From Models to Reality: A Plea for Caution...Illustrating Naive & Motivational Realism Elaborate Case Study: Absolute Mass in Newtonian Gravity Intro Defining the dichotomies Illustrations

From Models to Reality: A Plea for Caution

Niels Martens

SOPhiA 2017 - Satellite Workshop ‘Modeling Physical Reality’

Slides available athttps://martensniels.wordpress.com

13 Sept 2017

https://martensniels.wordpress.com

An old, trivial claim?

Main task of interest: Drawing metaphysical conclusions fromphysical models (i.e. a realist project)Main claim: Care is needed!

A trivial claim? Who would advise against caution?Underdetermination of metaphysics by theories

Poincaré (1902)

Delicate middle way betweenconventionalism/instrumentalism and naive realism

Working posit realism? (Kitcher, 2001)Motivational realism

Outline

1 Illustrating Naive & Motivational Realism

2 Elaborate Case Study: Absolute Mass in Newtonian Gravity

Illustrating Naive & Motivational RealismElaborate Case Study: Absolute Mass in Newtonian Gravity

IntroDefining the dichotomiesIllustrations

Naive realism

Seeming consensus in Phys and PhilPhys communities onSymmetry-to-reality inferencesDuality-to-reality inferences

Typical claims1 Invariance Principle: Only quantities invariant under the

symmetries of our theory are real. (Saunders, 2007; Baker, 2010;Dasgupta, 2015, 2016; Dewar, 2015; Dirac, 1930; Earman, 1989; Greaves and

Wallace, 2014; Møller-Nielsen, 2017; North, 2009; Nozick, 2001; Weyl, 1952)2 The equivalence class of dual/ symmetry-related models is what

is real (Weyl, 1918a,b)3 Dual/ symmetry-related models represent the same physical

state of a�airs (Rickles, 2016; de Haro, 2016, for unextendable theories only;see Read & Moller-Nielsen, ms, for an opposing view)

Paradigmatic case: Newton was at no point in time justifiedin believing in absolute velocities.

Niels Martens From Models to Reality 5/30



Some worries

What is supposed to motivate the Invariance Principle?

Undetectability? (Møller-Nielsen, 2017; Read & Møller-Nielsen, ms)

Are we guaranteed that a reformulated theory that does mapmodels to possible worlds in a one-to-one fashion could alwaysbe found? (Møller-Nielsen: No)

Without such a reformulation, which picture of the world arewe subscribing to exactly?

Dualities: o�en clearly distinct physical states of a�airs




Some more worries

Is it always clear what the symmetries are?

What about symmetries that are spontaneously broken?(Earman, 2004; Smeenk, 2006)

Haecceitism, qualitativism & essentialism

Many models are designed for a specific purpose (description,prediction, explanation) and specific domain of applicationonly, involving strong idealizations. (Jacquart, 2016)




Interpretational vs motivational view [Symmetries]

Interpretational View [Symmetries]

Symmetries allow us to interpret theories as being commi�ed solelyto the existence of invariant quantities, even in the absence of ametaphysically perspicuous characterisation of the reality which isalleged to underlie symmetry-related models. (Møller-Nielsen, 2017, p.4)

Motivational View [Symmetries]

Symmetries only motivate us to find a metaphysically perspicuouscharacterisation of the reality which is alleged to underliesymmetry-related models, but they do not allow us to interpret thattheory as being solely commi�ed to the existence of invariantquantities in the absence of any such characterisation.

(Møller-Nielsen, 2017, p.4)




Motivational view [Two Variants]

Isomorphic models→ no reformulation needed; only modeststructuralism

Non-isomorphic models→ reformulation needed

(Moller-Nielsen, 2017)




Interpretational vs motivational view [Dualities](Read & Møller-Nielsen, manuscript)

Interpretational View [Dualities]

1 Interpret duality-related models as representing the same possibleworld;

Then we may but don’t have to:

2 Identify those models and quotient them out of the space ofdynamically possible models (DPM);

3 Find a metaphysically perspicuous characterisation of the reducedset of DPMs

Motivational View [Dualities]

Existence of dual models motivates finding a shared metaphysicallyperspicuous characterisation (3); only if that is found do we move on tointerpret the models as representing the same possible worlds (1) andpotentially identify them (2).




Naive vs Motivational Realism

Naive realismModels that are empirically equivalent are invariably interpreted asrepresenting the same possible world; they may be identified andquotiented out of the space of DPMs.

Motivational or Sophisticated Realism

The existence of empirically equivalent models only motivates us tofind an underlying metaphysically and explanatorily perspicuouscharacterisation, but these models cannot be interpreted asrepresenting the same possible world in the absence of any suchcharacterisation.




The motivational view illustrated IAbsolute Position

Static Leibniz Shi� & Hole argument against manifoldsubstantivalismMotivational view: models are isomorphic→ No reformulation needed→ A modest structuralism (sophisticated substantivalism) su�ices

to find a shared metaphysically perspicuous characterisation→ Symmetry-related models can then be identified




The motivational view illustrated IIAbsolute velocity

Kinematic Leibniz Shi�Motivational view: models are non-isomorphic→ We are motivated to find a shared metaphysically perspicuous

characterisation: Neo-Newtonian Spacetime→ In the absence of such, Newton was justified in believing in

absolute velocity.




The motivational view illustrated IIIThe Aharonov-Bohm E�ect

Electromagnetism: Leibniz Gauge Shi� ofvector potential

Møller-Nielsen: models are not isomorphic→ we are motivated to find areformulation in terms of the Faradaytensor; once found the gauge shi�edmodels can be interpreted as representingthe same physical state of a�airs.

What about the Aharonov-Bohm E�ect?

Other theoretical virtues, such asproviding a local explanation, are alsorelevant!

A-B e�ect

Source

Screen

Solenoid

(Wu & Yang, 1975; Healey,

1997; Maudlin, 1998;

Healey, 1999; Holland, 1993;

Wallace, 2014)


Outline

1 Illustrating Naive & Motivational Realism

2 Elaborate Case Study: Absolute Mass in Newtonian Gravity


Naive realismThe bucketMotivated to find a new theory

Absolutism vs Comparativism about Mass

AbsolutismMass ratios are true in virtue of more fundamental determinateabsolute masses.

Comparativism

The denial of absolutism.




Bad reasons for comparativism

Numerical value used to represent absolute masses depends onconventional choice of unit

A mass of ‘4kg’ does not represent anything intrinsically ‘4-ish’about the object in the way that the number of corners of asquare does.

Determinable magnitudes of an object such as mass can onlybe expressed, non-dynamically, by comparing it to themagnitude of another object. (‘kinematic comparativism’)

(NM, 2017)




Some more bad reasons for comparativism

Since absolute mass magnitudes are qualitativelyindistinguishable, the mapping from mass magnitudes to the[quantity · unit] representing them is underdetermined.A passive mass scaling (i.e. change of units) does not changethe physics, and is thus a symmetry.

Even if an active mass scaling leads to observable di�erences,we could and should compensate for this by changingNewton’s constant accordingly. (Roberts, ms)

(NM, 2017)




Response

We don’t think a vector is not real because it’s coordinatedescription depends on a frame. (North, 2009) So why would wethink absolute masses are not real just because the quantitiesused to represent them change when we change units?

Dynamic Comparativism: Physical observables depend onlyon mass ratios, not on further absolute masses in virtue ofwhich the mass ratios hold. (NM, 2017)




Comparativism’s bucket

Fg = G mMr2 ve =√

2GMr

v0 v0

F F

Double Mass

v0 v0

F F

(Baker, 2014; NM, 2017)




Motivation to find a new theory

Active mass scaling is not a symmetry, but leads to detectabledi�erences.

→ Absolute masses explain the di�erent possible evolutions of thesystem!

Nevertheless, absolute masses in some sense still undetectable:expressible (non-dynamically) only via comparisons

Moreover, we only have empirical access to the mass timesNewton Constant→ wiggle room

→ Motivation to find a reformulated theory without absolutemasses




Machian comparativism

G =γ∑

kmk

→ Fgrav = γmimj

r2∑k

mk

Despite being empirically equivalent to absolutist NewtonianGravity, mass scaling is a symmetry and absolute masses are not

required.




Conclusions

1 Drawing metaphysical conclusions from models of a theory ishighly non-trivial, but possible.

2 When there is a symmetry, or a quantity that is in some senseundetectable, we are only motivated to find a reformulation ofthe theory (or a more metaphysically perspicuouscharacterisation of it) that does without that quantity. Untilsuch is found we are justified in commi�ing to that quantity.

3 Paradigmatic case: Newton was justified in believing inabsolute velocities, until Neo-Newtonian spacetime waspostulated.

4 Despite absolute masses being in some senseundetectable/unexpressible, comparativism only stands afighting chance once Machian comparativism is put on thetable.


A1. Virtual particlesA2. NaturalnessA3. LHC, dark ma�er & gravity

B1. Computer simulationsB2. Model buildingB3. Novelty & Credibility

www.lhc-epistemologie.uni-wuppertal.de/

www.lhc-epistemologie.uni-wuppertal.de/

References

D.J. Baker (2010), ‘Symmetry and the Metaphysics of Physics’,Philosophy Compass, 5:1157–66.

D.J. Baker (2014), ‘Some consequences of physics for thecomparative metaphysics of quantity’,http://philsci-archive.pitt.edu/12674/

S. Dasgupta (2015), ‘Substantivalism vs Relationalism AboutSpace in Classical Physics’, Philosophy Compass 10/9:601–624.

S. Dasgupta (2016), ‘Symmetry as an Epistemic Notion (TwiceOver)’, The British Journal for the Philosophy of Science,67.3:837-878.

N. Dewar (2015), ‘Symmetries and the Philosophy of Language’,Studies in the History and Philosophy of Modern Physics,52:317-327.

http://philsci-archive.pitt.edu/12674/

References - continued

P.A.M. Dirac (1930 [1958, 4th edition]), The Principles of�antum Mechanics, Oxford University Press.

J. Earman (1989), World-Enough and Space-Time, Cambridge,MA: MIT Press.

J. Earman (2004), ‘Curie’s Principle and Spontaneous SymmetryBreaking’, International Studies in the Philosphy of Science18:173-198

H. Greaves, & D. Wallace (2014), ‘Empirical Consequences ofSymmetries’, The British Journal for the Philosophy of Science,65/1:59-89.

S. de Haro (2016), ‘Spacetime and Physical Equivalence’,available athttp://philsciarchive.pitt.edu/12279/

http://philsciarchive. pitt.edu/12279/


R. Healey (1997), ‘Nonlocality and the Aharonov-Bohm E�ect’,Philosophy of Science, 64/1:18-41.

R. Healey (1999), ‘�antum Analogies: A Reply to Maudlin’,Philosophy of Science, 66/3:440-447.

P.R. Holland (1993), The �antum Theory of Motion, Cambridge:Cambridge University Press.

M. Jacquart (2016), Similarity, Adequacy, and Purpose:Understanding the Success of Scientific Models, PhD thesis,Electronic Thesis and Dissertation Repository,h�p://ir.lib.uwo.ca/etd/4129

P. Kitcher (2001), ‘Real Realism: The Galilean Strategy’, ThePhilosophical Review, 110:151–197.


N.C.M. Martens (2017), Against Comparativism about Mass inNewtonian Gravity - a Case Study in the Metaphysics of Scale,DPhil thesis, Magdalen College, Oxford University

T. Maudlin (1998), ‘Healey on the Aharonov-Bohm E�ect’,Philosophy of Science, 65/2:361-368.

T. Møller-Nielsen (2017), ‘Invariance, Interpretation, andMotivation’, forthcoming in Philosophy of Science.

J. North (2009), ‘The “Structure” of Physics: A Case Study’,Journal of Philosophy, 106: 57–88.

R. Nozick (2001), Invariances: The Structure of the ObjectiveWorld, Cambridge, MA: Harvard University Press.


H. Poincaré (1902 [1952]), Science and Hypothesis, Dover, NewYork, Translated by W. Sco�.

J. Read & T. Møller-Nielsen (manuscript), ‘Motivating Dualities’

D. Rickles (2016), ‘Dual Theories: ‘Same but Di�erent’ or’Di�erent but Same’?’, forthcoming in Studies in History andPhilosophy of Modern Physics.

J.T. Roberts (ms), ‘A case for comparativism about physicalquantities’, academia.edu

S. Saunders (2007), ‘Mirroring as an a priori symmetry’,Philosophy of Science, 74:452-480


C. Smeenk (2006), ‘The Elusive Higgs Mechanism’, Philosophyof Science 73/5:487-499.

D. Wallace (2014), ‘Deflating the Aharanov-Bohm E�ect’,arxiv:1407.5073

H. Weyl (1952), Symmetry, Princeton University Press.

H. Weyl (1918a), ‘Reine Infinitesimalgeometrie’, Math. Z.,2:384-411.

H. Weyl (1918b), ‘Gravitation und Elektrizität’, SitzungsberichteAkademie der Wissenscha�en Berlin, 465-480.

T.T. Wu & C.N. Yang (1975), ‘Concept of Nonintegrable PhaseFactors and Global Formulation of Gauge Fields’, PhysicalReview D,12:3845

Illustrating Naive & Motivational RealismIntroDefining the dichotomiesIllustrations

Elaborate Case Study: Absolute Mass in Newtonian GravityNaive realismThe bucketMotivated to find a new theory

Documents

From Models to Reality: A Plea for Caution...Illustrating Naive & Motivational Realism Elaborate Case Study: Absolute Mass in Newtonian Gravity Intro Defining the dichotomies Illustrations