The (un)detectability of absolute Newtonian masses

Abstract

Absolutism about mass claims that mass ratios obtain in virtue of absolute masses. Comparativism denies this. Dasgupta (2013) argues for comparativism about mass, in the context of Newtonian Gravity. Such an argument requires proving that comparativism is empirically adequate. Dasgupta equates this to showing that absolute masses are undetectable, and attempts to do so. This paper develops an argument by Baker to the contrary: absolute masses are in fact empirically meaningful, that is detectable (in some weak sense). Additionally, it is argued that the requirement of empirical adequacy should not be cashed out in terms of undetectability in the first place. The paper closes by sketching the possible strategies that remain for the comparativist. Along the way a framework is developed that is useful for thinking about these issues: Ozma games-how could one explain to an alien civilisation what an absolute mass is?

Machian Comparativism about Mass

“…For instance, regularity comparativism is a form of comparativism that is nevertheless realist about absolute masses, i.e. it admits the empirical meaningfulness of objective, non-conventional absolute masses (Martens [2017a(Martens [ , 2019), recovering them from a purely comparativist Humean mosaic (i.e. a spatiotemporal Humean mosaic including fundamental mass relations).…”

“…Besides improving upon Dasgupta's proposal, it does save the spirit of comparativism (contra regularity comparativism), that is anti-realism about absolute masses: absolute masses are not empirically meaningful. In other words, an Active Leibniz Mass Scaling (Martens [2019])-a uniform scalar multiplication of each of the absolute mass magnitudes of all the particles, ceteris paribus (i.e. whilst keeping everything else unchanged)-does not generate an empirically distinct evolution of the system, and thus constitutes nothing more than an identity operation as far as comparativism is concerned.…”

“…On one popular 12 approach to cashing out empirical adequacy-or, more broadly, empirical equivalence-one checks whether the theory generates the correct set of empirically possible worlds (Martens [2017a(Martens [ , 2019). To every metaphysically possible world corresponding to a structure of mass relations, one would expect 13 there to correspond (via active Leibniz scalings) uncountably many possible 'absolutist worlds' with different absolute masses that are all nevertheless compatible with the mass structure in the corresponding 'comparativist world'.…”

“…The required notion of empirical equivalence (and its counterpart, empirical distinctness) of worlds relevant to the current context will become clear in the next section. Alternatives in the literature to the above 'possibility checking' approach to cashing out empirical equivalency-and by extension empirical adequacy 15 -focus either on mass scaling symmetries or absolute masses being undetectable (Martens [2019]). A comparativist using the symmetry approach will claim that Leibniz Scaling is a symmetry of Newtonian Gravity, and that models related by that transformation (therefore) represent the same possible world.…”

“…The following argument, the comparativist's bucket 18 , a simple instance of an inter-world Leibniz Mass Scaling derived from Baker [2013b], serves to challenge the empirical equivalence and by extension the empirical adequacy of comparativism (Martens [2019]). Consider a simple world, governed by the laws of Newtonian Gravity, with two equally massive particles a distance r apart, with a relative positive initial velocity v (such that there is zero angular momentum).…”