From Models to Reality: A Plea for Caution Niels Martens SOPhiA - - PowerPoint PPT Presentation

From Models to Reality: A Plea for Caution

Niels Martens

SOPhiA 2017 - Satellite Workshop ‘Modeling Physical Reality’ Slides available at https://martensniels.wordpress.com

13 Sept 2017

An old, trivial claim?

Main task of interest: Drawing metaphysical conclusions from physical 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 between conventionalism/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

Outline

1

Illustrating Naive & Motivational Realism

2

Elaborate Case Study: Absolute Mass in Newtonian Gravity

Illustrating Naive & Motivational Realism Elaborate Case Study: Absolute Mass in Newtonian Gravity Intro Defining the dichotomies Illustrations

Naive realism

Seeming consensus in Phys and PhilPhys communities on

Symmetry-to-reality inferences Duality-to-reality inferences

Typical claims

1

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 affairs (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 justified in believing in absolute velocities.

Niels Martens From Models to Reality 5/30

Illustrating Naive & Motivational Realism Elaborate Case Study: Absolute Mass in Newtonian Gravity Intro Defining the dichotomies Illustrations

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 map models to possible worlds in a one-to-one fashion could always be found? (Møller-Nielsen: No) Without such a reformulation, which picture of the world are we subscribing to exactly? Dualities: ofen clearly distinct physical states of affairs

Niels Martens From Models to Reality 6/30

Illustrating Naive & Motivational Realism Elaborate Case Study: Absolute Mass in Newtonian Gravity Intro Defining the dichotomies Illustrations

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 application

• nly, involving strong idealizations. (Jacquart, 2016)

Niels Martens From Models to Reality 7/30

Illustrating Naive & Motivational Realism Elaborate Case Study: Absolute Mass in Newtonian Gravity Intro Defining the dichotomies Illustrations

Interpretational vs motivational view [Symmetries]

Interpretational View [Symmetries] Symmetries allow us to interpret theories as being commited solely to the existence of invariant quantities, even in the absence of a metaphysically perspicuous characterisation of the reality which is alleged to underlie symmetry-related models.

(Møller-Nielsen, 2017, p.4)

Motivational View [Symmetries] Symmetries only motivate us to find a metaphysically perspicuous characterisation of the reality which is alleged to underlie symmetry-related models, but they do not allow us to interpret that theory as being solely commited to the existence of invariant quantities in the absence of any such characterisation.

(Møller-Nielsen, 2017, p.4)

Niels Martens From Models to Reality 8/30

Illustrating Naive & Motivational Realism Elaborate Case Study: Absolute Mass in Newtonian Gravity Intro Defining the dichotomies Illustrations

Motivational view [Two Variants]

Isomorphic models → no reformulation needed; only modest structuralism Non-isomorphic models → reformulation needed

(Moller-Nielsen, 2017)

Niels Martens From Models to Reality 9/30

Illustrating Naive & Motivational Realism Elaborate Case Study: Absolute Mass in Newtonian Gravity Intro Defining the dichotomies Illustrations

Interpretational vs motivational view [Dualities]

(Read & Møller-Nielsen, manuscript)

Interpretational View [Dualities]

1

Interpret duality-related models as representing the same possible world; Then we may but don’t have to:

2

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

3

Find a metaphysically perspicuous characterisation of the reduced set of DPMs Motivational View [Dualities] Existence of dual models motivates finding a shared metaphysically perspicuous characterisation (3); only if that is found do we move on to interpret the models as representing the same possible worlds (1) and potentially identify them (2).

Niels Martens From Models to Reality 10/30

Illustrating Naive & Motivational Realism Elaborate Case Study: Absolute Mass in Newtonian Gravity Intro Defining the dichotomies Illustrations

Naive vs Motivational Realism

Naive realism Models that are empirically equivalent are invariably interpreted as representing the same possible world; they may be identified and quotiented out of the space of DPMs. Motivational or Sophisticated Realism The existence of empirically equivalent models only motivates us to find an underlying metaphysically and explanatorily perspicuous characterisation, but these models cannot be interpreted as representing the same possible world in the absence of any such characterisation.

Niels Martens From Models to Reality 11/30

Illustrating Naive & Motivational Realism Elaborate Case Study: Absolute Mass in Newtonian Gravity Intro Defining the dichotomies Illustrations

The motivational view illustrated I

Absolute Position

Static Leibniz Shif & Hole argument against manifold substantivalism Motivational view: models are isomorphic

→ No reformulation needed → A modest structuralism (sophisticated substantivalism) suffices to find a shared metaphysically perspicuous characterisation → Symmetry-related models can then be identified

Niels Martens From Models to Reality 12/30

Illustrating Naive & Motivational Realism Elaborate Case Study: Absolute Mass in Newtonian Gravity Intro Defining the dichotomies Illustrations

The motivational view illustrated II

Absolute velocity

Kinematic Leibniz Shif 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.

Niels Martens From Models to Reality 13/30

Illustrating Naive & Motivational Realism Elaborate Case Study: Absolute Mass in Newtonian Gravity Intro Defining the dichotomies Illustrations

The motivational view illustrated III

The Aharonov-Bohm Effect

Electromagnetism: Leibniz Gauge Shif of vector potential Møller-Nielsen: models are not isomorphic → we are motivated to find a reformulation in terms of the Faraday tensor; once found the gauge shifed models can be interpreted as representing the same physical state of affairs. What about the Aharonov-Bohm Effect? Other theoretical virtues, such as providing a local explanation, are also relevant! A-B effect

Source Screen Solenoid (Wu & Yang, 1975; Healey, 1997; Maudlin, 1998; Healey, 1999; Holland, 1993; Wallace, 2014)

Niels Martens From Models to Reality 14/30

Outline

1

Illustrating Naive & Motivational Realism

2

Elaborate Case Study: Absolute Mass in Newtonian Gravity

Illustrating Naive & Motivational Realism Elaborate Case Study: Absolute Mass in Newtonian Gravity Naive realism The bucket Motivated to find a new theory

Absolutism vs Comparativism about Mass

Absolutism Mass ratios are true in virtue of more fundamental determinate absolute masses. Comparativism The denial of absolutism.

Niels Martens From Models to Reality 16/30

Illustrating Naive & Motivational Realism Elaborate Case Study: Absolute Mass in Newtonian Gravity Naive realism The bucket Motivated to find a new theory

Bad reasons for comparativism

Numerical value used to represent absolute masses depends on conventional 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 a square does. Determinable magnitudes of an object such as mass can only be expressed, non-dynamically, by comparing it to the magnitude of another object. (‘kinematic comparativism’)

(NM, 2017)

Niels Martens From Models to Reality 17/30

Illustrating Naive & Motivational Realism Elaborate Case Study: Absolute Mass in Newtonian Gravity Naive realism The bucket Motivated to find a new theory

Some more bad reasons for comparativism

Since absolute mass magnitudes are qualitatively indistinguishable, the mapping from mass magnitudes to the [quantity · unit] representing them is underdetermined. A passive mass scaling (i.e. change of units) does not change the physics, and is thus a symmetry. Even if an active mass scaling leads to observable differences, we could and should compensate for this by changing Newton’s constant accordingly. (Roberts, ms)

(NM, 2017)

Niels Martens From Models to Reality 18/30

Illustrating Naive & Motivational Realism Elaborate Case Study: Absolute Mass in Newtonian Gravity Naive realism The bucket Motivated to find a new theory

Response

We don’t think a vector is not real because it’s coordinate description depends on a frame. (North, 2009) So why would we think absolute masses are not real just because the quantities used to represent them change when we change units? Dynamic Comparativism: Physical observables depend only

• n mass ratios, not on further absolute masses in virtue of

which the mass ratios hold. (NM, 2017)

Niels Martens From Models to Reality 19/30

Illustrating Naive & Motivational Realism Elaborate Case Study: Absolute Mass in Newtonian Gravity Naive realism The bucket Motivated to find a new theory

Comparativism’s bucket

Fg = G mM

r2

ve =

• 2GM

r

v0 v0 F F

Double Mass

v0 v0 F F

(Baker, 2014; NM, 2017)

Niels Martens From Models to Reality 20/30

Illustrating Naive & Motivational Realism Elaborate Case Study: Absolute Mass in Newtonian Gravity Naive realism The bucket Motivated to find a new theory

Motivation to find a new theory

Active mass scaling is not a symmetry, but leads to detectable differences. → Absolute masses explain the different possible evolutions of the system! Nevertheless, absolute masses in some sense still undetectable: expressible (non-dynamically) only via comparisons Moreover, we only have empirical access to the mass times Newton Constant → wiggle room → Motivation to find a reformulated theory without absolute masses

Niels Martens From Models to Reality 21/30

Illustrating Naive & Motivational Realism Elaborate Case Study: Absolute Mass in Newtonian Gravity Naive realism The bucket Motivated to find a new theory

Machian comparativism

G = γ

• k

mk → Fgrav = γ mimj r2

k

mk Despite being empirically equivalent to absolutist Newtonian Gravity, mass scaling is a symmetry and absolute masses are not required.

Niels Martens From Models to Reality 22/30

Illustrating Naive & Motivational Realism Elaborate Case Study: Absolute Mass in Newtonian Gravity Naive realism The bucket Motivated to find a new theory

Conclusions

1

Drawing metaphysical conclusions from models of a theory is highly non-trivial, but possible.

2

When there is a symmetry, or a quantity that is in some sense undetectable, we are only motivated to find a reformulation of the theory (or a more metaphysically perspicuous characterisation of it) that does without that quantity. Until such is found we are justified in commiting to that quantity.

3

Paradigmatic case: Newton was justified in believing in absolute velocities, until Neo-Newtonian spacetime was postulated.

4

Despite absolute masses being in some sense undetectable/unexpressible, comparativism only stands a fighting chance once Machian comparativism is put on the table.

Niels Martens From Models to Reality 23/30

• A1. Virtual particles
• A2. Naturalness
• A3. LHC, dark mater & gravity
• B1. Computer simulations
• B2. Model building
• B3. Novelty & Credibility

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 the comparative metaphysics of quantity’, http://philsci-archive.pitt.edu/12674/

• S. Dasgupta (2015), ‘Substantivalism vs Relationalism About

Space in Classical Physics’, Philosophy Compass 10/9:601–624.

• S. Dasgupta (2016), ‘Symmetry as an Epistemic Notion (Twice

Over)’, 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.

References - continued

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

• J. Earman (1989), World-Enough and Space-Time, Cambridge,

MA: MIT Press.

• J. Earman (2004), ‘Curie’s Principle and Spontaneous Symmetry

Breaking’, International Studies in the Philosphy of Science 18:173-198

• H. Greaves, & D. Wallace (2014), ‘Empirical Consequences of

Symmetries’, The British Journal for the Philosophy of Science, 65/1:59-89.

• S. de Haro (2016), ‘Spacetime and Physical Equivalence’,

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

References - continued

• R. Healey (1997), ‘Nonlocality and the Aharonov-Bohm Effect’,

Philosophy of Science, 64/1:18-41.

• R. Healey (1999), ‘Qantum Analogies: A Reply to Maudlin’,

Philosophy of Science, 66/3:440-447. P.R. Holland (1993), The Qantum 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, htp://ir.lib.uwo.ca/etd/4129

• P. Kitcher (2001), ‘Real Realism: The Galilean Strategy’, The

Philosophical Review, 110:151–197.

References - continued

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

• T. Maudlin (1998), ‘Healey on the Aharonov-Bohm Effect’,

Philosophy of Science, 65/2:361-368.

• T. Møller-Nielsen (2017), ‘Invariance, Interpretation, and

Motivation’, 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 Objective

World, Cambridge, MA: Harvard University Press.

References - continued

• H. Poincaré (1902 [1952]), Science and Hypothesis, Dover, New

York, Translated by W. Scot.

• J. Read & T. Møller-Nielsen (manuscript), ‘Motivating Dualities’
• D. Rickles (2016), ‘Dual Theories: ‘Same but Different’ or

’Different but Same’?’, forthcoming in Studies in History and Philosophy of Modern Physics. J.T. Roberts (ms), ‘A case for comparativism about physical quantities’, academia.edu

• S. Saunders (2007), ‘Mirroring as an a priori symmetry’,

Philosophy of Science, 74:452-480

References - continued

• C. Smeenk (2006), ‘The Elusive Higgs Mechanism’, Philosophy
• f Science 73/5:487-499.
• D. Wallace (2014), ‘Deflating the Aharanov-Bohm Effect’,

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’, Sitzungsberichte

Akademie der Wissenschafen Berlin, 465-480. T.T. Wu & C.N. Yang (1975), ‘Concept of Nonintegrable Phase Factors and Global Formulation of Gauge Fields’, Physical Review D,12:3845