The Hole Argument. Physical Events and the Superspace

Details The Hole Argument. Physical Events and the Superspace The Hole Argument. Physical Events and the Superspace

2006-10-21

arxiv.org/abs/gr-qc/0610105v2

Syst. Integrables et Theorie des Champs Quant., eds J. Kouneiher et all, Hermann's Editeurs, pp. 241-254, 2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages

Scientific paper

The 'hole argument'(the English translation of German 'Lochbetrachtung') was formulated by Albert Einstein in 1913 in his search for a relativistic theory of gravitation. The hole argument was deemed to be based on a trivial error of Einstein, until 1980 when John Stachel (Talk on Einsteins Search for General Covariance, 1912-1915 at the GRG meeting in Jena 1980) recognized its highly non-trivial character. Since then the argument has been intensively discussed by many physicists and philosophers of science. (See e.g., Earman & Norton (1987), Gaul & Rovelli (1999), Stachel & Iftime(2005}, and Iftime & Stachel(2006).) I shall provide here a coordinate-free formulation of the argument using the language of categories and bundles, and generalize the argument for arbitrary covariant and permutable theories (see Iftime & Stachel(2006). In conclusion I shall point out a way of avoiding the hole argument, by looking at the structure of the space of solutions of Einstein's equations on a space-time manifold. This superspace Q(M) is defined as the orbit space of space-time solutions on M under the action of the diffeomorphisms of M, and it plays an important role in the study of the gravitational field and attempts to find a theory of quantum gravity (QG).

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