General Relativity and Gravitation

, Volume 41, Issue 5, pp 1107–1124 | Cite as

Measurement of the space–time interval between two events using the retarded and advanced times of each event with respect to a time-like world-line

Research Article


Several recent studies have been devoted to investigating the limitations that standard quantum mechanics and/or quantum gravity might impose on the measurability of space–time observables. These analyses are often confined to the simplified context of 2D flat space–time and rely on a simple procedure for the measurement of space-like distances based on the exchange of light signals. We present a generalization of this measurement procedure applicable to all three types of space–time intervals between two events in space–times of any number of dimensions. We also present a preliminary account of an alternative measurement procedure that can be applied taking into account the gravitational field of the macroscopic measuring apparatus.


Relativity Quantum mechanics Quantum gravity Uncertainty principles 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Veneziano G.: Europhys. Lett. 2, 199 (1986)CrossRefADSGoogle Scholar
  2. 2.
    Gross D.J., Mende P.F.: Nucl. Phys. B303, 407 (1988)CrossRefADSMathSciNetGoogle Scholar
  3. 3.
    Amati D., Ciafaloni M., Veneziano G.: Phys. Lett. B216, 41 (1989)ADSGoogle Scholar
  4. 4.
    Mead C.A.: Phys. Rev. 135, B849 (1964)CrossRefADSMathSciNetGoogle Scholar
  5. 5.
    Padmanabhan T.: Class. Quantum Grav. 4, L107 (1987)CrossRefADSGoogle Scholar
  6. 6.
    Doplicher S., Fredenhagen K., Roberts J.E.: Phys. Lett. B331, 39 (1994)ADSMathSciNetGoogle Scholar
  7. 7.
    Ahluwalia D.V.: Phys. Lett. B339, 301 (1994)ADSGoogle Scholar
  8. 8.
    Ng Y.J., Van Dam H.: Mod. Phys. Lett. A9, 335 (1994)ADSGoogle Scholar
  9. 9.
    Amelino-Camelia, G.: Mod. Phys. Lett. A9, 3415 (1994) gr-qc/9603014Google Scholar
  10. 10.
    Amelino-Camelia, G.: Mod. Phys. Lett. A11, 1411 (1996) gr-qc/9603013Google Scholar
  11. 11.
    Garay L.J.: Int. J. Mod. Phys. A10, 145 (1995)ADSGoogle Scholar
  12. 12.
    Dowker F.: New Sci. 180, 36 (2003)Google Scholar
  13. 13.
    Bronstein M.P.: Quantentheorie schwacher Gravitationsfelder. Physikalische Zeitschrift der Sowjetunion 9, 140 (1936)MATHGoogle Scholar
  14. 14.
    Thiemann, T.: Introduction to modern canonical quantum general relativity. gr-qc/0110034Google Scholar
  15. 15.
    Thiemann, T.: Lectures on loop quantum gravity. gr-qc/0210094Google Scholar
  16. 16.
    Heisenberg, W.: The Physical Principles of the Quantum Theory. University of Chicago Press, Chicago (1930). (cited from the Dover Publications reprint)Google Scholar
  17. 17.
    Bohr, N., Rosenfeld, L.: Zur frage der Messbarkeit der elektromagnetischen Feldgrössen. Kgl. Danske Videnskab S. Nat. Fys. Medd. 12, 1 (1933) [English translation in selected papers of Leon Rosenfeld, pp. 357–400 (Reidel 1979)]Google Scholar
  18. 18.
    Landau L.D., Peierls R.: Erweiterung des Unbestimmtheitsprinzips fur die relativistische Quantentheorie. Zeitschrift fur Physik 69, 56 (1931)MATHCrossRefADSGoogle Scholar
  19. 19.
    DeWitt B.S.: The quantization of geometry. In: Witten, L. (eds) Gravitation: an Introduction to Current Research., pp. 266–381. Wiley, London (1962)Google Scholar
  20. 20.
    Wigner E.P.: Rev. Mod. Phys. 29, 255 (1957)MATHCrossRefADSMathSciNetGoogle Scholar
  21. 21.
    Salecker H., Wigner E.P.: Phys. Rev. 109, 571 (1958)MATHCrossRefADSMathSciNetGoogle Scholar
  22. 22.
    Adler R.J., Nemenman I.M., Overduin J.M., Santiago D.I.: Phys. Lett. B477, 424 (2000)ADSGoogle Scholar
  23. 23.
    Amelino-Camelia, G.: Nature 398, 216 (1999) gr-qc/9808029Google Scholar
  24. 24.
    Calmet, X.: Eur. Phys. J. C54, 501 (2008) hep-th/0701073Google Scholar
  25. 25.
    Lloyd S., Ng Y.J.: Sci. Am. 291(5), 52 (2004)CrossRefGoogle Scholar
  26. 26.
    Christiansen, W.A., Ng, Y.J., van Dam, H.: Phys. Rev. Lett. 96, 051301 (2006) gr-qc/0508121Google Scholar
  27. 27.
    Stachel, J.: Special relativity from measuring rods. In: Physics Philosophy and Psychoanalysis Essays in Honor of Adolf Gruenbaum, pp. 255–272 (Reidel 1979)Google Scholar
  28. 28.
    Stachel J.: Feynman paths and quantum entanglement: is there any more to the story?. In: Cohen, R.S., Horne, M., Stachel, J. (eds) Potentiality Entanglement and Passion-at-a-distance/Quantum Mechanical Studies for Abner Shimony, vol. 2., pp. 244–256. Kluwer, Dordrecht (1997)Google Scholar
  29. 29.
    Stachel J.: Quantum logic. In: Sarkar, S., Pfeiffer, J. (eds) The Philosophy of Science: an Encyclopedia, vol. 2., pp. 633–644. Routledge, London (2005)Google Scholar
  30. 30.
    Bohr N.: Can quantum-mechanical description of physical reality be considered complete. Phys. Rev. 48, 696 (1935)MATHCrossRefADSGoogle Scholar
  31. 31.
    Bohr N.: Discussion with einstein on epistemological problems in atomic physics. In: Schilpp, P.A. (eds) Albert Einstein: Philosopher-Scientist., pp. 199–241. Cambridge University Press, London (1949)Google Scholar
  32. 32.
    Bai, T. (2003) Philosophy and physics: action-at-a-distance and locality doctoral dissertation. Boston University, BostonGoogle Scholar
  33. 33.
    Bai, T., Stachel, J.: Bohr’s diaphragms (preprint)Google Scholar
  34. 34.
    Bergmann P.G., Smith G.J.: Gen. Rel. Grav. 4, 1131 (1982)CrossRefADSMathSciNetGoogle Scholar
  35. 35.
    Stachel, J.: Prolegomena to any future quantum gravity. In: Oriti, D. (ed.) Approaches to Quantum Gravity- Toward a New Understanding of Space and Time. Cambridge University Press, London (in press) gr-qc/0609108Google Scholar
  36. 36.
    Stachel, J.: A brief history of space–time. In: Ciufolini, I., Dominici, D., Lusanna, L. (eds.) A Relativistic Space–time Odyssey, pp. 15–34 (World Scientific 2003)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Dipartimento di FisicaUniversitá di Roma “La Sapienza”, INFNRomeItaly
  2. 2.Department of Physics, Center for Einstein StudiesBoston UniversityBostonUSA

Personalised recommendations