Machian Comparativism about Mass

Abstract

Absolutism about mass within Newtonian gravity claims that mass ratios obtain in virtue of absolute masses. Comparativism denies this. Defenders of comparativism promise to recover all the empirical and theoretical virtues of absolutism, but at a lower ‘metaphysical cost’. This article develops a Machian form of comparativism about mass in Newtonian gravity, obtained by replacing Newton’s constant in the law of universal gravitation by another constant divided by the sum over all masses. Although this form of comparativism is indeed empirically equivalent to the absolutist version of Newtonian gravity—thereby meeting the challenge posed by the comparativist’s bucket argument—it is argued that the explanatory power and metaphysical parsimony of comparativism (and especially its Machian form) are highly questionable. 1Absolutism versus Comparativism2Absolute Masses and Mass Ratios3The Argument for Comparativism4Empirical Equivalency via Possibility Checking5A Challenge for Comparativism: The Comparativist’s Bucket6Novel Comparativist Laws 6.1Varying Newton’s constant6.2The Alpha mass6.3Summing over all the masses: Machian comparativism7Metaphysical Parsimony and Explanatory Power 7.1Quantitative and qualitative metaphysical parsimony7.2The conspiracy of mass relations7.3Chain comparativism7.4Metaphysical parsimony at the level of worlds8Conclusion

Sophistry about symmetries?

“…These non-qualitative mappings of initial states lead to empirically distinguishable evolutions-escape versus non-escape. (This transformation is thus not a symmetry (Martens 2017(Martens , 2019a)-pace Dasgupta 2013). Although this does not make absolute masses detectable in the same sense as relative velocities, it does make them detectable in some weaker sense, that still makes them more empirically relevant than, say, absolute velocities (Martens 2019b).…”

“…34 The most obvious option is to throw away absolute masses altogether. It was for this exact reason-obtaining an ontology with no absolute masses but only mass ratios m i j (i.e., primitive and symmetric relations of 'comparative masshood' holding between particles i and j)-that this theory was designed in the first place (Martens 2019a). However, if the fundamental ontology in this theory consists only of mass relations, there is nothing to ensure the transitivity of those mass relations,…”

Against Laplacian Reduction of Newtonian Mass to Spatiotemporal Quantities

“…Narlikar responds by echoing the thought that underlies the suggested operational definition of the absolute mass scale: accelerations might be insufficient, but we have other spatiotemporal notions at our disposal [26]. In particular, we can measure inter-particle distances as well as accelerations, and insert them into the Gravitational Law 21 . Setting Newton's constant to one for convenience, we get the following equation for the (arbitrarily chosen 22 ) xcomponent of the acceleration of particle 1 due to the gravitational interaction of all the other particles, at t 0 :…”

“…the masses from the appearance of the four-dimensional mosaic generated by God 24 . Therefore, 21 Pendse [27] objects that we do not have independent empirical access to the Gravitational Law. However, in the context of the project in this paper we simply take the laws as given.…”

“…For comparativism about mass-defined below-an analogous issue of consistency or transitivity arises[21] [7, Ch.5] 16. Mass relations, more generally.…”