Permanent Underdetermination from Approximate Empirical Equivalence in Field Theory: Massless and Massive Scalar Gravity, Neutrino, Electromagnetic, Yang-Mills and Gravitational Theories

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The British Journal for the Philosophy of Science, ISSN: 0007-0882, Vol: 62, Issue: 2, Page: 259-299

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Pitts, J. Brian
Oxford University Press (OUP), Oxford University Press
Arts and Humanities
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Classical and quantum field theory provide not only realistic examples of extant notions of empirical equivalence, but also new notions of empirical equivalence, both modal and occurrent. A simple but modern gravitational case goes back to the 1890s, but there has been apparently total neglect of the simplest relativistic analog, with the result that an erroneous claim has taken root that Special Relativity could not have accommodated gravity even if there were no bending of light. The fairly recent acceptance of nonzero neutrino masses shows that widely neglected possibilities for nonzero particle masses have sometimes been vindicated. In the electromagnetic case, there is permanent underdetermination at the classical and quantum levels between Maxwell's theory and the one-parameter family of Proca's electromagnetisms with massive photons, which approximate Maxwell's theory in the limit of zero photon mass. While Yang-Mills theories display similar approximate equivalence classically, quantization typically breaks this equivalence. A possible exception, including unified electroweak theory, might permit a mass term for the photons but not the Yang-Mills vector bosons. Underdetermination between massive and massless (Einstein) gravity even at the classical level is subject to contemporary controversy. 1Introduction2Types of Inexact Empirical Equivalence3Approximate Empirical Equivalence4Approximate Empirical Equivalence in Scalar Gravity: the Neglected Rivalry5Massive Spinor Fields: The Neutrino Case6Approximate Empirical Equivalence in Electromagnetism6.1Proca massive versus Maxwell massless photons6.2Bayesian treatment of the photon mass6.3Possible inductive lessons about underdetermination in particle physics7No Approximate Equivalence in Yang-Mills Theories?8Approximate Equivalence in Electroweak Theory: Yang-Mills Theory with Essentially Abelian Sector9Is There Approximate Equivalence for Gravity? General Relativity and its Massive Variants10Conclusion © The Author 2010.

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