Principle of locality
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- This article is about the principle of locality in physics. For its use in computer science, see locality of reference.
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. (The vast majority of 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 where the wavefunction is assumed to have no direct physical interpretation or reality, the 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 has a restricted interpretation as nothing more than a mathematical tool used to calculate the probabilities of experimental outcomes, in agreement with positivism in philosophy as the only topic that science should discuss.
In the version of the Copenhagen interpretation where the wavefunction is assumed to have a physical interpretation or reality (the nature of which is unspecified), the principle of locality is violated during the measurement process via wavefunction collapse. This is a non-local process because Born's Rule, when applied to the system's wave function, yields a probability density for all regions of space and time. Upon measurement of the physical system, the probability density vanishes everywhere instantaneously, except where (and when) the measured entity is found to exist. This "vanishing" would be a real physical process, and clearly non-local (faster-than-lightspeed), if the wave function is considered physically real and the probability density converged to zero at arbitrarily far distances during the finite time required for the measurement 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 possible exception of the Bohm theory).
Locality is one of the axioms of relativistic quantum field theory, as required for causality. The formalization of locality in this case is as follows: if we have two observables, each localized within two distinct spacetime regions which happen to be at a spacelike separation from each other, the observables must commute. This interpretation of the word "locality" is closely related to the relativistic version of in physics.