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Historically, in physics, hidden variable theories were espoused by some physicists who argued that the state of a physical system, as formulated by quantum mechanics, does not give a complete description for the system; i.e., that quantum mechanics is ultimately incomplete, and that a complete theory would provide descriptive categories to account for all observable behavior and thus avoid any indeterminism. The existence of indeterminacy for some measurements is a characteristic of prevalent interpretations of quantum mechanics; moreover, bounds for indeterminacy can be expressed in a quantitative form by the Heisenberg uncertainty principle. Albert Einstein, the most famous proponent of hidden variables, objected to the fundamentally probabilistic nature of quantum mechanics,〔, (Private letter from Einstein to Max Born, 3 March 1947: "I admit, of course, that there is a considerable amount of validity in the statistical approach which you were the first to recognize clearly as necessary given the framework of the existing formalism. I cannot seriously believe in it because the theory cannot be reconciled with the idea that physics should represent a reality in time and space, free from spooky actions at a distance.... I am quite convinced that someone will eventually come up with a theory whose objects, connected by laws, are not probabilities but considered facts, as used to be taken for granted until quite recently".)〕 and famously declared "I am convinced God does not play dice".〔private letter to Max Born, 4 December 1926, (Albert Einstein Archives ) reel 8, item 180〕 Einstein, Podolsky, and Rosen argued that "elements of reality" (hidden variables) must be added to quantum mechanics to explain entanglement without action at a distance.〔"The debate whether Quantum Mechanics is a complete theory and probabilities have a non-epistemic character (i.e. nature is intrinsically probabilistic) or whether it is a statistical approximation of a deterministic theory and probabilities are due to our ignorance of some parameters (i.e. they are epistemic) dates to the beginning of the theory itself". See: arXiv:quant-ph/0701071v1 12 Jan 2007〕 Later, Bell's theorem would suggest that local hidden variables of certain types are impossible, or that they evolve non-locally. A famous non-local theory is De Broglie–Bohm theory. == Motivation == Under the standard Copenhagen interpretation, quantum mechanics is non-deterministic, meaning that it generally does not predict the outcome of any measurement with certainty. Instead, it indicates what the probabilities of the outcomes are, with the indeterminism of observable quantities constrained by the uncertainty principle. The question arises whether there might be some deeper reality hidden beneath quantum mechanics, to be described by a more fundamental theory that can always predict the outcome of each measurement with certainty: if the exact properties of every subatomic particle were known the entire system could be modeled exactly using deterministic physics similar to classical physics. In other words, it is conceivable that the standard interpretation of quantum mechanics is an incomplete description of nature. The designation of variables as underlying "hidden" variables depends on the level of physical description (so, for example, "if a gas is described in terms of temperature, pressure, and volume, then the velocities of the individual atoms in the gas would be hidden variables".). Physicists supporting De Broglie–Bohm theory maintain that underlying the observed probabilistic nature of the universe is a deterministic objective foundation/property—the hidden variable. Others, however, believe that there is no deeper deterministic reality in quantum mechanics—experiments have shown a vast class of hidden variable theories to be incompatible with observations. Lack of a kind of realism (the latter understood here as asserting independent existence and evolution of physical quantities, such as position or momentum, without the process of measurement) is crucial in the Copenhagen interpretation. Realistic interpretations (which were already incorporated, to an extent, into the physics of Feynman〔Individual diagrams are often split into several parts, which may occur beyond observation; only the diagram as a whole describes an observed event.〕), on the other hand, assume that particles have certain trajectories. Under such view, these trajectories will almost always be continuous, which follows both from the finiteness of the perceived speed of light ("leaps" should rather be precluded) and, more importantly, from the principle of least action, as deduced in quantum physics by Dirac. But continuous movement, in accordance with the mathematical definition, implies deterministic movement for a range of time arguments;〔For every subset of points within a range, a value for every argument from the subset will be determined by the points in the neighbourhood. Thus, as a whole, the evolution in time can be described (for a specific time interval) as a function, e.g. a linear one or an arc. See Continuous function#Definition in terms of limits of functions〕 and thus realism is, under modern physics, one more reason for seeking (at least certain limited) determinism and thus a hidden variable theory (especially that such theory exists: see De Broglie–Bohm interpretation). Although determinism was initially a major motivation for physicists looking for hidden variable theories, nondeterministic theories trying to explain what the supposed reality underlying the quantum mechanics formalism looks like are also considered hidden variable theories; for example Edward Nelson's stochastic mechanics. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「hidden variable theory」の詳細全文を読む スポンサード リンク
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