A physical theory is said to exhibit nonlocality if, in that theory, it is not possible to treat widely separated systems as independent.

Or, more technical: A physical theory is said to exhibit nonlocality if, in that theory, it is possible to violate a Bell inequality. Examples: quantum mechanics, nonlocal boxes. This definition implies a possibility to measure nonlocality of a certain theory in a simple way - as the extent of the maximal possible violation of a Bell inequality (for example CHSH Bell test). Fig. ... Introduction The CHSH Bell test is an application of Bells theorem, intended to distinguish between quantum mechanics (QM) and local hidden variable theories. ...

Simple example of a non-local object is a wave. Because all objects in Universe posess wave-particle duality, they are non-local too. This article is about waves in the most general scientific sense. ... In physics, wave-particle duality holds that light and matter exhibit properties of both waves and of particles. ...

The term is most often reserved, however, for hypothetical interactions that occur outside the backward light cone, i.e. superluminal influences. Nonlocality does not imply a lack of causality only in the case when "ethereal," not "causal," information is transmitted between systems. Special relativity shows that in the case where causal information is transmitted at superluminal rates, causality is violated. For example, if information could be exchanged at superluminal rates, it would be possible to arrange for you to be killed before your grandfather is born, which leads to causal paradoxes. Some effects that appear nonlocal in quantum mechanics may actually obey locality, e.g. quantum entanglement. Entanglement produces non-classical correlations between spatially separated particles in specific states, such as the famous singlet state. Einstein, (see EPR paradox), was one of the first to notice very strange features of entanglement. He used it to criticise the Copenhagen interpretation of quantum mechanics, on the grounds that entanglement implied what he called "spooky action at a distance". His claim was addressed by Bell in 1964. Bell's theorem shows that Einstein's dream to complete quantum theory with new deterministic local theory with additional variables ("elements of reality") must fail. Such a theory must be non-local. Still this does not imply nonlocality of quantum mechanics, because this theory does not require, or imply, existence of an underlying deterministic structure. There is an interpretation of quantum mechanics which uses additional, experimentally inaccessible variables, that make it a deterministic theory. This is the Bohm interpretation. It is inherently nonlocal. Quantum field theory, which is the relativistic generalization of quantum mechanics, contains mathematical features that relate to locality (see Principle of locality). If two observables are localized within distinct spacetime regions that happen to be at a spacelike separation from each other, then the two observables must commute (see Canonical_commutation_relation). The nonlocality in quantum optics cannot be avoided by appealing to such commutation of field "observables" at spacelike intervals. The electromagnetic field observables are operators, and the violation of Bell inequalities in quantum_optics (QO) arises because the field states are vectors on which the observables act. These vectors are alleged to possess certain symmetries, owing to the way in which they are generated, either in atomic cascades or in nonlinear solid-state devices. The origin of these symmetries is the interaction of the electromagnetic field with the electric current vector of the source, which is a bilinear form in the anti-commuting Dirac-field operators (see Fermionic_field#Dirac_field; whether these operators may be regarded as "observable" is debatable). Ultimately the validity of the QO argument depends on whether it describes correctly the various "two-photon" states, which in turn depends on the definition of the QO "vacuum". By a suitable change in the latter, semiclassical optics [[1]]transforms all apparently "nonlocal" phenomena so far observed in optics to local ones [[2]] In special relativity, a light cone is the pattern describing the temporal evolution of a flash of light in Minkowski spacetime. ... Faster-than-light (also superluminal or FTL) communications and travel are staples of the science fiction genre. ... It has been suggested that this article be split into multiple articles accessible from a disambiguation page. ... Fig. ... The term locality has different meanings in different disciplines: Geography In geography, a locality is a place. ... It has been suggested that Quantum coherence be merged into this article or section. ... In theoretical physics, a singlet usually refers to a one-dimensional representation (e. ... Einstein redirects here. ... In quantum mechanics, the EPR paradox is a thought experiment which challenged long-held ideas about the relation between the observed values of physical quantities and the values that can be accounted for by a physical theory. ... The Copenhagen interpretation is an interpretation of quantum mechanics formulated by Niels Bohr and Werner Heisenberg while collaborating in Copenhagen around 1927. ... In physics, action at a distance is the interaction of two objects which are separated in space with no known mediator of the interaction. ... Bells theorem is the most famous legacy of the late Irish phyisicist John Bell. ... The Bohm interpretation of quantum mechanics, sometimes called the Bohmian Mechanics or Ontological interpretation is an interpretation postulated by David Bohm in 1952, which was an extension of the de Broglie-pilot-wave theory of 1927. ... Quantum field theory (QFT) is the application of quantum mechanics to fields. ... Fig. ... 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. ... In physics, the canonical commutation relation is the relation among the position and momentum of a point particle in one dimension, where is the so-called commutator of and , is the imaginary unit and is the reduced Plancks constant . ... Quantum optics is a field of research in physics, dealing with the application of quantum mechanics to phenomena involving light and its interactions with matter. ... In quantum field theory, a fermionic field is a quantum field whose quanta are fermions; that is, they obey Fermi-Dirac statistics. ...

1. TW Marshall & E Santos: Semiclassical optics as an alternative to nonlocality, Recent Research Developments in Optics 2:683-717 (2002)

2. T W Marshall: The party may be over (2002)

See also

• Principle of locality
• Nonlocal Lagrangian
• Bell's theorem