Foundations of Physics

, Volume 22, Issue 6, pp 839–852 | Cite as

Quantum stochastic models

  • Stanley Gudder
Part II. Invited Papers Dedicated To Henry Margenau


Quantum stochastic models are developed within the framework of a measure entity. An entity is a structure that describes the tests and states of a physical system. A measure entity endows each test with a measure and equips certain sets of states as measurable spaces. A stochastic model consists of measurable realvalued function on the set of states, called a generalized action, together with measures on the measurable state spaces. This structure is then employed to compute quantum probabilities of test outcomes. We characterize those measure entities that are isomorphic to a quantum probability space. We also show that stochastic models provide a phase space description of quantum mechanics and a realistic model of spin.


Phase Space State Space Quantum Mechanic Generalize Action Measurable State 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. K. Bennett and D. Foulis, “Superpositions in quantum and classical mechanics,”Found. Phys. 20, 733 (1990).Google Scholar
  2. 2.
    R. Feynman, “The space-time approach to nonrelativistic quantum mechanics,”Rev. Mod. Phys. 20, 367 (1948).Google Scholar
  3. 3.
    R. Feynman and A. Hibbs,Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).Google Scholar
  4. 4.
    D. Foulis and C. Randall, “Operational statistics I. Basic concepts,”J. Math. Phys. 13, 1167 (1972).Google Scholar
  5. 5.
    D. Foulis and C. Randall, “Operational statistics II. Manual of operations and their logics,”J. Math. Phys. 14, 1472 (1972).Google Scholar
  6. 6.
    D. Foulis and C. Randall, “Properties and operational propositions in quantum mechanics,”Found. Phys. 13, 843 (1983).Google Scholar
  7. 7.
    D. Foulis, C. Piron, and C. Randall, “Realism, operationalism, and quantum mechanics,”Found. Phys. 13, 813 (1983).Google Scholar
  8. 8.
    D. Foulis, “Coupled physical systems,”Found. Phys. 19, 905 (1989).Google Scholar
  9. 9.
    S. Gudder,Quantum Probability (Academic Press, Boston, 1988).Google Scholar
  10. 10.
    S. Gudder, “A theory of amplitudes,”J. Math. Phys. 29, 2020 (1988).Google Scholar
  11. 11.
    S. Gudder, “Realistic quantum probability,”Int. J. Theor. Phys. 20, 193 (1988).Google Scholar
  12. 12.
    S. Gudder, “Realism in quantum mechanics,”Found. Phys. 19, 949 (1989).Google Scholar
  13. 13.
    S. Gudder, “Quantum probability and operational statistics,”Found. Phys. 20, 499 (1990).Google Scholar
  14. 14.
    S. Gudder, “Combined systems in quantum probability,”Int. J. Theor. Phys. 30, 757 (1990).Google Scholar
  15. 15.
    S. Gudder, “Amplitudes on entities,” to appear.Google Scholar
  16. 16.
    S. Gudder, “Amplitudes and the universal influence function,”J. Math. Phys. 32, 2106 (1991).Google Scholar
  17. 17.
    G. Hemion, “A discrete geometry: speculations on a new framework for classical electrodynamics,”Int. J. Theor. Phys. 27, 1145 (1988).Google Scholar
  18. 18.
    G. Hemion, “Quantum mechanics in a discrete model of classical physics,”Int. J. Theor. Phys. 29, 1335 (1990).Google Scholar

Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • Stanley Gudder
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of DenverDenver

Personalised recommendations