International Journal of Theoretical Physics

, Volume 27, Issue 4, pp 473–519 | Cite as

“Superconducting” causal nets

  • David Finkelstein
Article

Abstract

The world is described as a relativistic quantum neural net with a quantum condensation akin to superconductivity. The sole dynamical variable is an operator representing immediate causal connection. The net enjoys a quantum principle of equivalence implying local LorentzSL(2,C) invariance and causality. The past-future asymmetry of its cell is similar to that of the neutrino. A net phase transition is expected at temperatures on the order of theW mass rather than the Planck mass, and near gravitational singularities.

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References

  1. Alexandroff, A. (1956). The space-time of the theory of relativity,Helvetical Physica Acta, Supplementum 4, 44–45.Google Scholar
  2. Barnabei, M., Brini, A., and Rota, G.-C. (1985). On the exterior calculus of invariant theory,Journal of Algebra 96, 120–160.Google Scholar
  3. Bekenstein, J. D. (1973).Physical Review D7, 2333–2346.Google Scholar
  4. Bergmann, P. G. (1957). Two component spinors in general relativity,Physical Review,107, 624–629.Google Scholar
  5. Bennett, C. H. (1973). Logical reversibility of computation,IBM Journal of Research and Development,6, 525–532.Google Scholar
  6. Bombelli, L., Lee, J., Meyer, D., and Sorkin, R. (1987). Spacetime as a locally finite causal set, Preprint, Department of Physics, Syracuse University.Google Scholar
  7. Chew, G. F., and Stapp, H. P. (1987).3-space from Quantum Mechanics, Lawrence Berkeley Laboratory, preprint LBL-23595.Google Scholar
  8. De Witt, B. S. (1964)Dynamical Theory of Groups and Fields, inRelativity, Groups and Topology, C. deWitt and B. S. deWitt, eds., Gordon and Breach, Problem No. 77.Google Scholar
  9. Eguchi, T., Gilkey, P. B., and Hanson, A. J. (1980). Gravitation, gauge theories and differential geometry.Physics Reports,66, 213–393.Google Scholar
  10. Feynman, R. P., and Hibbs, A. R. (1965).Quantum Mechanics Via Path Integrals, McGraw-Hill, New York, Chapter 2; see also R. P. Feynman, Nobel Address.Google Scholar
  11. Finkelstein, D. (1955). Internal structure of spinning particles,Physical Review,100, 924–931.Google Scholar
  12. Finkelstein, D. (1958). Past-future asymmetry of the gravitational field of a point particle,Physical Review,110, 965–967.Google Scholar
  13. Finkelstein, D. (1969). Space-time code,Physical Review,184, 1261–1271.Google Scholar
  14. Finkelstein, D. (1987a). Coherent quantum logic,International Journal of Theoretical Physics,26, 109–129.Google Scholar
  15. Finkelstein, D. (1987b). Finite physics,The Universal Turing Machine-A Half-Century Survey, R. Herken, Kammerer & Unverzagt, Hamburg.Google Scholar
  16. Finkelstein, D., and Misner, C. W. (1959). New conservation laws,Annals of Physics 6, 230–243.Google Scholar
  17. Finkelstein, D., and Rodriguez, E. (1986). Algebras and manifolds,Physica,18D, 197–208.Google Scholar
  18. Finkelstein, S. R. (1987). Gravity in hyperspin manifolds, Ph.D. Thesis, School of Physics, Georgia Institute of Technology.Google Scholar
  19. Finkelstein, S. R. (1988). Gravity in hyperspin manifolds,International Journal of Theoretical Physics, in press.Google Scholar
  20. Fredkin, D., and Toffoli, T. (1982). Conservative logic,International Journal of Theoretical Physics,21, 219–253.Google Scholar
  21. Hawking, S. (1975). Particle creation by black holes,Communications in Mathematical Physics,43, 199–220.Google Scholar
  22. Holm, C. (1986). Christoffel formula and geodesic motion in hyperspin manifolds,International Journal of Theoretical Physics,25, 1209.Google Scholar
  23. Holm, C. (1987). Hyperspin structure of Einstein universes and their neutrino spectrum, Ph. D. Thesis, Georgia Institute of Technology.Google Scholar
  24. Holm, C. (1988). The hyperspin structure of unitary groups,Journal of Mathematical Physics, in press.Google Scholar
  25. Kronheimer, E. H., and Penrose, R. (1965). On the structure of causal spaces,Proceedings of the Cambridge Philosophical Society 63, 481.Google Scholar
  26. Kruskal, M. (1960). Maximal extension of Schwarzschild metric,Physical Review,119, 1743–1745.Google Scholar
  27. Latzer, R. W. (1972). Non-directed light signals and the structure of time,Synthese,24, 236.Google Scholar
  28. Misner, C. W., Thorne, K. S., and Wheeler, J. A. (1973).Gravitation, p. 1210, Freeman, San Francisco.Google Scholar
  29. Peano, G. (1988).Calcolo geometrico secondo l'Ausdehnungslehre di H. Grassman, Fratelli Bocea Editori, Torino.Google Scholar
  30. Penrose, R. (1965). Gravitational collapse and space-time singularities,Physical Review Letters,14, 57–59.Google Scholar
  31. Penrose, R. (1971). Angular momentum: An approach to combinatorial space-time, inQuantum Theory and Beyond, T. Bastin, ed., Cambridge University Press.Google Scholar
  32. Pimenov, R. (1968).Spaces of Kinematic Type (Mathematical Theory of Space-Time), Nauka, Leningrad (in Russian) [English translation,Kinematic Spaces, Consultants Bureau, New York].Google Scholar
  33. Regge, T. (1961). General relativity without coordinates,Nuovo Cimento,29, 558–571.Google Scholar
  34. Robb, A. A. (1936).Geometry of Space and Time, Cambridge University Press.Google Scholar
  35. Ruffini, R., and Wheeler, J. A. (1970). Collapse of wave to black hole,Bulletin of the American Physical Society,15, 76.Google Scholar
  36. Skyrme, T. H. R. (1961).Proceedings of the Royal Society of London A,260, 127.Google Scholar
  37. Sorkin, R. (1987). Private communication. See also Bombelliet al., 1987.Google Scholar
  38. Susskin, L. (1977). Lattice fermions,Physical Review D,16, 3031.Google Scholar
  39. T'hooft, G. (1979). Quantum Gravity: A Fundamental Problem and some Radical Ideas, inRecent Developments in Gravitation. Cargese 1978, M. Lévy and S. Deser, eds., Plenum, New York.Google Scholar
  40. Weinberg, S. (1984). Quasi-Riemannian theories of gravitation in more than four dimensions,Physics Letters,138B, 47–51.Google Scholar
  41. Von Weizsäcker, C. F. (1955).Komplementarität und Logik Naturwissenschaften,19, 548.Google Scholar
  42. Von Weizsäcker, C. F. (1985).Aufbau der Physik, Hanser, Munich.Google Scholar
  43. Zeeman, C. Causality implies the Lorentz group.Journal of Mathematical Physics 5, 490–493.Google Scholar
  44. Żenczykowski, P. (1988). Combinatorial descriptions of space and strong interactions,International Journal of Theoretical Physics,27, 9.Google Scholar

Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • David Finkelstein
    • 1
  1. 1.School of PhysicsGeorgia Institute of TechnologyAtlanta

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