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The two-state vector formalism (TSVF) is a description of quantum mechanics in terms of a causal relation in which the present is caused by quantum states of the past and of the future taken in combination. ==Theory== The two-state vector formalism is one example of a time-symmetric interpretation of quantum mechanics (see Minority interpretations of quantum mechanics). Time-symmetric interpretations of quantum mechanics were first suggested by Walter Schottky in 1921,〔Schottky, Walter. Das Kausalproblem der Quantentheorie als eine Grundfrage der modernen Naturforschung uberhaupt. Naturwissenschaften vol. 9, issue 25, pp. 492-496 (1921); vol. 9, issue 26, pp. 506-511 (1921);〕 and later by several other scientists. The two-state vector formalism was first developed by Satosi Watanabe〔Watanabe, Satosi. "Symmetry of physical laws. Part III. Prediction and retrodiction." Reviews of Modern Physics 27.2 (1955): 179.〕 in 1955, who named it the Double Inferential state-Vector Formalism (DIVF). Watanabe proposed that information given by forwards evolving quantum states is not complete; rather, both forwards and backwards evolving quantum states are required to describe a quantum state: a first state vector that evolves from the initial conditions towards the future, and a second state vector that evolves backwards in time from future boundary conditions. Past and future measurements, taken together, provide complete information about a quantum system. Watanabe's work was later rediscovered by Yakir Aharonov, Peter Bergmann and Joel Lebowitz in 1964, who later renamed it the Two-State Vector Formalism (TSVF).〔Yakir Aharonov, Lev Vaidman: ''Protective measurements of two-state vectors'', in: Robert Sonné Cohen, Michael Horne, John J. Stachel (eds.): ''Potentiality, Entanglement and Passion-At-A-Distance'', Quantum Mechanical Studies for A. M. Shimony, Volume Two, 1997, ISBN 978-0792344537, pp. 1–8, (p. 2 )〕 Conventional prediction, as well as retrodiction, can be obtained formally by separating out the initial conditions (or, conversely, the final conditions) by performing sequences of coherence-destroying operations, thereby cancelling out the influence of the two state vectors.〔Yakir Aharonov, Peter G. Bergmann, Joel L. Lebowitz: ''Time symmetry in the quantum process of measurement'', Physical Review B., vol. 134, no. 6, pp. 1410–1416, 1964〕 The ''two-state vector'' is represented by: where the state evolves backwards from the future and the state evolves forwards from the past. In the example of the double-slit experiment, the first state vector evolves from the electron leaving its source, the second state vector evolves backwards from the final location of the electron on the detection screen, and the combination of forwards and backwards evolving state vectors determines what occurs when the electron passes the slits. The two-state vector formalism provides a time-symmetric description of quantum mechanics, and is constructed such as to be time-reversal invariant.〔Michael Dickson: ''Non-relativistic quantum mechanics'', Jeremy Butterfield, John Earman (eds.): ''Philosophy of Physics'', Handbook of the Philosophy of Science, North-Holland, Elsevier, pp. 275–416, (Footnote on p. 327 )〕 It can be employed in particular for analyzing pre- and post-selected quantum systems. Building on the notion of two-state, Reznik and Aharonov constructed a time-symmetric formulation of quantum mechanics that encompasses probabilistic observables as well as nonprobabilistic weak observables.〔B. Reznik, and Y. Aharonov: ''Time-symmetric formulation of quantum mechanics'', Phys. Rev. A, vol. 52, no. 4, pp. 2538–2550, 1995〕 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「Two-state vector formalism」の詳細全文を読む スポンサード リンク
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