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

In: Symmetries in Science X

Author

Listed:
  • Tsunehiro Kobayashi

    (University of Tsukuba, Institute of Physics)

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.

Suggested Citation

  • Tsunehiro Kobayashi, 1998. "Physical Equivalence Based on Observations and Equivalence in Terms of Free Ultra-Filters in Quantum Mechanics on Non-Standard Space," Springer Books, in: Bruno Gruber & Michael Ramek (ed.), Symmetries in Science X, pages 153-163, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4899-1537-5_9
    DOI: 10.1007/978-1-4899-1537-5_9
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