Refining the Motivational Approach to Symmetry-to-(un)reality Inferences

Transcription

1 Refining the Motivational Approach to Symmetry-to-(un)reality Inferences Case Study: Aharonov-Bohm Effect Niels Martens Foundations2018, Utrecht 12 July 2018

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

3 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)

4 The orthodoxy Seeming consensus in Phys and PhilPhys communities on Symmetry-to-(un)reality inferences Typical claims 1 Symmetry-related models invariably represent the same physical state of affairs. (Weyl, 1918a,b; Greaves & Wallace, 2014) 2 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. Niels Martens Motivationalism & the AB-effect 4/17

5 The Interpretationalist Dogma Interpretational View 1 Symmetries [invariably] allow us to interpret theories as being committed 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: 2 Identify symmetry-related models; 3 Quotient them out of the space of kinematically possible models to obtain a reduced theory; 4 Find a metaphysically perspicuous characterisation of the models in the reduced theory Niels Martens Motivationalism & the AB-effect 5/17

6 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 committed to the existence of 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: 2 Interpret the original symmetry-related models as representing the same physically possible worlds/ state of affairs; 3 Identify those models Niels Martens Motivationalism & the AB-effect 6/17

7 Motivational view: two scenarios Isomorphic models no reformulation needed; only modest structuralism Example: Static Leibniz Shift & Hole argument sophisticated substantivalism Non-isomorphic models reformulation needed Example: Kinematic Leibniz Shift motivated to find a reformulation: Neo-Newtonian Spacetime. In absence of such, Newton was justified in believing in absolute velocity. (Moller-Nielsen, 2017) Niels Martens Motivationalism & the AB-effect 7/17

8 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 Niels Martens Motivationalism & the AB-effect 8/17

9 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 Niels Martens Motivationalism & the AB-effect 9/17

10 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 committed to the existence of invariant quantities in the absence of any such characterisation. Niels Martens Motivationalism & the AB-effect 10/17

11 Refined Motivationalism Illustrated Classical Electromagnetism in terms of Vector Potential Classical Electromagnetism in terms of vector potential A: Leibniz Gauge Shift: A µ A µ + µ f 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: F µν (= µ A ν ν A µ ); only with this reformulation in hand can the gauge shifted models can be interpreted as representing the same physical state of affairs. (Møller-Nielsen, 2017) What about the Aharonov-Bohm Effect? (Aharonov & Bohm, 1959) Niels Martens Motivationalism & the AB-effect 11/17

12 Refined Motivationalism Illustrated The Aharonov-Bohm Effect Source A-B effect Solenoid Screen A may be undetectable, but it provides a local explanation, which F µν 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) Niels Martens Motivationalism & the AB-effect 12/17

13 Conclusions 1 I have sided with Møller-Nielsen, Read & Dasgupta against the interpretational approach to symmetries 2 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 3 This added constraint is a virtue, not a vice: helps avoiding underdetermination arguments against realism 4 Only this refined approach correctly analyses the A-B effect, and is consistent with the literature/ practice Niels Martens Motivationalism & the AB-effect 13/17

14 References Y. Aharonov & D. Bohm (1959), Significance of Electromagnetic Potentials in the Quantum Theory, Phys. Rev. 115:485 D.J. Baker (2010), Symmetry and the Metaphysics of Physics, Philosophy Compass, 5: S. Dasgupta (2015), Substantivalism vs Relationalism About Space in Classical Physics, Philosophy Compass 10/9: S. Dasgupta (2016), Symmetry as an Epistemic Notion (Twice Over), The British Journal for the Philosophy of Science, 67.3: N. Dewar (2015), Symmetries and the Philosophy of Language, Studies in the History and Philosophy of Modern Physics, 52:

15 References - continued P.A.M. Dirac (1930 [1958, 4th edition]), The Principles of Quantum 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: R. Healey (1997), Nonlocality and the Aharonov-Bohm Effect, Philosophy of Science, 64/1: T. Maudlin (1998), Healey on the Aharonov-Bohm Effect, Philosophy of Science, 65/2:

16 References - continued T. Møller-Nielsen (2017), Invariance, Interpretation, and Motivation, Philosophy of Science, 84(5): J. North (2009), The Structure of Physics: A Case Study, Journal of Philosophy, 106: 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. Scott. J. Read & T. Møller-Nielsen (manuscript), Motivating Dualities, forthcoming in Synthese

17 References - continued S. Saunders (2007), Mirroring as an a priori symmetry, Philosophy of Science, 74: D. Wallace (2014), Deflating the Aharanov-Bohm Effect, arxiv: H. Weyl (1952), Symmetry, Princeton University Press. H. Weyl (1918a), Reine Infinitesimalgeometrie, Math. Z., 2: H. Weyl (1918b), Gravitation und Elektrizität, Sitzungsberichte Akademie der Wissenschaften Berlin, T.T. Wu & C.N. Yang (1975), Concept of Nonintegrable Phase Factors and Global Formulation of Gauge Fields, Physical Review D,12:3845