Probability, geometry, and irreversibility in quantum mechanics |
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| Authors: | Karl Gustafson |
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| Institution: | 1. International Center for Mathematical Modeling in Physics, Engineering, Economics, and Cognitive Science, Linnaeus University, Växjö-Kalmar, Sweden;2. Prokhorov General Physics Institute, Vavilov str. 38D, Moscow, Russia;1. Image Processing Center, Beihang University, Beijing 100191, China;2. ShanghaiTech University, Shanghai 200031, China;3. Departamento de Ciencias de la Computación e I.A., Universidad de Granada, Granada 18071, Spain;4. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL 60208-3118, USA |
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| Abstract: | The main conclusion of this paper is that the Bell–Wigner–Accardi theory of quantum probabilities in spin systems may be placed within the general operator trigonometry developed independently by this author about 30 years ago. The use of the Grammian from the operator trigonometry simplifies and clarifies the analysis of Wigner. A general triangle inequality from the operator trigonometry clarifies and generalizes the analysis of Accardi. The statistical meaning of the complex numbers in quantum mechanics is seen to be that of the natural geometry of the operator trigonometry. A new connection of the operator trigonometry to CP symmetry violation is established. |
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