What represents spacetime? And what follows for substantivalism vs. relationalism and gravitational energy?

Abstract

The questions of what represents space-time in GR, the status of gravitational energy, the substantivalist-relationalist issue, and the (non-)exceptional status of gravity are interrelated. If space-time has energy-momentum, then space-time is substantival. Two extant ways to avoid the substantivalist conclusion deny that the energybearing metric is part of space-time or deny that gravitational energy exists. Feynman linked doubts about gravitational energy to GRexceptionalism, as do Curiel and Duerr; particle physics egalitarianism encourages realism about gravitational energy.In that spirit, this essay proposes a third possible view about spacetime, one involving a particle physics-inspired non-perturbative split that characterizes space-time with a constant background matrix (not a metric tensor), a sort of vacuum value, thus avoiding the inference from gravitational energy to substantivalism. On this proposal, spacetime is M, η , where η = diag(−1, 1, 1, 1) is a spatio-temporally constant numerical signature matrix, a matrix already used in GR with spinors. The gravitational potential, to which any gravitational energy can be ascribed, is g µν (x) − η (up to field redefinitions), an affine geometric object with a tensorial Lie derivative and a vanishing covariant derivative. This non-perturbative split permits strong fields, * Forthcoming in Antonio Vassallo (Ed.), The Foundations of Spacetime Physics: Philosophical Perspectives, Routledge

On Two Slights to Noether’s First Theorem: Mental Causation and General Relativity

“…)energy t µν (little t). Earlier I used the Gothic letter with one index up and one down, t µ ν , which is better for technical reasons (Pitts, 2022;Sorkin, 1977). Hence the best form of the continuity equation involves the Gothic 5 material energy T µ ν and the Gothic gravitational energy t µ ν ; their sum T µ ν + t µ ν satisfies the continuity equation:…”

“…Hence Schrödinger's false-negative worry is answered by noticing that there are lots of gravitational energies surrounding the round heavy body, many or most of which are not 0, so the fact that one of them is 0 hardly shows the absence of gravitational energy and so is of no concern. Bauer's false positive objection has some other answers, which can be quite technical (Pitts, 2010;Pitts, 2022).…”

“…There is a measure of nonuniqueness, which can sometimes be physically interesting, for the Lagrangian density. That seems true for GR(Pitts, 2022)(Ohanian and Ruffini, 1994, p. 647).…”