Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Statistical mechanics and the ontological interpretation

Abstract

To complete our ontological interpretation of quantum theory we have to conclude a treatment of quantum statistical mechanics. The basic concepts in the ontological approach are the particle and the wave function. The density matrix cannot play a fundamental role here. Therefore quantum statistical mechanics will require a further statistical distribution over wave functions in addition to the distribution of particles that have a specified wave function. Ultimately the wave function of the universe will he required, but we show that if the universe in not in thermodynamic equilibrium then it can he treated in terms of weakly interacting large scale constituents that are very nearly independent of each other. In this way we obtain the same results as those of the usual approach within the framework of the ontological interpretation.

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

References

  1. 1.

    D. Bohm,Phys. Rev. 85, 116–179, 180–193 (1952).

  2. 2.

    D. Bohm and B. J. Hiley,Phys. Rep. 144, 323–348 (1987).

  3. 3.

    J. S. Bell,Int. J. Quantum Chem:. Quantum Chem. Symp. 14, 155–159 (1980); or inSpeakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987), pp. 111–116.

  4. 4.

    R. C. Tolman,The Principles of Statistical Mechanics (Dover, New York, 1979).

  5. 5.

    R. Balescu,Equilibrium and Non-Equilibrium Statistical Mechanics (Wiley-Interscience. New York, 1975).

  6. 6.

    R. Fowler and E. A. Guggenheim,Statistical Thermodynamics (Cambridge University Press, Cambridge, 1949), p. 13.

  7. 7.

    H. D. Zeh,Found. Phys. 1, 69–76 (1970);Ann. Phys. (New York) 76, 405–418 (1973).

Download references

Author information

Additional information

Professor D. Bohm died on 28 October 1992, shortly after this paper was completed.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bohm, D., Hiley, B.J. Statistical mechanics and the ontological interpretation. Found Phys 26, 823–846 (1996). https://doi.org/10.1007/BF02058636

Download citation

Keywords

  • Wave Function
  • Density Matrix
  • Quantum Theory
  • Basic Concept
  • Statistical Mechanic