The empirical adequacy of comparativism about mass in … · 2015-07-29 · Counter-argument:...

The empirical adequacy of comparativism aboutmass in Newtonian Gravity

Niels C.M. MartensDPhil candidate Philosophy of Physics

Oxford University

4th Tübingen Summer School in HPS 2015Idealizations in Physics

Slides available athttp://users.ox.ac.uk/~corp2044

29 July 2015

http://users.ox.ac.uk/~corp2044

Outline

1 Absolutism vs. Comparativism about mass

2 Dasgupta’s argument for Comparativism

3 Counter-argument: Empirical Inadequacy

4 Responses

5 Bonus: Ontological Parsimony

Absolutism vs. ComparativismDasgupta’s argument for Comparativism

Counter-argument: Empirical InadequacyResponses

Bonus: Ontological Parsimony

Absolutism vs. ComparativismAssumptions

“ The property of having mass is a determinable that appears tohave two kinds of determinates. On the one hand, we naturallythink that something with mass has a determinate intrinsicproperty, a property it has independently of its relationshipswith other material bodies. But we also think that things withmass stand in various determinate mass relationships withone another, such as x being more massive than y or x beingtwice as massive as y.

(Dasgupta, 2013, p.105) ”Niels Martens Comparativism about mass 4/34





Absolutism vs. Comparativism

(Weak) AbsolutismThe most fundamental facts about material bodies vis-à-vis their

mass are intrinsic properties (i.e. intrinsic masses). The massrelations hold in virtue of these intrinsic masses.

(Weak) ComparativismThe most fundamental facts about material bodies vis-à-vis theirmass just concern how they are related in mass. All other facts

about their mass, if any, hold in virtue of those relationships (and aconvention).

(Dasgupta, 2013)

Niels Martens Comparativism about mass 5/34





Collectively exhaustive?

Strong Absolutism1 Weak Absolutism2 Intrinsic masses are

fundamental

Strong Comparativism1 Weak Comparativism2 Mass relations are

fundamental

Eliminativism / Reductionism / Emergentism1 Mass is not fundamental

→ Compatible with Weak Abs & Comp






Assumptions

Newtonian Gravity

Mass ratios (Baker, manuscripts)

Equivalence between gravitational and inertial mass


Outline




4 Responses





Dasgupta’s Razor

The argument for comparativismDasgupta’s Razor

Pu Empirical adequacy of comparativism.

Po Occamist norm: All other things being equal (i.e. Pu),we should favour theories that are ontologically moreparsimonious.

Pp Comparativism about mass is ontologically more parsimo-nious than absolutism.

Cc Comparativism about mass is favoured.

(Dasgupta, 2013)


Outline




4 Responses





Defining Empirical AdequacyInitial Variable ProblemArgument against Empirical Adequacy of Comparativism

Empirical adequacy

Empirical Adequacy:The comparativist laws of naturepick out a set of dynamically possiblemodels from the set of possiblemodels such that all empiricallydistinct models generated by theabsolutist theory are included(i.e. completeness) and all models thatare empirically distinct from each ofthe absolutist solutions are excluded(i.e. soundness).

1 ∀m E(m, φ(m))

2 Completeness:∀Ei(Ei ∩ S1 6= ∅ →(∃m ∈ Ei : φ(m) ∈ S2))

3 Soundness:∀Ei(Ei ∩ S1 = ∅ →(¬∃m ∈ Ei : φ(m) ∈ S2))

T1 (absolutism) T2 (comparativism)

P1 (possible models)P2 (possible models)

S1 (dynamicallypossible models)







Empirical adequacy

Laplacean Determinism:A model m is deterministic i�, forany time t , there is only oneempirically possible world whosestate at t is identical to m’s.

→ Unique solution to the InitialValue Problem

1 ∀m E(m, φ(m))












Empirical adequacy

Empirical Adequacy:The laws of nature uniquely(i.e. deterministically) evolve each setof initial conditions allowed by thetheory into a dynamically possiblemodel, such that the whole set ofempirically distinct dynamicallypossible models generated by theabsolutist theory is reproduced(i.e. completeness) and no modelsthat are empirically distinct fromeach of the absolutist solutions aregenerated (i.e. soundness).

1 ∀m E(m, φ(m))












Empirical adequacy

1 ∀m E(m, φ(m))





E1

E2 E2

E1






Empirical adequacy

For comparativism to beempirically adequate, we need tofind a map φ: P1 → P2, such that

1 ∀m E(m, φ(m))





φ






Empirical adequacy

For comparativism to beempirically adequate, we need tofind a map φ: P1 → P2, such that

1 ∀m E(m, φ(m))





φ

S1S2






How to find φ

Recipe for φ: m{mi,α2,...,αn},abs → m{mimj,α2,...,αn},comp

For instance: φ: m{mi ,rij ,vij},abs → m{mimj

,rij ,vij},comp


P1 P2

φ

S1 S2

m{mi ,rij ,vij} m{ mimj

,rij ,vij}






The Initial Variable Problem I

General Initial Variable Problem

Finding a set of independent variables α = {α1, α2, . . . , αn} suchthat specifying the initial conditions of a theory in terms of thevalues of that set of variables renders the theory empiricallyadequate.

Comparativist Initial Variable Problem

General IVP + Handicap: the set of initial variables has to containmass relations, but may not include intrinsic masses.






The Initial Variable Problem IIA four-step program

1 Choose a set of absolutist initial variablesαabs = {mi, α2, . . . , αn}, thereby fixing the corresponding setfor the comparativist αcomp = {mi

mj, α2, . . . , αn}

2 Choose values for each variable, and find a unique solution toboth of the corresponding Initial Value Problems

3 Check whether the absolutist and comparativist solution areempirically equivalent

i.e. check whether E(mabs,mcomp), or equivalentlyE(mabs, φ(mabs))

4 Repeat step 2 & 3 for all possible values of α and check thewhole set of solutions for soundness and completeness.






Argument against Comparativism

Standard choice of initial variables: α = {rij, vij,mi}Problem: this choice for α does not solve the Initial VariableProblem, suggesting that comparativism is not empiricallyadequate.






Argument against Comparativism - continued

Fg = GmMr2 ve =

√2GMr

v0 v0

F F

Double Mass

v0 v0

F F

(Baker, manuscripts)


Outline




4 Responses





Three types of responsesAnalogue of Machian responseMixed Comparativism/ Absolutism

The analogous debate about space and motionThree types of relationalist reponses

same modelsdi�erent ideology

Enriched Relationalism(Poincaré, Sklar,

Maudlin, Binkoski)

same ideologydi�erent models

Machianism(Mach, Barbour-Berto�i)

same modelssame ideology

Regularity Relationalism(Hugge�, Stevens)

(Pooley, 2013; Hugge�, 1999)






Three types of responses for the comparativistOverview of the research program

same modelsdi�erent ideology

Enlarged ideology:

Transtemporal relations(Dasgupta?, Poincaré?)

Di�erent ideology,

but of the same size:

Mixed Comparativism/Absolutism

(Baker, manuscripts)

same ideologydi�erent models

Empirically distinct,but successful

same modelssame ideology

RegularityComparativismFuture project

(Pooley, 2013; Hugge�, 1999)






Analogue of Machian responseSame ideology as standard comp, di�erent models from abs

Newton’s globes: two (categories of) possibilities

Mach’s response: deny the possibility of the cord breaking

Argument contra comparativism: two (categories of)possibilitiesMachian response?

Which possibility should be denied?






Mixed Comparativism/ AbsolutismSame models as abs, di�erent ideology from standard comp

The escape velocity argument only shows that α = {mi, rij, vij}does not solve the IVP, not that it is unsolvable.→ choose a di�erent α

But first: Baker’s response→ boils down to a(n) (unsuccessful) specific choice of α






Baker’s response

Escape if v > ve =√

2Gmr

a = Gmr2

v >√

2ra

Baker: Uniform mass scaling does not change whether thisinequality is satisfied

v >√

2ra(m)

Baker, manuscripts






Baker’s response - continued

fundamental instantaneous velocities→ reductive definition

v(t) = drdt (t) = lim

dt→0

r(t+dt)−r(t)dt

Similarly for accelerations

Escape inequality:( drdt

)2< 2r d

2rdt2

Baker: Uniform length scaling does not change whether thisequation is satisfied

Baker, manuscripts






What is going on here?

1 Laplacean Determinism→ Bakerian Determinisminitial t → initial [t − dt, t + dt]

2 α = {rij}?Violates completenessa(t) = lim

dt→0

r(t+dt)−2r(t)+r(t−dt)dt2

3 α = {r ij, v ij, aij} ≡ {r(t)ij, r(t + dt)ij, r(t − dt)ij}?Does this solve IVP?Eliminativism about mass






What is going on here?






Alternative Initial Variables IMomentum

Escape: v >√

2Gmr

α = {rij, pi,mi}?℘ ≡ v√

m

Escape: ℘ >√

2Gr

Mixed comparativism? (Baker, manuscripts)

Absolutism about ℘Mix of kinematics & dynamics

Extra law connecting ℘ and v?Does fundamental ℘ fix m?






Alternative Initial Variables I - continuedMomentum

α = ?

{rij, ℘i}?{rij, vij, ℘i}?{rij,mi, ℘i}?{rij, mi

mj, ℘i}?

α = ?

More particles, higher dimensions?

Fixes m: Weak Absolutism

Abs℘ + Compm: not ontologicallyparsimonious






Alternative Initial Variables IINewton’s Constant

Change Newton’s Constant: G = G(m)γ ≡ G ·m

vi >√

2γr

mim

α?= {rij, vij, mi

m , γ}Which m?

Particular mi?∑i mi?

What is γ?true constant→ violation of completenessvariable→ absolutism in disguise






Alternative Initial Variables III

α = {Fi, . . .}α = {mi

ri, . . . }

α = { vi√mj, . . . }

Combined scaling of x , t and m by the same factor


Outline




4 Responses





A miraculous conspiracy of mass relations






x1






? ?


Conclusions

1 Initial mass relations, inter-particle distances and velocities failto solve the Initial Variable Problem, seemingly suggesting thatcomparativism is empirically inadequate

2 There is no analogue of the Machian defence of relationalismin the debate about space

3 Baker’s response throws out the baby with the bath water

Conclusions - continued

4 Including a generalised momentum ℘ ≡ v√m amongst the

initial variables seems to solve the General Initial VariableProblem, but it is unclear what to conclude from this.Moreover, it is unclear whether this generalises beyond thecase of two particles in one dimension. A detailed Newtoniantheory in terms of ℘ is required.

5 Varying Newton’s Constant is problematic.6 Alternative choices for initial variables require exploring.7 The ontological parsimony of comparativism is highly

questionable.

Future projects

Newtonian Gravity in terms of ℘

Alternative Initial Variables (Force, miri

, vi√mj

)

Eliminativism about mass

Regularity Comparativism

Dasgupta’s mass-counterpart theory solution

Cashing out ontological parsimony in terms of possible models

References

D.J. Baker, ‘Some Consequences of Physics for the ComparativeMetaphysics of �antity’, Manuscript

D.J. Baker, ‘Comparativism with Mixed Relations’, Manuscript

S. Dasgupta (2013), ‘Absolutism vs Comparativism about�antity’, Oxford Studies in Metaphysics: Volume 8, OxfordUniversity Press

N. Hugge� (1999), ‘Why manifold substantivalism is probablynot a consequence of classical mechanics’, International Studiesin the Philosophy of Science 13: 17–34.

O. Pooley (2013), ‘Substantivalist and Relationalist Approachesto Spacetime’, R. Ba�erman (ed.), The Oxford Handbook ofPhilosophy of Physics, Oxford University Press

The empirical adequacy of comparativism about mass in … · 2015-07-29 · Counter-argument:...

Documents

Transcript of The empirical adequacy of comparativism about mass in … · 2015-07-29 · Counter-argument:...