Abstract
We address the problem of observables in generally invariant spacetime theories such as Einstein’s general relativity. Using the refined notion of an event as a “point-coincidence” between scalar fields that completely characterise a spacetime model, we propose a generalisation of the relational local observables that does not require the existence of four everywhere invertible scalar fields. The collection of all point-coincidences forms in generic situations a four-dimensional manifold, that is naturally identified with the physical spacetime.
References
Friedman, M.: Foundations of Space-Time Theories. Princeton University Press, Princeton (1983)
Westman, H., Sonego, S.: Coordinates, observables and symmetry in relativity. arXiv:0711.2651 [gr-qc]
Kretschmann, E.: Über den physikalischn Sinn der Relativitätspostulate, A. Einstein neue und seine ursprüngliche Relativitätstheorie. Ann. Phys. (Leipz.) 53, 575–614 (1917)
Norton, J.D.: General covariance and general relativity: eight decades of dispute. Rep. Prog. Phys. 56, 791–858 (1993)
Giulini, D.: Remarks on the notions of general covariance and background independence. In: Seiler, E., Stamatescu, I.-O. (eds.) Approaches to Fundamental Physics: An Assessment of Current Theoretical Ideas. Lecture Notes in Physics, vol. 721, pp. 105–120. Springer, Berlin (1962). gr-qc/0603087
Earman, J., Norton, J.D.: What price substantivalism? The hole story. British J. Phil. Sci. 38, 515–525 (1987)
Earman, J.: World Enough and Space-Time. Cambridge University Press, Cambridge (1989)
Bergmann, P.G.: Observables in general relativity. Rev. Mod. Phys. 33, 510–514 (1961)
DeWitt, B.S.: The quantization of geometry. In: Witten, L. (ed.) Gravitation: An Introduction to Current Research, pp. 266–381. Wiley, New York (1962)
Rovelli, C.: What is observable in classical and quantum gravity? Class. Quantum Grav. 8, 297–316 (1991)
Rovelli, C.: Quantum Gravity. Cambridge University Press, Cambridge (2004)
Dittrich, B.: Partial and complete observables for canonical general relativity. Class. Quantum Grav. 23, 6155–6184 (2006). gr-qc/0507106
Einstein, A.: Die Grundlagen der allgemeinen Relativitätstheorie. Ann. Phys. (Leipz.) 49, 769–822 (1916). English translation in: Sommerfeld, A., Perrett, W., Jeffery, G.B. (eds.) The Principle of Relativity, pp. 109–164. Dover, New York (1952)
Einstein, A.: Relativity: The Special and General Theory. Crown, New York (1961). Appendix V (Relativity and the problem of space), pp. 135–157; and preface to the 15th edition
Einstein, A.: Foreword to Concepts of Space by M. Jammer. Harvard University Press, Cambridge (1954)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Westman, H., Sonego, S. Events and Observables in Generally Invariant Spacetime Theories. Found Phys 38, 908–915 (2008). https://doi.org/10.1007/s10701-008-9235-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10701-008-9235-z