Skip to main content
Springer Nature Link
Log in

The logic of quantum mechanics derived from classical general relativity

  • Published:
Foundations of Physics Letters

Abstract

For the first time it is shown that the logic of quantum mechanics can be derived from classical physics. An orthomodular lattice of propositions characteristic of quantum logic, is constructed for manifolds in Einstein’s theory of general relativity. A particle is modelled by a topologically non-trivial 4-manifold with closed timelike curves—a 4-geon, rather than as an evolving 3-manifold. It is then possible for both the state preparationand measurement apparatus to constrain the results of experiments. It is shown that propositions about the results of measurements can satisfy a non-distributive logic rather than the Boolean logic of classical systems. Reasonable assumptions about the role of the measurement apparatus leads to an orthomodular lattice of propositions characteristic of quantum logic.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
€32.70 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Netherlands)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. E. G. Beltrametti and G. Cassinelli,The Logic of Quantum Mechanics (Addison-Wesley, Reading, 1981).

    MATH  Google Scholar 

  2. S. S. Holland, Jr.,Bull. Am. Math. Soc. 32, 205 (1995).

    MATH  MathSciNet  Google Scholar 

  3. A. Einstein and Rosen,Phys. Rev. 48, 73 (1935).

    Article  MATH  ADS  Google Scholar 

  4. C. W. Misner and J. A. Wheeler,Ann. Phys. 2, 525 (1957).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  5. J. Friedman, M. S. Morris, I. D. Novikov, and U. Yurtsever,Phys. Rev. D 42, 1915 (1990).

    Article  ADS  MathSciNet  Google Scholar 

  6. K. S. Thorne, “Closed timelike curves” inProceedings, 13th International Conference on General Relativity and Gravity, 1992 (Institute of Physics Publishing, Bristol, 1992).

    Google Scholar 

  7. L. E. Ballentine,Quantum Mechanics (Prentice Hall, New Jersey, 1989).

    Google Scholar 

  8. P. R. Holland,The Quantum Theory of Motion (Cambridge University Press, Cambridge, 1993).

    Google Scholar 

  9. P. A. Schilpp, ed.,Albert Einstein: Philosopher-Scientist (Cambridge University Press, Cambridge, 1970).

    Google Scholar 

  10. J. L. Friedman and R. D. Sorkin,Gen. Rel. Grav. 14, 615 (1982).

    ADS  MathSciNet  Google Scholar 

  11. J. M. Jauch,Foundations of Quantum Mechanics (Addison-Wesley, Reading, 1968).

    MATH  Google Scholar 

  12. C. J. Isham, “Structural issues in quantum gravity,” plenary session lecture given at the GRG 14 Conference, Florence, grqc/9510063, August 1995.

  13. R. Penrose,Rev. Mod. Phys. 137, 215 (1973).

    MathSciNet  Google Scholar 

  14. D. N. Page and C. D. Geilker,Phys. Rev. Lett. 147, 979 (1981).

    Article  ADS  MathSciNet  Google Scholar 

  15. L. E. Ballentine and J. P. Jarrett,Am. J. Phys. 155, 696 (1987).

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, University of Warwick, CV4 7AL, Coventry, United Kingdom

    Mark J. Hadley

Authors
  1. Mark J. Hadley
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mark J. Hadley.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hadley, M.J. The logic of quantum mechanics derived from classical general relativity. Found Phys Lett 10, 43–60 (1997). https://doi.org/10.1007/BF02764119

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02764119

Key words

Search

Navigation