Spacetime Probabilities in Nonrelativistic Quantum Mechanics : General and Mathematical Physics
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概要
- 論文の詳細を見る
We demonstrate the existence of spacetime probabilities in nonrelativistic quantum mechanics, that is, quantum mechanical probabilities for a set of alternatives which are associated, not with a surface of constant time, but with spacetime domains with nonzero spatial and temporal width in Newtonian spacetime. We use the criterion that quantum mechanical probabilities can be defined for a set of alternatives if and only if the interference between any two different alternatives vanishes. Although generalized quantum mechanics was formulated on the basis of this criterion, the actual existence of spacetime probabilities has not been known. In this paper we consider a rectangular spacetime domain Ω and introduce a set of spacetime alternatives {Yes, No}: "Yes" is to find a particle in Ω and "No" is the complement to "Yes". We show that, if the initial amplitude of the particle belongs to a specific class, then the criterion of vanishing interference is met by "Yes" and "No" and spacetime probabilities can be therefore defined for the set {Yes, No}. Owing to the property of the initial amplitude belonging to the class, the resultant probabilities are associated with a clear measurement theoretical meaning.
- 理論物理学刊行会の論文
- 1992-01-25
著者
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Takagi Shin
Department Of Oral And Maxillofacial Reconstructive Surgery In Okayama University Graduate School Of
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高木 伸
Nagoya Univ. Nagoya Jpn
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Yamada Norifumi
Department Of Physics
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Yamada Norifumi
Department Of Physics Tohoku University
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Takagi Shin
Department Of Anatomy Kyoto Prefectural University Of Medicine
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YAMADA Norifumi
Department of Physics, Tohoku University
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Yamada Norifumi
Department of Information Science, Fukui University, 3-9-1 Bunkyo, Fukui, Fukui 910-8507, Japan
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