The empirical adequacy of comparativism about mass in Newtonian - - PowerPoint PPT Presentation

The empirical adequacy of comparativism about mass in Newtonian Gravity

Niels C.M. Martens

DPhil candidate Philosophy of Physics Oxford University

4th Tübingen Summer School in HPS 2015 Idealizations in Physics Slides available at http://users.ox.ac.uk/~corp2044

29 July 2015

Outline

1

Absolutism vs. Comparativism about mass

2

Dasgupta’s argument for Comparativism

3

Counter-argument: Empirical Inadequacy

4

Responses

5

Bonus: Ontological Parsimony

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. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony Absolutism vs. Comparativism Assumptions

“

The property of having mass is a determinable that appears to have two kinds of determinates. On the one hand, we naturally think that something with mass has a determinate intrinsic property, a property it has independently of its relationships with other material bodies. But we also think that things with mass stand in various determinate mass relationships with

• ne another, such as x being more massive than y or x being

twice as massive as y.

(Dasgupta, 2013, p.105)”

Niels Martens Comparativism about mass 4/34

Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony Absolutism vs. Comparativism Assumptions

Absolutism vs. Comparativism

(Weak) Absolutism

The most fundamental facts about material bodies vis-à-vis their mass are intrinsic properties (i.e. intrinsic masses). The mass relations hold in virtue of these intrinsic masses.

(Weak) Comparativism

The most fundamental facts about material bodies vis-à-vis their mass just concern how they are related in mass. All other facts about their mass, if any, hold in virtue of those relationships (and a convention).

(Dasgupta, 2013)

Niels Martens Comparativism about mass 5/34

Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony Absolutism vs. Comparativism Assumptions

Collectively exhaustive?

Strong Absolutism

1

Weak Absolutism

2

Intrinsic masses are fundamental

Strong Comparativism

1

Weak Comparativism

2

Mass relations are fundamental Eliminativism / Reductionism / Emergentism

1

Mass is not fundamental

→ Compatible with Weak Abs & Comp

Niels Martens Comparativism about mass 6/34

Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony Absolutism vs. Comparativism Assumptions

Assumptions

Newtonian Gravity Mass ratios

(Baker, manuscripts)

Equivalence between gravitational and inertial mass

Niels Martens Comparativism about mass 7/34

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. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony Dasgupta’s Razor

The argument for comparativism

Dasgupta’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 more parsimonious. Pp Comparativism about mass is ontologically more parsimo- nious than absolutism. Cc Comparativism about mass is favoured.

(Dasgupta, 2013)

Niels Martens Comparativism about mass 9/34

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. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony Defining Empirical Adequacy Initial Variable Problem Argument against Empirical Adequacy of Comparativism

Empirical adequacy

Empirical Adequacy: The comparativist laws of nature pick out a set of dynamically possible models from the set of possible models such that all empirically distinct models generated by the absolutist theory are included (i.e. completeness) and all models that are empirically distinct from each of the absolutist solutions are excluded (i.e. soundness). T1 (absolutism) T2 (comparativism)

P1 (possible models) P2 (possible models) S1 (dynamically possible models) S2 (dynamically possible models) Niels Martens Comparativism about mass 11/34

Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony Defining Empirical Adequacy Initial Variable Problem Argument against Empirical Adequacy of Comparativism

Empirical adequacy

Laplacean Determinism: A model m is deterministic iff, for any time t, there is only one empirically possible world whose state at t is identical to m’s. → Unique solution to the Initial Value Problem T1 (absolutism) T2 (comparativism)

P1 (possible models) P2 (possible models) S1 (dynamically possible models) S2 (dynamically possible models) Niels Martens Comparativism about mass 11/34

Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony Defining Empirical Adequacy Initial Variable Problem Argument against Empirical Adequacy of Comparativism

Empirical adequacy

Empirical Adequacy: The laws of nature uniquely (i.e. deterministically) evolve each set

• f initial conditions allowed by the

theory into a dynamically possible model, such that the whole set of empirically distinct dynamically possible models generated by the absolutist theory is reproduced (i.e. completeness) and no models that are empirically distinct from each of the absolutist solutions are generated (i.e. soundness). T1 (absolutism) T2 (comparativism)

P1 (possible models) P2 (possible models) S1 (dynamically possible models) S2 (dynamically possible models) Niels Martens Comparativism about mass 11/34

Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony Defining Empirical Adequacy Initial Variable Problem Argument against Empirical Adequacy of Comparativism

Empirical adequacy

T1 (absolutism) T2 (comparativism)

P1 (possible models) P2 (possible models) E1 E2 E2 E1 Niels Martens Comparativism about mass 11/34

Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony Defining Empirical Adequacy Initial Variable Problem Argument against Empirical Adequacy of Comparativism

Empirical adequacy

For comparativism to be empirically adequate, we need to find a map φ: P1 → P2, such that

1

∀m E(m, φ(m))

T1 (absolutism) T2 (comparativism)

P1 (possible models) P2 (possible models)

φ

Niels Martens Comparativism about mass 11/34

Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony Defining Empirical Adequacy Initial Variable Problem Argument against Empirical Adequacy of Comparativism

Empirical adequacy

For comparativism to be empirically adequate, we need to find a map φ: P1 → P2, such that

1

∀m E(m, φ(m))

2

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

T1 (absolutism) T2 (comparativism)

P1 (possible models) P2 (possible models)

φ

S1 S2 Niels Martens Comparativism about mass 11/34

Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony Defining Empirical Adequacy Initial Variable Problem Argument against Empirical Adequacy of Comparativism

Empirical adequacy

For comparativism to be empirically adequate, we need to find a map φ: P1 → P2, such that

1

∀m E(m, φ(m))

2

Completeness: ∀Ei(Ei ∩ S1 = ∅ → (∃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)

φ

S1 S2 Niels Martens Comparativism about mass 11/34

Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony Defining Empirical Adequacy Initial Variable Problem Argument against Empirical Adequacy of Comparativism

How to find φ Recipe for φ: m{mi,α2,...,αn},abs → m{ mi

mj ,α2,...,αn},comp

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

mj ,rij,vij},comp

T1 (absolutism) T2 (comparativism)

P1 P2 φ S1 S2

m{mi,rij,vij}

m{ mi

Niels Martens Comparativism about mass 12/34

Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony Defining Empirical Adequacy Initial Variable Problem Argument against Empirical Adequacy of Comparativism

The Initial Variable Problem I

General Initial Variable Problem Finding a set of independent variables α = {α1, α2, . . . , αn} such that specifying the initial conditions of a theory in terms of the values of that set of variables renders the theory empirically adequate. Comparativist Initial Variable Problem General IVP + Handicap: the set of initial variables has to contain mass relations, but may not include intrinsic masses.

Niels Martens Comparativism about mass 13/34

Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony Defining Empirical Adequacy Initial Variable Problem Argument against Empirical Adequacy of Comparativism

The Initial Variable Problem II

A four-step program

1

Choose a set of absolutist initial variables αabs = {mi, α2, . . . , αn}, thereby fixing the corresponding set for the comparativist αcomp = { mi

mj , α2, . . . , αn}

2

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

3

Check whether the absolutist and comparativist solution are empirically equivalent

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

4

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

Niels Martens Comparativism about mass 14/34

Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony Defining Empirical Adequacy Initial Variable Problem Argument against Empirical Adequacy of Comparativism

Argument against Comparativism

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

Niels Martens Comparativism about mass 15/34

Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony Defining Empirical Adequacy Initial Variable Problem Argument against Empirical Adequacy of Comparativism

Argument against Comparativism - continued

Fg = G mM

r2

ve =

• 2GM

r

v0 v0 F F

Double Mass

v0 v0 F F

(Baker, manuscripts)

Niels Martens Comparativism about mass 16/34

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. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony Three types of responses Analogue of Machian response Mixed Comparativism/ Absolutism

The analogous debate about space and motion

Three types of relationalist reponses

same models different ideology Enriched Relationalism

(Poincaré, Sklar, Maudlin, Binkoski)

same ideology different models Machianism

(Mach, Barbour-Bertoti)

same models same ideology Regularity Relationalism

(Hugget, Stevens) (Pooley, 2013; Hugget, 1999)

Niels Martens Comparativism about mass 18/34

Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony Three types of responses Analogue of Machian response Mixed Comparativism/ Absolutism

Three types of responses for the comparativist

Overview of the research program

same models different ideology

Enlarged ideology:

Transtemporal relations

(Dasgupta?, Poincaré?) Different ideology, but of the same size:

Mixed Comparativism/ Absolutism

(Baker, manuscripts)

same ideology different models Empirically distinct, but successful same models same ideology Regularity Comparativism Future project

(Pooley, 2013; Hugget, 1999)

Niels Martens Comparativism about mass 19/34

Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony Three types of responses Analogue of Machian response Mixed Comparativism/ Absolutism

Analogue of Machian response

Same ideology as standard comp, different 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) possibilities Machian response?

Which possibility should be denied?

Niels Martens Comparativism about mass 20/34

Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony Three types of responses Analogue of Machian response Mixed Comparativism/ Absolutism

Mixed Comparativism/ Absolutism

Same models as abs, different 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 different α But first: Baker’s response → boils down to a(n) (unsuccessful) specific choice of α

Niels Martens Comparativism about mass 21/34

Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony Three types of responses Analogue of Machian response Mixed Comparativism/ Absolutism

Baker’s response

Escape if v > ve =

• 2Gm

r

a = Gm

r2

v > √ 2ra Baker: Uniform mass scaling does not change whether this inequality is satisfied v >

• 2ra(m)

Baker, manuscripts

Niels Martens Comparativism about mass 22/34

Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony Three types of responses Analogue of Machian response Mixed Comparativism/ Absolutism

Baker’s response - continued

fundamental instantaneous velocities → reductive definition v(t) = dr

dt (t) = lim dt→0 r(t+dt)−r(t) dt

Similarly for accelerations Escape inequality: dr

dt

2 < 2r d2r

dt2

Baker: Uniform length scaling does not change whether this equation is satisfied

Baker, manuscripts

Niels Martens Comparativism about mass 23/34

Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony Three types of responses Analogue of Machian response Mixed Comparativism/ Absolutism

What is going on here?

1

Laplacean Determinism → Bakerian Determinism

initial t → initial [t − dt, t + dt]

2

α = {rij}?

Violates completeness a(t) = lim

dt→0 r(t+dt)−2r(t)+r(t−dt) dt2

3

α = {rij, vij, aij} ≡ {r(t)ij, r(t + dt)ij, r(t − dt)ij}?

Does this solve IVP? Eliminativism about mass

Niels Martens Comparativism about mass 24/34

Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony Three types of responses Analogue of Machian response Mixed Comparativism/ Absolutism

What is going on here?

Niels Martens Comparativism about mass 24/34

Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony Three types of responses Analogue of Machian response Mixed Comparativism/ Absolutism

Alternative Initial Variables I

Momentum

Escape: v >

• 2Gm

r

α = {rij, pi, mi}? ℘ ≡

v √m

Escape: ℘ >

• 2G

r

Mixed comparativism? (Baker, manuscripts)

Absolutism about ℘ Mix of kinematics & dynamics

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

Niels Martens Comparativism about mass 25/34

Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony Three types of responses Analogue of Machian response Mixed Comparativism/ Absolutism

Alternative Initial Variables I - continued

Momentum

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 ontologically parsimonious

Niels Martens Comparativism about mass 26/34

Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony Three types of responses Analogue of Machian response Mixed Comparativism/ Absolutism

Alternative Initial Variables II

Newton’s Constant

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

vi >

• 2γ

r mi m

α ? = {rij, vij, mi

m , γ}

Which m?

Particular mi?

• i mi?

What is γ?

true constant → violation of completeness variable → absolutism in disguise

Niels Martens Comparativism about mass 27/34

Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony Three types of responses Analogue of Machian response Mixed Comparativism/ Absolutism

Alternative Initial Variables III

α = {Fi, . . .} α = {mi

ri , . . . }

α = { vi

√mj , . . . }

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

Niels Martens Comparativism about mass 28/34

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. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony

A miraculous conspiracy of mass relations

Niels Martens Comparativism about mass 30/34

Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony

A miraculous conspiracy of mass relations

x1

Niels Martens Comparativism about mass 30/34

Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony

A miraculous conspiracy of mass relations

Niels Martens Comparativism about mass 30/34

Absolutism vs. Comparativism Dasgupta’s argument for Comparativism Counter-argument: Empirical Inadequacy Responses Bonus: Ontological Parsimony

A miraculous conspiracy of mass relations

? ?

Niels Martens Comparativism about mass 30/34

Conclusions

1

Initial mass relations, inter-particle distances and velocities fail to solve the Initial Variable Problem, seemingly suggesting that comparativism is empirically inadequate

2

There is no analogue of the Machian defence of relationalism in 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 Variable Problem, but it is unclear what to conclude from this. Moreover, it is unclear whether this generalises beyond the case of two particles in one dimension. A detailed Newtonian theory 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, mi

ri , 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 Comparative Metaphysics of Qantity’, Manuscript D.J. Baker, ‘Comparativism with Mixed Relations’, Manuscript

• S. Dasgupta (2013), ‘Absolutism vs Comparativism about

Qantity’, Oxford Studies in Metaphysics: Volume 8, Oxford University Press

• N. Hugget (1999), ‘Why manifold substantivalism is probably

not a consequence of classical mechanics’, International Studies in the Philosophy of Science 13: 17–34.

• O. Pooley (2013), ‘Substantivalist and Relationalist Approaches

to Spacetime’, R. Baterman (ed.), The Oxford Handbook of Philosophy of Physics, Oxford University Press