Advertisement

Logic, states, and quantum probabilities

  • Rachel Wallace Garden
Article
  • 64 Downloads

Abstract

A careful analysis of mechanical descriptions provides a new logical foundation for the states and probabilities of mechanics which leads to a new understanding of quantum probabilities and their representation in Hilbert space. It is argued that all mechanical theories use a logic which is distributive but only relatively orthocomplemented, and that this, too, is the structure of its states. Probabilities are derived from this analysis using standard Kolmogorov definitions in a way that accounts for the nonstandard peculiarities of the quantum transitional probabilities as well as classicial probability assignments. At the end of the paper this analysis is used to refute arguments that quantum mechanics is nondistributive and that the failure of Bell's inequality in quantum theory threatens our conceptual scheme. Instead we reach a much less drastic interpretation of quantum mechanics.

Keywords

Hilbert Space Field Theory Elementary Particle Quantum Field Theory Quantum Mechanic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bell, J. (1987).Speakable and Unspeakable in Quantum Mechanics, Cambridge University Press, Cambridge.Google Scholar
  2. Birkhoff, G., and von Neumann, J. (1936). The logic of quantum mechanics,Annals of Mathematics,37, 823–843 [reprinted in Hooker (1975)].MathSciNetGoogle Scholar
  3. Constantini, D. (1993). A statistical analysis of the two-slit experiment: Or some remarks on quantum probability,International Journal of Theoretical Physics,32(12), 2349–2362.MathSciNetGoogle Scholar
  4. D'Espagnat, B. (1979). The quantum theory and reality,Scientific American,241, 128.Google Scholar
  5. D'Espagnat, B. (1989).Reality and the Physicist: Knowledge, Duration and the Quantum World, Cambridge University Press, Cambridge.Google Scholar
  6. Einstein, A., Podolsky, B., and Rosen, N. (1935). Can quantum mechanical description of reality be considered complete?Physical Review,47, 777–790.CrossRefADSGoogle Scholar
  7. Garden, R. (1984).Modern Logic and Quantum Mechanics, Adam Hilger, Bristol.Google Scholar
  8. Hooker, C. A., ed. (1975).The Logic Algebraic Approach to Quantum Mechanics, Vol. 1, Reidel, Dordrecht, Holland.Google Scholar
  9. Jauch, J. M. (1968).Foundations of Quantum Mechanics, Addison-Wesley, Reading, Massachusetts.Google Scholar
  10. Rescher, N. (1969).Many Valued Logic, McGraw-Hill, New York.Google Scholar
  11. Von Neumann, J. (1955).Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton, New Jersey.Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Rachel Wallace Garden
    • 1
  1. 1.New Zealand

Personalised recommendations