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Leggett-Garg inequality : ウィキペディア英語版
Leggett–Garg inequality
The Leggett–Garg inequality,〔Quantum Mechanics versus macroscopic realism: is the flux there when nobody looks? A. J. Leggett and Anupam Garg. Phys. Rev. Lett. 54, 857 (1985)〕 named for Anthony James Leggett and Anupam Garg, is a mathematical inequality fulfilled by all macrorealistic physical theories. Here, macrorealism (macroscopic realism) is a classical worldview defined by the conjunction of two postulates:〔
# Macrorealism per se: "A macroscopic object, which has available to it two or more macroscopically distinct states, is at any given time in a definite one of those states."
# Noninvasive measurability: "It is possible in principle to determine which of these states the system is in without any effect on the state itself, or on the subsequent system dynamics."
==In quantum mechanics==
In quantum mechanics, the Leggett–Garg inequality is violated, meaning that the time evolution of a system cannot be understood classically. The situation is similar to the violation of Bell's inequalities in Bell test experiments which plays an important role in understanding the nature of the Einstein–Podolsky–Rosen paradox. Here quantum entanglement plays the central role. The violation of Bell's inequalities rules out local hidden variable theories which attempt to restore the realism in the sense that definiteness of the outcome in a single measurement can be ensured by using a supplementary variable along with the wave function which can not be obtained in the standard Copenhagen Interpretation of quantum mechanics in its various formulations.
As well as Einstein's famous "God does not play dice" objection to quantum mechanics, there was Einstein's still more fundamental objection that the Moon is still there when nobody looks. If the violation of the Leggett–Garg inequality can be demonstrated on the ''macroscopic scale'', this would challenge even this notion of realism.

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