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- A1. Virtual particles
- A2. Naturalness
- A3. LHC, dark mater & gravity
- B1. Computer simulations
- B2. Model building
- B3. Novelty & Credibility
Refining the Motivational Approach to Symmetry-to-(un)reality - - PowerPoint PPT Presentation
Refining the Motivational Approach to Symmetry-to-(un)reality - - PowerPoint PPT Presentation
Refining the Motivational Approach to Symmetry-to-(un)reality Inferences Case Study: Aharonov-Bohm Effect Niels Martens Foundations2018, Utrecht 12 July 2018 A1. Virtual particles B1. Computer simulations A2. Naturalness B2. Model building
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An old, trivial claim?
Main task of interest: Drawing metaphysical conclusions in the face of empirically equivalent models (i.e. a realist project)—specifically symmetry-related models Main claim: Caution is needed! A trivial claim? – Yes! An old claim? – Yes! (Poincaré, 1902) Delicate middle way between conventionalism/instrumentalism and naive realism: motivationalism (Møller-Nielsen, 2017; Read & Møller-Nielsen, ms)
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The orthodoxy
Seeming consensus in Phys and PhilPhys communities on Symmetry-to-(un)reality inferences Typical claims
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Symmetry-related models invariably represent the same physical state of affairs. (Weyl, 1918a,b; Greaves & Wallace, 2014)
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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; Møller-Nielsen, 2017; North, 2009; Nozick, 2001; Weyl, 1952)
3
The equivalence class of symmetry-related models is what is real (Weyl, 1918a,b)
Paradigmatic example: Newton was at no point in time justified in believing in absolute velocities.
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The Interpretationalist Dogma
Interpretational View
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“Symmetries [invariably] 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)
One may then, but is not required to:
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Identify symmetry-related models;
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Qotient them out of the space of kinematically possible models to obtain a reduced theory;
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Find a metaphysically perspicuous characterisation of the models in the reduced theory
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The motivational approach to symmetries
Motivational View
1
“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
- f invariant quantities in the absence of any such
characterisation.”
(Møller-Nielsen, 2017)
Only once such a characterisation is found, if that is at all possible, may one:
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Interpret the original symmetry-related models as representing the same physically possible worlds/ state of affairs;
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Identify those models
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Motivational view: two scenarios
Isomorphic models → no reformulation needed; only modest structuralism
Example: Static Leibniz Shif & Hole argument → sophisticated substantivalism
Non-isomorphic models → reformulation needed
Example: Kinematic Leibniz Shif → motivated to find a reformulation: Neo-Newtonian Spacetime. In absence of such, Newton was justified in believing in absolute velocity.
(Moller-Nielsen, 2017)
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Motivations for the interpretational approach
Undetectability? Methodological norm against undetectable stuff: Ockham’s razor
No metaphysical commitment to anything unnecessary? Comparative norm (cf. Hossenfelder’s keynote: pragmatism): Only if multiple empirically adequate theories are on the table, then, ceteris paribus, should we discard the theory that posits the ‘most’ undetectable stuff
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Some other worries
No guarantee objection Opaqueness objection Cherry-picking objection → Anti-realism in disguise Different symmetries leading to distinct interpretations Inconsistent with actual practice in physics and philosophy of physics
Møller-Nielsen, 2017; Read & Møller-Nielsen, ms
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Refining the Motivational Approach
Refined motivational approach Symmetries only motivate us to find a characterisation that both provides a metaphysically perspicuous reality underlying the symmetry-related models and retains all theoretical virtues, such as explanatory power, 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.
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Refined Motivationalism Illustrated
Classical Electromagnetism in terms of Vector Potential
Classical Electromagnetism in terms of vector potential A: Leibniz Gauge Shif: Aµ → Aµ + ∇µf Interpretationalism: gauge symmetry implies that A is not
- real. No requirement to say anything more than that.
Standard Motivationalism: models are not isomorphic → we are motivated to find a reformulation: Fµν (= ∂µAν − ∂νAµ);
- nly with this reformulation in hand can the gauge shifed
models can be interpreted as representing the same physical state of affairs. (Møller-Nielsen, 2017) What about the Aharonov-Bohm Effect? (Aharonov & Bohm, 1959)
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Refined Motivationalism Illustrated
The Aharonov-Bohm Effect
A-B effect
Source Screen Solenoid
A may be undetectable, but it provides a local explanation, which Fµν does not Refined Motivationalism: We are motivated to find a reformulation that provides a fully local explanation (i.e. no action-at-a-distance) without undetectable
- stuff. Until we succeed, we are justified in
reifying A. (Aharonov & Bohm; Feynman; Maudlin) The whole community did exactly that!
Dirac phase factor/holonomies: no undetectability, but still non-separability (Wu & Yang, 1975; Healey, 1997) Alternative gauge-invariant quantity: no undetectability, no action-at-a-distance, separable (Wallace, 2014)
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Conclusions
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I have sided with Møller-Nielsen, Read & Dasgupta against the interpretational approach to symmetries
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The only defensible motivation for symmetry-to-reality inferences is a comparative version of Ockham’s razor that does not only speak against the interpretational approach, but also indicates extending the motivational approach: consideration of theoretical virtues
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This added constraint is a virtue, not a vice: helps avoiding underdetermination arguments against realism
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Only this refined approach correctly analyses the A-B effect, and is consistent with the literature/ practice
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References
- Y. Aharonov & D. Bohm (1959), ‘Significance of Electromagnetic
Potentials in the Qantum Theory’, Phys. Rev. 115:485 D.J. Baker (2010), ‘Symmetry and the Metaphysics of Physics’, Philosophy Compass, 5:1157–66.
- 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.
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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.
- H. Greaves, & D. Wallace (2014), ‘Empirical Consequences of
Symmetries’, The British Journal for the Philosophy of Science, 65/1:59-89.
- R. Healey (1997), ‘Nonlocality and the Aharonov-Bohm Effect’,
Philosophy of Science, 64/1:18-41.
- T. Maudlin (1998), ‘Healey on the Aharonov-Bohm Effect’,
Philosophy of Science, 65/2:361-368.
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References - continued
- T. Møller-Nielsen (2017), ‘Invariance, Interpretation, and
Motivation’, Philosophy of Science, 84(5):1253-1264.
- 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.
- H. Poincaré (1902 [1952]), Science and Hypothesis, Dover, New
York, Translated by W. Scot.
- J. Read & T. Møller-Nielsen (manuscript), ‘Motivating Dualities’,
forthcoming in Synthese
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References - continued
- S. Saunders (2007), ‘Mirroring as an a priori symmetry’,
Philosophy of Science, 74:452-480
- 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