International Journal of Theoretical Physics

, Volume 22, Issue 9, pp 803–820 | Cite as

Reformulating classical and quantum mechanics in terms of a unified set of consistency conditions

  • Robert F. Bordley
Article
Received:

Abstract

This paper imposes consistency conditions on the path of a particle and shows that they imply Hamilton's principle in classical contexts and Schrödinger's equation in quantum mechanical contexts. Thus this paper provides a common, intuitive foundation for classical and quantum mechanics. It also provides a very new perspective on quantum mechanics.

Keywords

Field Theory Elementary Particle Quantum Field Theory Quantum Mechanic Consistency Condition 
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.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Debreu, G. (1960). Topological methods in cardinal group utility theory, inMathematical Models in the Social Sciences. Stanford University Press, Stanford, California.Google Scholar
  2. Dugas, R. (1955).A History of Mechanics. Central Book Company, New York.Google Scholar
  3. Goldstein, H. (1950).Classical Mechanics. Addison-Wesley, Reading, Massachusetts.Google Scholar
  4. Koopmans, T. C. (1960). Stationary ordinal utility and impatience,Econometrica,28. 2 (April 1960).Google Scholar
  5. Krantz, D., Luce, R. D., Suppes, P., and Tversky, A. (1971).The Foundations of Measurement. Academic Press, New York.Google Scholar
  6. Marion, J. (1970).Classical Dynamics. Academic Press, New York.Google Scholar
  7. Marschak, J. (1950). Rational behavior uncertain prospects and measurable utility,Econometrica,18, 111.Google Scholar
  8. Merzbacher, E. (1970).Quantum Mechanics. John Wiley & Sons, New York.Google Scholar
  9. Nelson, E. (1966). Derivation of the Schrödinger equation from Newtonian mechanics,Physical Review 28, 1079.Google Scholar
  10. Savage, L. J. (1975).The Foundations of Statistics. Dover Publications, New York.Google Scholar
  11. Schwinger, J. (1951). The theory of quantized fields. I,Physical Review,82, 914, Part I: The theory of quantized fields. II,Physical Review,91, 713 (1953); The theory of quantized fields. III,Physical Review,91, 728 (1953); The theory of quantized fields. IV,Physical Review,92. 1283 (1953); The theory of quantized fields. V,Physical Review,93. 615 (1954); The theory of quantized fields. VI,Physical Review.94, 1362 (1954).Google Scholar
  12. Tolman, R. C. (1948).The Principles of Statistical Mechanics. Oxford University Press, London.Google Scholar
  13. Weinstock, R. (1970).Calculus of Variations. McGraw-Hill Book Company. New York.Google Scholar

Copyright information

© Plenum Publishing Corporation 1983

Authors and Affiliations

  • Robert F. Bordley
    • 1
  1. 1.University of Michigan, DearbornDearborn

Personalised recommendations