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, c {\displaystyle c} . 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 A {\displaystyle A} cannot cause a result at point B {\displaystyle B} in a time less than T = D / c {\displaystyle T=D/c} , where D {\displaystyle D} is the distance between the points and c {\displaystyle c} is the speed of light in vacuum. 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 (referred to as local realism in later work), a result now considered equivalent to precluding local hidden variables. Progressive variations on those Bell test experiments have since shown that quantum mechanics broadly violates Bell's inequalities. According to some interpretations of quantum mechanics, this result implies that some quantum effects violate the principle of locality.
Pre-quantum mechanics
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. Coulomb's law of electric forces was initially also formulated as instantaneous action at a distance, but in 1880, James Clerk Maxwell showed that field equations – which obey locality – predict all of the phenomena of electromagnetism. These equations show that electromagnetic forces propagate at the speed of light. In 1905, Albert Einstein's special theory of relativity postulated that no matter or energy can travel faster than the speed of light, and Einstein thereby sought to reformulate physics in a way that obeyed the principle of locality. He later succeeded in producing an alternative theory of gravitation, general relativity, which obeys the principle of locality. However, a different challenge to the principle of locality developed subsequently from the theory of quantum mechanics, which Einstein himself had helped to create.
Models for locality
Simple spacetime diagrams can help clarify the issues related to locality. A way to describe the issues of locality suitable for discussion of quantum mechanics is illustrated in the diagram. A particle is created in one location, then split and measured in two other, spatially separated, locations. The two measurements are named for Alice and Bob. Alice performs measurements (A) and gets a result a {\displaystyle \mathbf {a} } . Bob performs ( B {\displaystyle B} ) and gets result b {\displaystyle \mathbf {b} } . The experiment is repeated many times and the results are compared.
Alice and Bob in spacetime
A spacetime diagram has a time coordinate going vertical and a space coordinate going horizontal. Alice, in a local region on the left, can affect events only in a cone extending in the future as shown; the finite speed of light prevents her from affecting other areas including Bob's location in this case. Similarly, we can use the diagram to reason that Bob's local circumstances cannot be altered by Alice at the same time: all events that cause an effect on Bob are in the cone below his location on the diagram. Dashed lines around Alice show her valid future locations; dashed lines around Bob show events that could have caused his present circumstance. When Alice measures quantum states in her location she gets the results labeled a {\displaystyle \mathbf {a} } ; similarly Bob gets b {\displaystyle \mathbf {b} } . Models of locality attempt to explain the statistical relationship between these measured values.
Action at a distance
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