Unweyling Three Mysteries of Nordström Gravity

The paper re-examines Nordström's scalar theory of gravity (NG) – arguably the most convincing relativistic theory of gravity before the advent of General Relativity. It exists in two different formulations. In Nordström's original one (1913), NG appears to describe a scalar gravitational field on Minkowski spacetime. In Einstein and Fokker’s (1914) version, NG seems to be a spacetime theory: It reconceptualises gravitational effects as manifestations of non-Minkowskian inertial structure. Both variants of NG give rise to three contradictory verdicts on the status and validity of fundamental principles: the Weak Equivalence Principle, the existence of gravitational energy, and energy conservation. Given the putative equivalence of both variants of NG, this ambiguity seems paradoxical to the spacetime realist. I'll proffer a resolution from the perspective of integrable Weyl geometry: The paradoxes rest on the failure to recognise a more apposite spacetime setting for NG.