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Fundamental discreteness of the gravitational field is predicted in some sense by many approaches to the problem of quantum gravity. Carlo Rovelli and Francesca Vidotto put things the other way around and take this discreteness to be a guiding principle in the search for a quantum theory of gravity, rather than a consequence of their particular (covariant loop) approach. One of the aims of quantum gravity research is to unify quantum mechanics, which takes time evolution to be discrete, with general relativity, which deals with a spacetime continuum. Assuming there is some unified fundamental reality, the basic structure of spacetime (equivalent to the gravitational field in general relativity) must be either discrete or continuous; it cannot be both. What reasons do we have for leaning towards fundamental discreteness? Is this just a bias towards quantum mechanics over general relativity?
Rovelli and Vidotto give an alternative motivation for a fundamentally discrete spacetime in the form of a reconstruction of the thought experiment originally put forward by Russian physicist Matvei Bronstein in 1936. In this talk I give a non-technical analysis of the steps in this reasoning, before pointing out several of its flaws, and finally I argue that it does not actually entail discreteness of spacetime or of the gravitational field. The focus throughout is on basic conceptual issues rather than being a full-blown formal analysis. I discuss, with some reference to Leibniz, the effects of one's view of the relationship between mathematical representation and the physical world on the issue of discreteness of spacetime.
