  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.
