The primacy of geometry

We argue that in current spacetime physics there can be no dynamical derivation of primitive geometrical notions such as length. We illustrate our argument by focusing on two case studies: the special theory of relativity and some approaches to quantum gravity, and we argue that in these cases, some geometrical notions are assumed rather than derived. Our argument suggests a new reading of Einstein's views on the status of geometry vs. dynamics.

►We present a no-go argument against attempts to “reduce“ geometry to dynamics in quantum gravity. ►We show why these attempts can be regarded at most as consistency proofs rather than derivations. ►We demonstrate our argument in loop quantum gravity and the causal set approach. ►As historical background we discuss the rarely cited correspondence between Einstein and Swann.