International Journal of Theoretical Physics

, Volume 27, Issue 10, pp 1145–1255 | Cite as

A discrete geometry: Speculations on a new framework for classical electrodynamics

  • Geoffrey Hemion


An attempt is made to describe the basic principles of physics in terms of discrete partially ordered sets. Geometric ideas are introduced by means of an action at a distance formulation of classical electrodynamics. The speculations are in two main directions: (i) Gravity, one of the four elementary forces of nature, seems to be fundamentally different from the other three forces. Could it be that gravity can be explained as a natural consequence of the discrete structure? (ii) The problem of the observer in quantum mechanics continues to cause conceptual problems. Can quantum statistics be explained in terms of finite ensembles of possible partially ordered sets? The development is guided at all stages by reference to the simplest, and most well-established principles of physics.


Field Theory Elementary Particle Quantum Field Theory Quantum Mechanic Basic Principle 
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. Bell, J. S. (1966). On the problem of hidden variables in quantum mechanics,Reviews of Modern Physics,38, 447.Google Scholar
  2. Cox, D. R., and Isham, V. (1980).Point Processes, Chapman and Hall.Google Scholar
  3. Dicke, R. H. (1964).The Theoretical Significance of Experimental Relativity, Gordon and Breach.Google Scholar
  4. Dirac, P. A. M. (1938). Classical theory and radiating electrons,Proceedings of the Royal London, Series A,167, 148.Google Scholar
  5. Einstein, A. (1956).The Meaning of Relativity, 5th ed., Princeton University Press.Google Scholar
  6. Einstein, A., and Grommer, J. (1927). Allgemeine Relativitätstheorie und Bewegungsgesetz,Sitzungsberichte Preussische Akademie der Wissenschaften,2.Google Scholar
  7. Einstein, A., Podolsky, B., and Rosen, N. (1935). Can quantum-mechanical discription of reality be considered complete?,Physical Review,2, 47.Google Scholar
  8. Eyges, L. (1972).The Classical Electromagnetic Field, Addison-Wesley.Google Scholar
  9. Feynman, R. P. (1962).Quantum Electrodynamics, Benjamin.Google Scholar
  10. Feynman, R. P., and Hibbs, A. R. (1965).Quantum Mechanics and Path Integrals, McGraw-Hill.Google Scholar
  11. Feynman, R. P., Leighton, R. B., and Sands, M. (1965).The Feynman Lectures on Physics, Vol. III, Addison-Wesley.Google Scholar
  12. Fokker, A. D. (1929). Ein Invarianter Variationssatz fur die Bewegung Meherer Elektrischer Massenteilchen,Zeitschrift für Physik,58, 386.Google Scholar
  13. Gauss, C. F. (1845). Letter to W. Weber (19 March, 1845), in C. F. Gauss,Werke, Vol. 5, p. 629.Google Scholar
  14. Glimm, J., and Jaffe, A. (1981).Quantum Mechanics: A Functional Integral Point of View, Springer-Verlag.Google Scholar
  15. Gödel, K. (1949). An example of a new type of cosmological solutions of Einstein's field equations of gravitation,Reviews of Modern Physics,21, 447.Google Scholar
  16. Hawking, S. W., and Ellis, G. F. R. (1973).The Large Scale Structure of Space-Time, Cambridge University Press.Google Scholar
  17. Hogarth, J. E. (1962). Cosmological considerations of the absorber theory of radiation,Proceedings of the Royal Society of London, Series A,267, 365.Google Scholar
  18. Hoyle, F., and Narlikar, J. V. (1974).Action at a Distance in Physics and Cosmology, Freeman.Google Scholar
  19. Jammer, M. (1974).The Philosophy of Quantum Mechanics, Wiley.Google Scholar
  20. Jauch, J. M. (1968).Foundations of Quantum Mechanics, Addison-Wesley.Google Scholar
  21. Landé, A. (1965).New Foundations of Quantum Mechanics, Cambridge University Press.Google Scholar
  22. Llosa, J., ed. (1981).Relativistic Action at a Distance: Classical and Quantum Aspects, Springer-Verlag.Google Scholar
  23. Mattuck, R. D. (1976).A Guide to Feynman Diagrams in the Many-Body Problem, McGraw-Hill.Google Scholar
  24. Messiah, A. (1970).Quantum Mechanics, North-Holland.Google Scholar
  25. Narlikar, J. V. (1978).Lectures on General Relativity and Cosmology, Macmillan.Google Scholar
  26. Nelson, E. (1967).Dynamical Theories of Brownian Motion, Princeton University Press.Google Scholar
  27. Rebbi, C. (1982). Lattice gauge theories and Monte Carlo simulations, inNon-Perturbative Aspects of Quantum Field Theory, World Scientific, Singapore.Google Scholar
  28. Roe, P. E. (1969). Time-symmetric electrodynamics in Friedmann universes,Monthly Notices of the Royal Astronomical Society,144, 219.Google Scholar
  29. Schupp, P. A., ed. (1949).Albert Einstein, Philosopher-Scientist, Library of Living Philosophers.Google Scholar
  30. Schrödinger, E. (1953). The meaning of wave mechanics, inLouis de Broglie Physicien et Penseur, A. George, ed., Albin Michel.Google Scholar
  31. Segal, I. E. (1976).Mathematical Cosmology and Extragalactic Astronomy, Academic Press.Google Scholar
  32. Von Neumann, J. (1955).Mathematical Foundations of Quantum Mechanics, Princeton University Press.Google Scholar
  33. Wells, R. O. (1976). Complex manifolds and mathematical physics,Bulletin (NS)of the American Mathematical Society,1, 296.Google Scholar
  34. Wheeler, J. A., and Feynman, R. P. (1945). Interaction with the absorber as the mechanism of radiation,Reviews of Modern Physics,17, 157.Google Scholar
  35. Wheeler, J. A., and Feynman, R. P. (1949). Classical electrodynamics in terms of direct interparticle action,Reviews of Modern Physics,21, 425.Google Scholar
  36. Yilmaz, H. (1965).Introduction to the Theory of Relativity and the Principles of Modern Physics, Blaisdell.Google Scholar

Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • Geoffrey Hemion
    • 1
  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldWest Germany

Personalised recommendations