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Quantum indeterminacy is the apparent ''necessary'' incompleteness in the description of a physical system, that has become one of the characteristics of the standard description of quantum physics. Prior to quantum physics, it was thought that :(a) a physical system had a determinate state which uniquely determined all the values of its measurable properties, and conversely :(b) the values of its measurable properties uniquely determined the state. Albert Einstein may have been the first person to carefully point out the radical effect the new quantum physics would have on our notion of physical state.〔Christopher Fuchs, ''Quantum mechanics as quantum information (and only a little more)'', in A. Khrenikov (ed.) ''Quantum Theory: Reconstruction of Foundations'' (Växjö: Växjö University Press, 2002). Fuchs says :.. He was the first person to say in absolutely unambiguous terms why the quantum state should be viewed as information ..〕 Quantum indeterminacy can be quantitatively characterized by a probability distribution on the set of outcomes of measurements of an observable. The distribution is uniquely determined by the system state, and moreover quantum mechanics provides a recipe for calculating this probability distribution. Indeterminacy in measurement was not an innovation of quantum mechanics, since it had been established early on by experimentalists that errors in measurement may lead to indeterminate outcomes. However, by the later half of the eighteenth century, measurement errors were well understood and it was known that they could either be reduced by better equipment or accounted for by statistical error models. In quantum mechanics, however, indeterminacy is of a much more fundamental nature, having nothing to do with errors or disturbance. ==Measurement== An adequate account of quantum indeterminacy requires a theory of measurement. Many theories have been proposed since the beginning of quantum mechanics and quantum measurement continues to be an active research area in both theoretical and experimental physics.〔V. Braginski and F. Khalili, ''Quantum Measurements'', Cambridge University Press, 1992.〕 Possibly the first systematic attempt at a mathematical theory was developed by John von Neumann. The kind of measurements he investigated are now called projective measurements. That theory was based in turn on the theory of projection-valued measures for self-adjoint operators which had been recently developed (by von Neumann and independently by Marshall Stone) and the Hilbert space formulation of quantum mechanics (attributed by von Neumann to Paul Dirac). In this formulation, the state of a physical system corresponds to a vector of length 1 in a Hilbert space ''H'' over the complex numbers. An observable is represented by a self-adjoint (i.e. Hermitian) operator ''A'' on ''H''. If ''H'' is finite dimensional, by the spectral theorem, ''A'' has an orthonormal basis of eigenvectors. If the system is in state ψ, then immediately after measurement the system will occupy a state which is an eigenvector ''e'' of ''A'' and the observed value λ will be the corresponding eigenvalue of the equation ''A'' ''e'' = λ ''e''. It is immediate from this that measurement in general will be non-deterministic. Quantum mechanics, moreover, gives a recipe for computing a probability distribution Pr on the possible outcomes given the initial system state is ψ. The probability is : where E(λ) is the projection onto the space of eigenvectors of ''A'' with eigenvalue λ. 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「Quantum indeterminacy」の詳細全文を読む スポンサード リンク
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