Skip to main content
Log in

Maximal proper acceleration and the structure of spacetime

  • Published:
Foundations of Physics Letters

Abstract

A limiting proper acceleration in nature follows deductively from known physics and compels the union of spacetime and four-velocity space into a maximal-acceleration invariant phase space having an intrinsic Kaluza-Klein-type fiber-bundle structure with manifest gauge properties. The Riemann curvature scalar of the bundle manifold is determined, and a possible action principle is considered to serve as a basis for the generation of field equations.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. H. E. Brandt, “Maximal proper acceleration relative to the vacuum,”Lett. Nuovo Cimento 38, 522 (1983);39, 192 (1984).

    Google Scholar 

  2. H. E. Brandt, “The maximal acceleration group” inProceedings, XIIIth International Colloquium on Group Theoretical Methods in Physics, W. W. Zachary, ed. (World Scientific, Singapore, 1984), pp. 519–522.

    Google Scholar 

  3. H. E. Brandt, “Maximal-acceleration invariant phase space” inThe Physics of Phase Space, Y. S. Kim and W. W. Zachary, eds. (Springer, Berlin, 1987), pp. 414–416.

    Google Scholar 

  4. H. E. Brandt, “Differential geometry and gauge structure of maximal-acceleration invariant phase space” inProceedings, X Vth International Colloquium on Group Theoretical Methods in Physics, R. Gilmore, ed. (World Scientific, Singapore, 1987), pp. 569–577.

    Google Scholar 

  5. H. E. Brandt, “Kinetic theory in maximal-acceleration invariant phase space,” to be published inProceedings, International Symposium on Spacetime Symmetries (University of Maryland, College Park, Maryland, 24–28 May 1988), Y. S. Kim and W. W. Zachary, eds.;Nucl. Phys. B, Proc. Suppl. 6, 367 (1989).

    Google Scholar 

  6. P. C. W. Davies, “Scalar particle production in Schwarzschild and Rindler metrics,”J. Phys. A 8, 609 (1975).

    Google Scholar 

  7. W. G. Unruh, “Notes on black-hole evaporation,”Phys. Rev. D 14, 870 (1976).

    Google Scholar 

  8. N. D. Birrell and P. C. W. Davies,Quantum Fields in Curved Space (Cambridge University Press, Cambridge, 1984).

    Google Scholar 

  9. A. D. Sakharov, “Maximum temperature of thermal radiation,”JETP Lett. 3, 288 (1966).

    Google Scholar 

  10. A. D. Sakharov,Collected Scientific Works (Marcel Dekker, New York, 1982).

    Google Scholar 

  11. E. R. Caianiello, “Is there a maximal acceleration?,”Lett. Nuovo Cimento 32, 65 (1981).

    Google Scholar 

  12. E. R. Caianiello, S. De Filippo, G. Marmo, and G. Vilasi, “Remarks on the maximal-acceleration hypothesis,”Lett. Nuovo Cimento 34, 112 (1982).

    Google Scholar 

  13. H. E. Brandt, “Heuristic estimate of the temperature of the vacuum in an accelerated frame,”Bull. Am. Phys. Soc. 27, 538 (1982).

    Google Scholar 

  14. H. E. Brandt, “Temperature of the massless component of the vacuum radiation in an accelerated frame,”Bull. Am. Phys. Soc. 28, 722 (1983).

    Google Scholar 

  15. L. P. Eisenhart,Riemannian Geometry (Princeton University Press, Princeton, 1964), p. 61.

    Google Scholar 

  16. H. Minkowski, “Space and time,” inThe Principle of Relativity, A. Einstein (Dover, New York, 1952), p. 75.

    Google Scholar 

  17. M. Born,The Born-Einstein Letters (Walker, New York, 1971), pp. 131–135.

    Google Scholar 

  18. A. Einstein,The Meaning of Relativity (Princeton University Press, Princeton, 1955).

    Google Scholar 

  19. H. E. Brandt, “Time dilatation for a static observer in a stationary spacetime,”Bull. Am. Phys. Soc. 30, 717 (1985).

    Google Scholar 

  20. G. Scarpetta, “Relativistic kinematics with Caianiello's maximal proper acceleration,”Lett. Nuovo Cimento 41, 51 (1984).

    Google Scholar 

  21. W. Guz and G. Scarpetta, “Special relativity with the maximal proper acceleration” inQuantum Field Theory, F. Mancini, ed. (North-Holland, Amsterdam, 1986), pp. 233–240.

  22. W. Rindler,Introduction to Special Relativity (Clarendon Press, Oxford, 1982), p. 48.

    Google Scholar 

  23. B. DeWitt, “Dynamical theory of groups and fields” inRelativity, Groups and Topology, C. DeWitt and B. DeWitt, eds. (Gordon Breach, New York, 1964), p. 725.

    Google Scholar 

  24. R. Kerner, “Generalization of the Kaluza-Klein theory for an arbitrary non-abelian gauge group,”Ann. Inst. H. Poincaré 9, 143 (1968).

    Google Scholar 

  25. L. N. Chang, K. I. Macrae, and F. Mansouri, “Geometrical approach to local gauge and supergauge invariance: Local gauge theories and supersymmetric strings,”Phys. Rev. D 13, 235 (1976).

    Google Scholar 

  26. T. Appelquist, A. Chodos, and P. Freund,Modern Kaluza-Klein Theories (Addison-Wesley, Menlo Park, 1987).

    Google Scholar 

  27. M. Born, “A suggestion for unifying quantum theory and relativity,”Proc. Roy. Soc. A 165, 291 (1938).

    Google Scholar 

  28. A. Das, “Extended phase space. I, II, and III.,”J. Math. Phys. 21, 1506, 1513, 1521 (1980).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Brandt, H.E. Maximal proper acceleration and the structure of spacetime. Found Phys Lett 2, 39–58 (1989). https://doi.org/10.1007/BF00690077

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00690077

Key words

Navigation