if violated in actual experiments, implies that quantum mechanics violates local causality, a result now considered equivalent to no local hidden variables. Later work refers to local causality as local realism.

Bell test experiments show that quantum mechanics broadly violates the inequalities established in Bell's theorem. According to some interpretations of quantum mechanics, this result implies that some quantum effects violate the principle of locality.

During the 17th century, Newton's principle of universal gravitation was formulated in terms of "action at a distance", thereby violating the principle of locality. Newton himself considered this violation to be absurd:

It is inconceivable that inanimate Matter should, without the Mediation of something else, which is not material, operate upon, and affect other matter without mutual Contact…That Gravity should be innate, inherent and essential to Matter, so that one body may act upon another at a distance thro' a Vacuum, without the Mediation of any thing else, by and through which their Action and Force may be conveyed from one to another, is to me so great an Absurdity that I believe no Man who has in philosophical Matters a competent Faculty of thinking can ever fall into it. Gravity must be caused by an Agent acting constantly according to certain laws; but whether this Agent be material or immaterial, I have left to the Consideration of my readers.^[1]

---