Against Laplacian Reduction of Newtonian Mass to Spatiotemporal Quantities

Abstract

Laplace wondered about the minimal choice of initial variables and parameters corresponding to a well-posed initial value problem. Discussions of Laplace's problem in the literature have focused on choosing between spatiotemporal variables relative to absolute space (i.e. substantivalism) or merely relative to other material bodies (i.e. relationalism) and between absolute masses (i.e. absolutism) or merely mass ratios (i.e. comparativism). This paper extends these discussions of Laplace's problem, in the context of Newtonian Gravity, by asking whether mass needs to be included in the initial state at all, or whether a purely spatiotemporal initial state suffices. It is argued that mass indeed needs to be included; removing mass from the initial state drastically reduces the predictive and explanatory power of Newtonian Gravity.

Sophistry about symmetries?

“…To make matters worse, without such a transitivity constraint holding, one could not even coherently interpret these mass relations as ratios in the first place (Martens 2019a). Only if one commits to absolute masses in virtue of which the mass ratios hold does one explain the transitivity of those mass relations, as the following becomes a mathematical truth (Armstrong 1988;Martens 2018aMartens , 2019aRoberts 2016;Russell 1903):…”

Machian Comparativism about Mass

“…31 Especially since 'mass' is the topic of this paper, it is important to point out that the name 'Machian' is not intended to imply any analogy with Mach's treatment of (inertial) mass-reducing mass ratios to acceleration ratios. Connections between that analogy and comparativism are discussed elsewhere (Martens [2017b(Martens [ , 2018a). In this paper the name derives purely from Mach's analogous treatment of inertial motion.…”

“…24 In this paper I am excluding indeterminism as a viable option (but see (Martens [2018a] Dasgupta [unpublished]) for further discussions), especially in light of the existence of a deterministic alternative: absolutism. (Absolute) mass is posited to provide predictive and explanatory power, as well as modal adequacy (i.e.…”

“…(Absolute) mass is posited to provide predictive and explanatory power, as well as modal adequacy (i.e. completeness and soundess) (Martens [2018a]). If one were willing to give up the absolute mass scale at the cost of determinism and thereby predictive power, what would prevent one from getting rid of mass altogether (cf.…”

“…If one were willing to give up the absolute mass scale at the cost of determinism and thereby predictive power, what would prevent one from getting rid of mass altogether (cf. Martens [2017bMartens [ , 2018a)-rendering the absolutism-comparativism debate moot? Moreover, if a theory is indeterministic at the initial time, it is presumably indeterministic at all times (pace (Dasgupta [unpublished])).…”