Skip to main content
Log in

Coupled physical systems

  • Part I. Invited Papers Dedicated To Peter Mittelstaedt
  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

The purpose of this paper is to sketch an attack on the general problem of representing a composite physical system in terms of its constituent parts. For quantum-mechanical systems, this is traditionally accomplished by forming either direct sums or tensor products of the Hilbert spaces corresponding to the component systems. Here, a more general mathematical construction is given which includes the standard quantum-mechanical formalism as a special case.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. E. Beltrametti and G. Cassinelli,The Logic of Quantum Mechanics (Encyclopeada of Mathematics and its Applications, Vol. 15, Gian-Carlo Rota, ed., Addison-Wesley, Reading, Massachusetts, 1981).

    Google Scholar 

  2. J. Dacey,Orthomodular Spaces, Ph.D. Thesis, University of Massachusetts, Amherst, 1968.

    Google Scholar 

  3. D. Foulis and C. Randall, “Empirical logic and tensor products,” inInterpretations and Foundations of Quantum Theory, H. Neumann, ed. (Bibliographisches Institut Mannheim, Wien, 1981).

    Google Scholar 

  4. D. Foulis and C. Randall, “What are quantum logics and what ought they to be?,” inCurrent Issues in Quantum Logic, E. Beltrametti and B. van Fraassen, eds. (Ettore Majorana International Science Series, 8) (Plenum, New York, 1981).

    Google Scholar 

  5. A. Gleason, “Measures on closed subspaces of a Hilbert space,”J. Math. Mech. 6, 885–893 (1957).

    Google Scholar 

  6. A. Golfin,Representations and Products of Lattices, Ph.D. Thesis, University of Massachusetts, Amherst, 1987.

    Google Scholar 

  7. R. Greechie and S. Gudder, “Quantum logics,” inThe Logico-Algebraic Approach to Quantum Mechanics, Vol. I:Historical Evolution, C. A. Hooker, ed. (Reidel, Dordrecht, 1975).

    Google Scholar 

  8. S. Gudder,Quantum Probability (Academic Press, San Diego, 1988).

    Google Scholar 

  9. G. Hardegree and P. Frazer, “Charting the labyrinth of quantum logics,” inCurrent Issues in Quantum Logic, E. Beltrametti and B. van Fraassen, eds. (Ettore Majorana International Science Series, 8) (Plenum, New York, 1981).

    Google Scholar 

  10. M. Janowitz, “The near center of an orthomodular lattice,”J. Aust. Math. Soc. 14, Part 1, 20–29 (1972).

    Google Scholar 

  11. G. Kalmbach,Orthomodular Lattices (Academic Press, New York, 1983).

    Google Scholar 

  12. M. Kläy,Stochastic Models on Empirical Systems, Empirical Logics and Quantum Logics, and States on Hypergraphs, Ph.D. Thesis, University of Bern, Switzerland, 1985.

    Google Scholar 

  13. M. Kläy, C. Randall, and D. Foulis, “Tensor products and probability weights,”Int. J. Theor. Phys. 26(3), 199–219 (1987).

    Google Scholar 

  14. P. Lock and G. Hardegree, “Connections among quantum logics, Part 1: Quantum propositional logics,”Int. J. Theor. Phys. 24(1), 43–53 (1984).

    Google Scholar 

  15. P. Lock and G. Hardegree, “Connections among quantum logics, Part 2: Quantum event logics,”Int. J. Theor. Phys. 24(1), 55–61 (1984).

    Google Scholar 

  16. R. Lock,Constructing the Tensor Product of Generalized Sample Spaces, Ph.D. Thesis, University of Massachusetts, Amherst, 1981.

    Google Scholar 

  17. P. Mittelstaedt,Philosophical Problems of Modern Physics (Reidel, Dordrecht, 1976).

    Google Scholar 

  18. P. Mittelstaedt,Quantum Logic (Reidel, Dordrecht, 1978).

    Google Scholar 

  19. P. Mittelstaedt, “The concepts of truth, possibility, and probability in the language of quantum physics,” inInterpretations and Foundations of Quantum Theory, H. Neumann, ed. (Bibliographisches Institut Mannheim, Wien, 1981).

    Google Scholar 

  20. C. Piron,Foundations of Quantum Physics (Mathematical Physics Monograph Series), A. Wightman, ed. (Benjamin, Reading, Massachusetts, 1976).

    Google Scholar 

  21. S. Pulmannová, “Tensor product of quantum logics,”J. Math. Phys. 26(1), 1–5 (1985).

    Google Scholar 

  22. C. Randall and D. Foulis, “Tensor products of quantum logics do not exist,”Not. Am. Math. Soc. 26(6), A-557 (1979).

    Google Scholar 

  23. C. Randall and D. Foulis, “Operational statistics and tensor products,” inInterpretations and Foundations of Quantum Theory, H. Neumann, ed. (Bibliographisches Institut Mannheim, Wien, 1981).

    Google Scholar 

  24. R. Streater and A. Wightman,PCT, Spin and Statistics, and All That (Mathematical Physics Monograph Series), A. S. Wightman, ed. (Benjamin, Reading, Massachusetts, 1964).

    Google Scholar 

  25. R. Wright, “Spin manuals,” inMathematical Foundations of Quantum Theory, A. R. Marlow, ed. (Academic Press, New York, 1978).

    Google Scholar 

  26. M. Younce,Random Variables on Non-Boolean Structures, Ph.D. Thesis, University of Massachusetts, Amherst, 1987.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Dedicated to Professor Peter Mittelstaedt.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Foulis, D.J. Coupled physical systems. Found Phys 19, 905–922 (1989). https://doi.org/10.1007/BF01889305

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01889305

Keywords

Navigation