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.
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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)
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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
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DOI: https://doi.org/10.1007/s10701-008-9235-z