The talk revisits Nordström Gravity (NoG) – arguably the most plausible relativistic scalar theory of gravity before the advent of GR. In Nordström’s original formulation (1913), NoG1, it appears to describe a scalar gravitational field on Minkowski spacetime. In 1914, Fokker and Einstein showed that NoG is mathematically equivalent to a purely metric theory, NoG2 - strikingly similar to the Einstein Equations. Like GR, NoG2 is plausibly construed as a geometrised theory of gravity: In NoG2, gravitational effects are reduced to manifestations of non-Minkowskian spacetime structure. Both variants of NoG, and their claimed physical equivalence, give rise to three conundrums that we will explore.
(P1) The (Weak) Equivalence Principle appears to be violated in NoG1 - but holds in NoG2. (P2) In NoG1, it appears unproblematic to ascribe the gravitational scalar an energy-momentum tensor. In trying to define gravitational energy in NoG2, by contrast, one faces problems akin to those in GR. (P3) In NoG1, total (i.e. gravitational plus non-gravitational) energy-momentum appears to be conserved, whereas in NoG2, no obvious candidate for gravitational energy is available, and furthermore it seems unclear whether non-gravitational energy is conserved.
In as far as NoG1 and NoG2 are equivalent formulations of the same theory, (P1)-(P3) appear paradoxical. For a resolution, I will proffer a metaphysically perspicuous articulation of NoG’s ontology that explicates the equivalence, and propose an instructive reformulation.
Philosophy of Physics Seminar Convenors for HT19: James Read and Simon Saunders