Principle of locality

In physics, the principle of locality is that distant objects cannot have direct influence on one another: an object is influenced directly only by its immediate surroundings. This was stated as follows by Albert Einstein in his article "Quantum Mechanics and Reality" ("Quanten-Mechanik und Wirklichkeit", Dialectica 2:320-324, 1948):

The following idea characterises the relative independence of objects far apart in space (A and B): external influence on A has no direct influence on B; this is known as the Principle of Local Action, which is used consistently only in field theory. If this axiom were to be completely abolished, the idea of the existence of quasienclosed systems, and thereby the postulation of laws which can be checked empirically in the accepted sense, would become impossible.

Local realism is the combination of the principle of locality with the assumption that all objects must objectively have their properties already before these properties are observed. Einstein liked to say that the Moon is "out there" even when no one is observing it.

Local realism is a significant feature of classical general relativity and classical Maxwell's theory, but quantum mechanics rejects this principle. Every theory that, like quantum mechanics, is compatible with violations of Bell's inequalities must abandon local realism. [Most physicists believe that experiments have demonstrated such violations, but some local realists dispute the claim, in view of the recognised loopholes in the tests.] Different interpretations of quantum mechanics reject different parts of local realism.

In most of the conventional interpretations (such as the version of the Copenhagen interpretation in which the wavefunction is not real, many-worlds interpretation, and the interpretation based on Consistent Histories), it is realism that is rejected. The actual definite properties of a physical system "do not exist" prior to the measurement and the wavefunction is only interpreted as a mathematical tool used to calculate the probabilities of the outcome of the experiments, which is, in agreement with positivism in philosophy, the only topic that science should discuss.

In the version of the Copenhagen interpretation where the wavefunction is real, it is the principle of locality that is violated. The wavefunction is a real object that exists prior to the measurement, but the measurement causes the wavefunction collapse which is a non-local process.

The Bohm interpretation always wants to preserve realism, and it needs to violate the principle of locality to achieve the required correlations. In fact, it needs to violate not only locality, but also causality which seems to imply a real conflict with the special theory of relativity because real, superluminal signals would have to be propagated.

Because the differences between the different interpretations are mostly philosophical ones (except for the Bohm interpretation), the physicists usually use the language in which the important statements are independent of the interpretation we choose. In this framework, only the measurable action at a distance - a superluminal propagation of real, physical information - would be usually considered to be a violation of locality by the physicists. Such phenomena have never been seen, and they are not predicted by the current theories (with the possibly exception of the Bohm theory). This is why relativistic quantum field theory is usually considered to be a local theory.

The above is only about one sense of locality. In another use of the term, if we have two observables, each localized within two distinct spacetime regions which happen to be at a spacelike separation from each other, both observables would commute and we have locality. This interpretation of the word "locality" is closely related to the relativistic version of causality in physics.

See also

• Bell's theorem
• EPR paradox
• quantum entanglement
• quantum mechanics
• nonlocality
• Bell test loopholes
• local hidden variable theory.

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In computer science, the principle of locality is sometimes used as an alternative name for locality of reference.