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A Characterisation of the Weylian Structure of Space-Time by Means of Low Velocity Tests

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Abstract

The compatibility axiom in Ehlers, Pirani and Schild's (EPS) constructive axiomatics of the space-time geometry that uses light rays and freely falling particles with high velocity, is replaced by several constructions with low velocity particles only. For that purpose we describe the radial acceleration, a Coriolis acceleration and the zig-zag construction in a space-time with a conformal structure and an arbitrary path structure. Each of these quantities gives effects whose requirement to vanish can be taken as alternative version of the compatibility axiom of EPS. The procedural advantage lies in the fact, that one can make null-experiments and that one only needs low velocity particles to test the compatibility axiom. We show in addition that Perlick's standard clock can exist in a Weyl space only.

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References

  • Audretsch, J., and Lämmerzahl, C. (1993). A New Constructive Axiomatic Scheme for the Geometry of Space-Time, in: Majer U., Schmidt Heinz-J. (eds.): Semantical Aspects of Space-Time Geometry, BI Verlag, Mannheim, p. 21.

    Google Scholar 

  • Coleman, R. A., and Korte, H. (1980). Jet bundles and path structures, J. Math. Phys. 21, 1340.

    Google Scholar 

  • Coleman, R. A., and Korte, H. (1984). Constraints on the nature of inertial motion arising from the universality of free fall and the conformal causal structure of spacetime, J. Math. Phys. 25, 3513.

    Google Scholar 

  • Coleman, R. A., and Korte, H. (1987). Any physical monopole equation of motion structure uniquely determines a projective structure and an (n?1)-force. J. Math. Phys. 28, 1492.

    Google Scholar 

  • Coleman, R. A., and Korte, H. (1993). Why fundamental structures are first or second order, preprint., Zentrum für interdisziplinäre Forschung, Universit #x00E4;t Bielefeld.

    Google Scholar 

  • Coleman, R. A., and Schmidt, Heinz-J. (1993). A geometric formulation of the equivalence principle, preprint, Zentrum für interdisziplinäre Forschung, Universität Bielefeld.

  • Douglas, J. (1928): The general geometry of paths, Ann. Math. 29, 143.

    Google Scholar 

  • Ehlers, J., Pirani, F. A. E., and Schild, A. (1972). The Geometry of Free Fall and Light Propagation, in: L. O'Raifeartaigh (ed.): General Relativity, Papers in Honour of J. L. Synge, Clarendon Press, Oxford.

    Google Scholar 

  • Ehlers, J., and Köhler, E. (1977). Path Structure on Manifolds, J. Math. Phys. 18, 2014.

    Google Scholar 

  • Ehlers, J., and Schild, A. (1973). Geometry in a Manifold with Projective Structure, Commun. Math. Phys. 32, 119.

    Google Scholar 

  • Heilig, U., and Pfister, H. (1991). Characterization of free fall paths by a global or local Desargues property, J. Geom. Phys. 7, 419.

    Google Scholar 

  • Perlick, V. (1987). Characterisation of Standard Clocks by Means of Light Rays and Freely Falling Particles, Gen. Rel. Grav. 19, 1059.

    Google Scholar 

  • Perlick, V. (1991). Observer fields in Weylian spacetime models, Class. Quantum Grav. 8, 1369.

    Google Scholar 

  • Pirani, F. A. E. (1965). A note on bouncing photons, Bull. Acad. Polon. Sci., Ser. Sci. Math. Astr. Phys. 13, 239.

    Google Scholar 

  • Rund, H. (1959). The Differential Geometry of Finsler Spaces, Grundlehren der Mathematischen Wissenschaften in Einzeldarstellungen, Springer-Verlag, Berlin.

    Google Scholar 

  • Schelb, U. (1992). An axiomatic basis of space-time theory, part III: Construction of a differentiable manifold, will appear in Rep. Math. Phys. 31, 297.

    Google Scholar 

  • Schelb, U. (1997). On a new condition distinguishing Weyl and Lorentz space-times, Int. J. Theor. Phys. 36, 1341.

    Google Scholar 

  • Schröter, J. (1988). 0An axiomatic basis of space-time theory, part I: Construction of a causal space with coordinates, Rep. Math. Phys. 26, 305.

    Google Scholar 

  • Schröter, J., and Schelb, U. (1992). An axiomatic basis of space-time theory, part II: Construction of a C 0-manifold, Rep. Math. Phys. 31, 5.

    Google Scholar 

  • Schröter, J., and Schelb, U. (1995). Remarks concerning the notion of free fall in axiomatic spacetime theory, Gen. Rel. Grav. 27, 605.

    Google Scholar 

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  1. Institute for Experimental Physics, Heinrich-Heine-University Düsseldorf Universitätsstraße 1, 40225, Düsseldorf, Germany

    Claus Lämmerzahl

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  1. Claus Lämmerzahl
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Lämmerzahl, C. A Characterisation of the Weylian Structure of Space-Time by Means of Low Velocity Tests. General Relativity and Gravitation 33, 815–831 (2001). https://doi.org/10.1023/A:1010203823865

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