Information AboutNonlocal |
| CATEGORIES ABOUT NONLOCALITY | |
| quantum measurement | |
| quantum field theory | |
| theoretical physics | |
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A physical theory is said to exhibit nonlocality if, in that theory, it is not possible to treat widely separated systems as independent. The simplest example of a non-local system is a Wave (which is not localized in Space nor in Time ), or a Wave Function . Because any object in our universe obeys the principle of Wave-particle Duality , then all objects in our universe are non-local. Or, more technically: 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 ). The term is most often reserved 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 AND LOCALITY 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 . 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 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; whether these operators may be regarded as "observable" is debatable). Ultimately the validity of the quantum optical argument depends on whether it describes correctly the various "two-photon" states, which in turn depends on the definition of the quantum optical "vacuum". By a suitable change in the latter, semiclassical optics transforms all apparently "nonlocal" phenomena so far observed in optics to local ones [http://arXiv.org/abs/quant-ph/0203042 SEE ALSO REFERENCES # TW Marshall & E Santos: ''Semiclassical optics as an alternative to nonlocality'', Recent Research Developments in Optics 2:683-717 (2002) # T W Marshall: ''The party may be over'' (2002) |
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