Recovering general relativity from a Planck scale discrete theory of quantum gravity - Butterfield,J; Dowker,F (Philosophy of Physics, 2024)
An argument is presented that if a theory of quantum gravity is physically discrete at the Planck scale and the theory recovers General Relativity as an approximation, then, at the current stage of our knowledge, causal sets must arise within the theory, even if they are not its basis.We lay out this argument in two claims. Roughly speaking, the first claim is that causal sets can recover continuum Lorentzian manifolds; and the second claim is that no other proposal for a set of discrete data that conforms to our sense of “fundamental discreteness at the Planck scale” is known to be able to recover continuum Lorentzian manifolds. To support this second claim, we show, in particular, that an apparent alternative discrete data set to causal sets, viz., a certain sort of combinatorial Lorentzian simplicial complex, cannot recover General Relativistic spacetimes in the appropriately unique way; for it cannot discriminate between Minkowski spacetime and a spacetime with a certain sort of gravitational wave burst.