Topologimeter and the problem of physical interpretation of topology lattice
The collection of all topologies on the set of three points is studied, treating the topology as a quantum-like observable. This turns out to be possible under the assumption of the asymmetry between the spaces of bra and ket vectors. Analogies between the introduced topologimeter and Stem-Gerlach experiments are outlined.
KeywordsField Theory Elementary Particle Quantum Field Theory Physical Interpretation Topology Lattice
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- Birkhoff, G., and von Neumann, J. (1936). The logic of quantum mechanics,Annals of Mathematics,37, 923.Google Scholar
- D'Espagnat, B. (1976).Conceptual Foundations of Quantum Mechanics, Benjamin, New York.Google Scholar
- Grib, A. A., and Zapatrin, R. R. (1992). Topology lattice as quantum logic,International Journal of Theoretical Physics,31, 1093.Google Scholar
- Larson, R. F., and Andima, S. (1975). The lattice of topologies: A survey.Rocky Mountain Journal of Mathematics,5, 177.Google Scholar
- Leinaas, J., and Myrheim, R. (1991). Quantum theories for identical particles.International Journal of Modern Physics B. 5, 2573.Google Scholar
- Sorkin, R. (1991). Finitary substitutes for continuous topology,International Journal of Theoretical Physics,30, 930.Google Scholar
- Von Neumann, J. (1955).Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton, New Jersey.Google Scholar
- Zapatrin, R. R. (1993). Pre-Regge calculus: Topology via logic,International Journal of Theoretical Physics,32, 779.Google Scholar
- Zapatrin, R. R. (1994). Quantum logic without negation,Helvetica Physica Acta,67, 188.Google Scholar