General-relativistic Spacetimes Are Not (so) Special (Culturas Científicas, 2026)
The invariance under diffeomorphisms of general relativity is a formal property of the theory that is not present in other theories. Some authors, closely related to research in quantum gravity, have argued that this symmetry means that spacetime in general relativity cannot be interpreted like other spacetimes. More specifically, spacetime would be only a structure for representing “correlations.” This position is supported by three arguments: the gauge argument, relationalist arguments such as the hole argument, and the relationship with quantum gravity. In this article, I study this position and these arguments and reject them. The position I defend is that invariance under diffeomorphisms does not make the spacetimes of general relativity different in any deep sense, and that they should be interpreted analogously to other spacetimes. More precisely, spacetime, both in general relativity and other theories, is a set of events with a series of causal, geometric, and inertial relations.
Keywords: General relativity; Gauge symmetry; Spacetime; Diffeomorphism invariance; Quantum gravity