Abstract
In a Weyl space it is possible to construct geometrical clocks along timelike geodesics using projective and conformal techniques. We present a precise definition of the limiting processes involved and prove analytically that the clock readings coincide with an affine parameter of the Weyl connection.
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Weyl, H. (1921).Nachr. Ges. Wiss. Göttingen, p. 99.
Weyl, H. (1923).Mathematische Analyse des Raumproblems (Springer, Berlin).
Ehlers, J. (1973). “Survey of General Relativity Theory,” inRelativity, Astrophysics, and Cosmology, ed. W. Israel (Reidel, Dordrecht) p. 1.
Ehlers, J., Pirani, F. A. E., and Schild, A. (1972). “The Geometry of Free Fall and Light Propagation,” inGeneral Relativity, ed. L. O'Raifeartaigh (Clarendon Press, Oxford), p. 63.
Castagnino, M. (1971).J. Math. Phys.,12, 2203.
Pirani, F. A. E. (1973). “Building Spacetime from Light Rays and Free Particles,” inSymposia Mathematica, vol. 12 (Academic Press, London), p. 67.
Woodhouse, N. M. J. (1973).J. Math. Phys.,14, 495.
Ehlers, J. and Schild, A. (1973).Commun. Math. Phys.,32, 119.
Kundt, W., and Hoffmann, B. (1962). InRecent Developments in General Relativity (PWN, s.d., Warsaw), p. 303.
Marzke, R. F., and Wheeler, J. A. (1964). “Gravitation as Geometry. I,” inGravitation and Relativity, ed. H. Y. Chin and W. F. Hoffmann (Benjamin, New York), p. 40.
Pirani, F. A. E., and Schild, A. (1966). “Conformal Geometry and the Interpretation of the Weyl Tensor,” inPerspectives in Geometry and Relativity, ed. B. Hoffmann (Indiana University Press, Bloomington, Indiana), p. 291.
Köhler, E. (1976). Thesis, Munich.
Ehlers, J., and Köhler, E. (1977). “Path Structures on Manifolds,”J. Math. Phys.,18, 2014.
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Köhler, E. Measurement of proper time in a Weyl space. Gen Relat Gravit 9, 953–959 (1978). https://doi.org/10.1007/BF00784656
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DOI: https://doi.org/10.1007/BF00784656