Clifford Algebra, Geometry and Physics

  • M. PavŠiČ
Part of the NATO Science Series book series (NAII, volume 95)

Abstract

In the usual theory of relativity there is no evolution. Worldlines are fixed, everything is frozen once for all in a 4-dimensional “ block universe” V 4. This is in contradiction with our subjective experience of the passage of time. It is in contradiction with what we actually observe.

Keywords

Manifold Soliton Eter Arena Dinates 

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References

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    Pavšič, M. (1986) Einstein’s gravity from a first order Lagrangian in an embedding space, Physics Letters A 116, 1–5; Pavšič, M. (2001) A brane world model with intersecting branes, Physics Letters A 283, 8-14.MathSciNetADSCrossRefGoogle Scholar
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    Castro, C. and Pavšič, M. (2001) Higher derivative gravity and torsion from the geometry of C-spaces, hep-th/0110079 (to appear in Phys. Lett. B).Google Scholar
  14. 1.
    Stueckelberg, E.C.G. (1941) Un Nouveau modèle de l’électron ponctuel en théorie classique, Helvetica Physica Acta 14, 51–55; Stueckelberg, E.C.G. (1941) Remarque à propos de la création de paires de particules en théorie de de relativité, Helvetica Physica Acta 14, 588 (1941); Stueckelberg, E.C.G. (1942) Helvetica Physica Acta 15, 23-37.MathSciNetGoogle Scholar
  15. 2.
    Feynman, R.P. (1950) Mathematical formulation of the quantum theory of electromagnetic interaction, Physical Review 80, 440–457; Schwinger, J. (1951) On gauge invariance and vacuum polarization, Physical Review 82, 664-679; Davidon, W.C. (1955) Proper-time electron formalism, Physical Review 97, 1131-1138; 97, 1139-1144.MathSciNetADSMATHCrossRefGoogle Scholar
  16. 3.
    Horwitz, L.P. and Piron, C. (1973) Relativistic dynamics, Helvetica Physica Acta 46, 316–326; Horwitz, L.P. and Rohrlich, F. (1981) Constrained relativistic quantum dynamics, Physical Review D 24, 1528-1542; Horwitz, L.P., Arshansky, R.I. and Elitzur, A.C. (1988) On the two aspects of time: the distinction and its implications, Foundations of Physics 18, 1159-1193; Arshansky, R., Horwitz, L.P. and Lavie, Y. (1983) Particles vs. events: the concatenated structure of world lines in relativistic quantum mechanics, Foundations of Physics 13, 1167-1194; Horwitz, L.P. (1983) On relativistic quantum theory, in A. van der Merwe (ed.), Old and New Questions in Physics, Cosmology, Philosophy and Theoretical Biology, Plenum Publishing Company, New York, pp. 169-188; Horwitz, L.P. and Lavie, Y. (1982) Scattering in relativistic quantum mechanics, Physical Review D 26, 819-838; Droz-Vincent, P. (1988) Proper time and evolution in quantum mechanics, Physics Letters A 134, 147-151; Burakovsky, L., Horwitz, L.P. and Schieve, W.C. (1996) New relativistic high-temperature Bose-Einstein-condensation, Physical Review D 54, 4029-4038; Horwitz, L.P., Schieve, W.C. and Piron, C. (1981) Gibbs ensemble in relativistic classical and quantum mechanics, Annals of Physics 137, 306-340; Fanchi, J.R. (1979) A generalized quantum field theory, Physical Review D 20, 3108-3119; see also the review Fanchi, J.R. (1993) Review of invariant time formulations of relativistic quantum theories, Foundations of Physics 23, 487-548, and many references therein; Fanchi, J.R. (1993) Parametrized Relativistic Quantum Theory, Kluwer Academic Publishers, Dordrecht; Enatsu, H. (1963) Relativistic Hamiltonian formalism in quantum field theory and micro-noncausality, Progress of Theoretical Physics 30, 236-264; Reuse, F. (1979) On classical and quantum relativistic dynamics, Foundations of Physics 9, 865-882: Kyprianidis, A. (1987) Scalar time parametrization of relativistic quantum mechanics: the covariant Schrödinger formalism, Physics Reports 155, 1-27; Kubo, R. (1985) Nuovo Cimento A 85, 293-309; Mensky, M.B. (1976) Relativistic quantum theory without quantized fields, Communications in Mathematical Physics 47, 97-108; Hannibal, L. (1991) First quantization of mass and charge, International Journal of Theoretical Physics 30, 1445-1459; Gaioli, F.H. and Garcia-Alvarez, E.T. (1994) The problem of time in parametrized theories, General Relativity and Gravitation 26, 1267-1275.Google Scholar
  17. 4.
    Pavšič, M. (1991) On the interpretation of the relativistic quantum mechanics with invariant evolution parameter, Foundations of Physics 21, 1005–1019; Pavsic, M. (1991) Relativistic quantum mechanics and quantum field theory with invariant evolution parameter, Nuovo Cimento A 104, 1337-1354; Pavšič, M. (1993) The role of the invariant evolution parameter in relativistic particles and strings, Doga, Turkish Journal of Physics 17, 768-784.MathSciNetADSCrossRefGoogle Scholar
  18. 5.
    Pezzaglia, W.M., Jr. (1997) Physical applications of a generalized Clifford calculus: Papapetrou equations and metamorphic curvature, gr-qc/9710027; Castro, C. (2000)) Hints of a new relativity principle from p-brane quantum mechanics, Chaos, Solitons and Fractals 11, 1721-1737; Castro, C. and Granik, A. (2000) On M-theory, quantum paradoxes and the new relativity, physics/0002019.Google Scholar
  19. 6.
    Pavšič, M. (2000) Clifford algebra as a useful language for geometry and physics, in H. Gauster, H. Grosse and L. Pittner (eds.), Geometry and Physics, Springer, Berlin, pp. 395–395; Pavšič, M. (2001) Clifford-algebra based polydimensional relativity and relativistic dynamics, Foundations of Physics 31, 1185-1209.Google Scholar
  20. 7.
    Pavšič, M. (2001) The Landscape of Theoretical Physics: A Global View, Kluwer Academic Publishers, Dordrecht.MATHGoogle Scholar
  21. 8.
    Franck, G. (2003) How time passes, this volume.Google Scholar
  22. 9.
    Pavšič, M. (1995) Relativistic p-branes without constrants and their relation to the wiggly extended objects, Foundations of Physics 25, 819–832; Pavšič, M. (1997) The Dirac-Nambu-Goto p-branes as particular solutions to a generalized, unconstrained theory, Nuovo Cimento 110, 369-395.MathSciNetADSCrossRefGoogle Scholar
  23. 10.
    Pavšič, M. (1996) On the resolution of time problem in quantum gravity induced from unconstrained membranes, Foundations of Physics 26, 159–195.MathSciNetADSCrossRefGoogle Scholar
  24. 11.
    Pavšič, M. (1986) Einstein’s gravity from a first order Lagrangian in an embedding space, Physics Letters A 116, 1–5; Pavšič, M. (2001) A brane world model with intersecting branes, Physics Letters A 283, 8-14.MathSciNetADSCrossRefGoogle Scholar
  25. 12.
    Hestenes, D. (1966) Space-time Algebra, Gordon and Breach, New York; Hestenes, D. (1984) Clifford Algebra to Geometric Calculus, D. Reidel Publishing Company, Dordrecht.MATHGoogle Scholar
  26. 13.
    Castro, C. and Pavšič, M. (2001) Higher derivative gravity and torsion from the geometry of C-spaces, hep-th/0110079 (to appear in Phys. Lett. B).Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • M. PavŠiČ
    • 1
  1. 1.J. Stefan InstituteLjubljanaSlovenia

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