Absolutism vs. Comparativism about Mass in Newtonian Gravity Niels Martens Lugano Qantities Conference Slides available at martensniels.wordpress.com 16 November 2019
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NCMM’17 Regularity Comparativism about Mass in Newtonian Gravity Philosophy of Science 84(5):1226-1238 NCMM’18 Against Laplacian Reduction of Newtonian Mass to Spatiotemporal Qantities Foundations of Physics 48(5):591-609 NCMM’20a Machian Comparativism about Mass The British Journal for the Philosophy of Science NCMM’20b The (Un)detectability of Absolute Newtonian Masses Synthese
Laplace’s problem Initial Variable & Parameter Problem What is the minimal choice of initial variables and parameters that corresponds to a well-posed initial value problem (in Newtonian Gravity)—that is, the associated determinate values, together with the laws of Newtonian Gravity, determine a unique evolution? (Poincaré, 1902; Skow, 2007)
Does a Mass Scaling lead to an empirical difference? (Active) Leibniz Mass Scaling A uniform scalar multiplication of each of the absolute mass magnitudes, ceteris paribus . Realism about Absolute Masses Absolute masses are empirically meaningful/relevant Anti-Realism about Absolute Masses Absolute masses are empirically meaningless/irrelevant
Absolutism vs. Comparativism (Weak, Metaphysical) Absolutism The determinate mass ratios obtain in virtue of determinate absolute masses. (Armstrong, 1978, 1988; Mundy, 1987; Lewis, 1986; Sider, ms) (Weak, Metaphysical) Comparativism The determinate mass relations do not obtain in virtue of determinate absolute masses. (Russell 1903; Mach, 1960; Ellis, 1966; Field, 1980; Bigelow et al. , 1988; Arntzenius, 2012; Dasgupta, 2013; Eddon, 2013; Baker, ms; Perry, 2016; Roberts, ms; Sider, ms; Wolff, ms)
Absolute fundamentality Strong (Metaphysical) Absolutism Weak (Metaphysical) Absolutism 1 Mass is fundamental. That is, the determinate absolute masses 2 do not themselves obtain in virtue of anything else. Strong (Metaphysical) Comparativism Weak (Metaphysical) Comparativism 1 Mass is fundamental. That is, the determinate mass 2 relationships do not themselves obtain in virtue of anything else. NCMM’20b
Assumptions Newtonian Gravity Equivalence between gravitational and inertial mass Scale-invariant mass relations: ‘Mass ratios’ (Baker, ms)
Definitions Absolute mass magnitudes Set of monadic properties Cardinality: 2 ℵ 0 Totally ordered & Concatenation structure (‘addition’) Transworld identity (quiddities) → totally ordered semi-group Mass relations Set of binary relations Cardinality: 2 ℵ 0 Totally ordered & Concatenation structure (‘multiplication’) Transworld identity (quiddities) → totally ordered group
Kinematic Comparativism Kinematic Comparativism ( ⇐ ⇒ dimensionfulness) For any dimensionful determinable, such as mass, the magnitude predicated of any particle can only be meaningfully reported or expressed in terms of how this magnitude relates to the magnitude of another particle having the same determinable property. Therefore, absolute mass magnitudes need to be represented by a numerical quantity times a unit. This representation is non-unique (conventional choice of unit). (Hugget, 1999)
Naive argument for comparativism Kinematic comparativism → (metaphysical) comparativism Metaphysical comparativism requires us to prove: Dynamic Comparativism Physics depends only on the mass ratios, not on further absolute masses in virtue of which those ratios obtain. In other words, metaphysical comparativism is empirically adequate.
Comparativist Argument P dyn Dynamic Comp: (Metaphysical) comp is empirically equiv- alent to (metaphysical) abs. P occ Occamist norm: All other things being equal (i.e. P dyn ), we should favour theories that are metaphysically more parsimonious. P par (Metaphysical) comp about mass is metaphysically more par- simonious than (metaphysical) abs. C (Metaphysical) comp about mass should be favoured over (metaphysical) abs.
Comparativist Argument P dyn Dynamic Comp: (Metaphysical) comp is empirically equiv- alent to (metaphysical) abs. P exp Explanatory Adequacy: (Metaphysical) comp is at least as explanatorily adequate as (metaphysical) abs. P occ Occamist norm: All other things being equal (i.e. P dyn ∧ P exp ), we should favour theories that are metaphysically more parsimonious. P par (Metaphysical) comp about mass is metaphysically more par- simonious than (metaphysical) abs. C (Metaphysical) comp about mass should be favoured over (metaphysical) abs.
Outline Absolutism vs. Comparativism 1 Empirical Adequacy 2 Dasgupta’s Comparativism Regularity Comparativism Machian comparativism Metaphysical parsimony & Explanatory adequacy 3 Eliminating mass altogether? 4
Outline Absolutism vs. Comparativism 1 Empirical Adequacy 2 Dasgupta’s Comparativism Regularity Comparativism Machian comparativism Metaphysical parsimony & Explanatory adequacy 3 Eliminating mass altogether? 4
Absolutism vs. Comparativism Dasgupta’s Comparativism Empirical Adequacy Regularity Comparativism Metaphysical parsimony & Explanatory adequacy Machian comparativism Eliminating mass altogether? Dasgupta’s Comparativism m 1 , q m 2 , q f q = m q · a q f q = G q r 2 q (L1) For any material thing x , (a) For any reals r 1 and r 2 , if x has mass r 1 M and acceleration r 2 A, then x has force r 1 r 2 F acting on it. (b) For any real r 3 , if x has force r 3 F acting on it, then there are reals r 4 and r 5 whose product is r 3 , such that x has mass r 4 M and acceleration r 5 A. (Dasgupta, 2013, p.130) Niels Martens Absolutism vs Comparativism about Mass 16/31
Absolutism vs. Comparativism Dasgupta’s Comparativism Empirical Adequacy Regularity Comparativism Metaphysical parsimony & Explanatory adequacy Machian comparativism Eliminating mass altogether? Dasgupta’s Comparativism m 1 , q m 2 , q f q = m q · a q f q = G q r 2 q (L2) For any material things x and y [in the same world], (a) For any reals r 1 and r 2 , if x is r 1 times as massive as y and is accelerating at r 2 times the rate of y , then x has r 1 r 2 times as much force acting on it as y . (b) For any real r 3 , if x has r 3 times as much force acting on it than y , then there are reals r 4 and r 5 whose product is r 3 , and such that x is r 4 times as massive as y and is accelerating r 5 times the rate of y . (Dasgupta, 2013, p.130-1) Niels Martens Absolutism vs Comparativism about Mass 16/31
Absolutism vs. Comparativism Dasgupta’s Comparativism Empirical Adequacy Regularity Comparativism Metaphysical parsimony & Explanatory adequacy Machian comparativism Eliminating mass altogether? Comparativism’s bucket � F g = G mM 2 GM v e = r 2 r F F v 0 v 0 Double Mass F F v 0 v 0 (Baker, ms; NCMM’20b) Niels Martens Absolutism vs Comparativism about Mass 17/31
Absolutism vs. Comparativism Dasgupta’s Comparativism Empirical Adequacy Regularity Comparativism Metaphysical parsimony & Explanatory adequacy Machian comparativism Eliminating mass altogether? Where to go from here? Absolutism The comp bucket shows that absolute masses are real, i.e. empirically meaningful → meta- physical absolutism Regularity comp Accept that the comp bucket proves realism about absolute masses, but insist that those can be grounded in mass ratios (and other non-mass facts). (NCMM’17) Machian comp Modify the syntax (i.e. equations) such that the comp bucket is avoided (whilst retaining empirical equivalence to abs) → anti-realism about absolute masses (NCMM’20a) Niels Martens Absolutism vs Comparativism about Mass 18/31
Absolutism vs. Comparativism Dasgupta’s Comparativism Empirical Adequacy Regularity Comparativism Metaphysical parsimony & Explanatory adequacy Machian comparativism Eliminating mass altogether? Regularity Relationalism Response to i.a. Newton’s bucket (i.e. inertial effects) Core Idea: It is merely the truth of Newton’s laws in certain frames that privileges those frames, not the structure of absolute space. (Van Fraassen, 1970) Regularity Protocol: Assume a relational Humean mosaic (with intrinsic masses). Consider all possible reference frames that are naturally adapted to that mosaic: only in some frames will the best axiomatisations be Newton’s laws. Claim: those are the best laws overall. → Inertial frames & laws supervene as a package deal. (Hugget, 2006) Niels Martens Absolutism vs Comparativism about Mass 19/31
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