Physical Equivalence Based on Observations and Equivalence in Terms of Free Ultra-Filters in Quantum Mechanics on Non-Standard Space

Tsunehiro Kobayashi
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Tsunehiro Kobayashi: University of Tsukuba, Institute of Physics

A chapter in Symmetries in Science X, 1998, pp 153-163 from Springer

Abstract: Abstract There is no experiment accompanied by no experimental error, that is, uncertainties of physical observables. The fundamental concept concerning the equivalence between different experiments essentially depends on these experimental uncertainties. We, however, have no theory which involves such a fundamental concept about the physical equivalence. We show that the equivalence in terms of free ultra-filters in quantum mechanics on non-standard analysis represents the physical equivalence. It is seen that the equivalence on non-standard physical spaces induces decoherence of quantum states on observed physical spaces. We conclude that the free ultra-filters correspond to the experimental apparatus in our observations.

Keywords: Hilbert Space; Quantum Mechanic; Density Matrix; Physical Observable; Microcanonical Ensemble (search for similar items in EconPapers)
Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4899-1537-5_9

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DOI: 10.1007/978-1-4899-1537-5_9

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