Skip to main content
SpringerLink
Log in

Conformal Proper Times According to the Woodhouse Causal Axiomatics of Relativistic Spacetimes

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

On the basis of the Woodhouse causal axiomatics, we show that conformal proper times and an extra variable in addition to those of space and time, together give a physical justification for the ‘chronometric hypothesis’ of general relativity. Indeed, we show that, with a lack of these latter two ingredients and of this hypothesis, clock paradoxes exist for which the unparadoxical asymmetry cannot be recovered when using the ‘clock and message functions’ only. These proper times originate from a given conformal structure of the spacetime when ascribing different compatible projective structures to each Woodhouse particle, and then, each defines a specific Weylian ‘sheaf structure’. In addition, the proper time parameterizations are defined via path-dependent conformal scale factors, which act like sockets for any kind of physical interaction and also represent the values of the variable associated with the extra dimension.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Woodhouse, N.M.J.: The differential and causal structures of space-time. J. Math. Phys. 14(4), 495–501 (1973)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  2. Ehlers, J., Pirani, F.A.E., Schild, A.: The geometry of free fall and light propagation. In: O’Raifeartaigh, L. (ed.) General Relativity, Papers in Honour of J.L. Synge, pp. 63–84. Clarendon, Oxford (1972)

    Google Scholar 

  3. Kundt, W., Hoffmann, B.: Determination of gravitational standard time. In: Recent Developments in General Relativity, pp. 303–306. Pergamon, Elmsford (1962). A book dedicated to Leopold Infeld’s 60th birthday

    Google Scholar 

  4. Audretsch, J.: Riemannian structure of space-time as a consequence of quantum mechanics. Phys. Rev. D 27(12), 2872–2884 (1983)

    MathSciNet  ADS  Google Scholar 

  5. Grandou, G., Rubin, J.L.: On the ingredients of the twin paradox. Int. J. Theor. Phys. 48, 101–114 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  6. Einstein, A.: Dialog über einwände gegen die relativitätstheorie. Die Naturwiss. 6(48), 697–702 (1918)

    Article  ADS  Google Scholar 

  7. Reinhardt, S., Saathoff, G., Buhr, H., Carlson, L.A., Wolf, A., Schwalm, D., Karpuk, S., Novotny, C., Huber, G., Zimmermann, M., Holzwarth, R., Udem, T., Hänsch, T.W., Gwinner, G.: Test of relativistic time dilatation with fast optical atomic clocks at different velocities. Nat. Phys. 3, 861–864 (2007)

    Article  Google Scholar 

  8. Coll, B., Ferrando, J.J., Morales, J.A.: Two-dimensional approach to relativistic positioning systems. Phys. Rev. D 73(8), 084017(12) (2006)

    Article  MathSciNet  ADS  Google Scholar 

  9. Coll, B., Pozo, J.M.: Relativistic positioning systems: the emission coordinates. Class. Quantum Gravity 23(24), 7395–7416 (2006)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  10. Garcìa-Parrado, A., Senovilla, J.M.M.: Causal structures and causal boundaries. Class. Quantum Gravity 22, R1–R84 (2005)

    Article  MATH  ADS  Google Scholar 

  11. Konheimer, E.H., Penrose, R.: On the structure of causal spaces. Proc. Camb. Philos. Soc. 63, 481–501 (1967)

    Article  Google Scholar 

  12. Malament, D.: The class of continuous timelike curves determines the topology of spacetime. J. Math. Phys. 18(7), 1399–1404 (1977)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  13. Zeghib, A.: Lipschitz regularity in some geometric problems. Geom. Dedic. 107(1), 57–83 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  14. Malament, D.: Causal theories of time and the conventionality of simultaneity. Noûs 7, 293–300 (1977)

    Article  Google Scholar 

  15. Hafele, J.C., Keating, R.E.: Around-the-world atomic clocks: Predicted relativistic time gains. Science 177, 166–168 (1972)

    Article  ADS  Google Scholar 

  16. Hafele, J.C., Keating, R.E.: Around-the-world atomic clocks: Observed relativistic time gains. Science 177, 168–170 (1972)

    Article  ADS  Google Scholar 

  17. Tennison, B.R.: Sheaf Theory. Cambridge University Press, Cambridge (1975)

    MATH  Google Scholar 

  18. Unnikrishnan, C.S.: On Einstein’s resolution of the twin clock paradox. Curr. Sci. 89(12), 2009–2015 (2005)

    MathSciNet  Google Scholar 

  19. Ghins, M., Budden, T.: The equivalence principle. Stud. Hist. Philos. Mod. Phys. 32(1), 33–51 (2001)

    Article  MathSciNet  Google Scholar 

  20. Allan, D.W.: Statistics of atomic frequency standards. Proc. IEEE 54(2), 221–230 (1966)

    Article  Google Scholar 

  21. Misner, C.W., Thorne, K.S., Wheeler, J.A.: Gravitation. Freeman, New York (1973)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut du Non-Linéaire de Nice—CNRS, UMR6618, Université de Nice—Sophia-Antipolis, UFR Sciences, 1361 route des Lucioles, 06560, Valbonne, France

    Jacques L. Rubin

Authors
  1. Jacques L. Rubin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jacques L. Rubin.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rubin, J.L. Conformal Proper Times According to the Woodhouse Causal Axiomatics of Relativistic Spacetimes. Found Phys 40, 158–178 (2010). https://doi.org/10.1007/s10701-009-9379-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10701-009-9379-5

Search

Navigation