  The relationship that is widely presumed to hold between physical theories
and their successors, in which the successors in some sense explain the success
of the theories they replace, is known commonly as 'reduction.' I argue that
one traditional approach to theory reduction in physics, founded on the notion
that a superseded theory should simply be a mathematical limit of the theory
that supersedes it, is misleading as a general picture of the relationship
whereby one theory encompasses the domain of empirical validity of another. I
defend an alternative account that builds upon a certain general type of
relationship between dynamical systems models describing the same physical
system. I demonstrate how this particular relationship resembles the
methodological prescriptions set out by Ernest Nagel's more general approach to
reduction across the sciences.
  After clarifying these points of general methodology, I go on to apply this
approach to a number of particular inter-theory reductions in physics involving
quantum theory. I consider three reductions: first, connecting classical
mechanics and non-relativistic quantum mechanics; second, connecting classical
electrodynamics and quantum electrodynamics; and third, connecting
non-relativistic quantum mechanics and quantum electrodynamics. In all cases, a
certain core set of mechanisms, employing decoherence together with variations
of Ehrenfest's Theorem, serves to underwrite the occurrence of approximately
classical behavior. For concreteness, I consider two particular realist
interpretations of quantum theory - the Everett and Bohm theories - as
potential bases for these reductions. However, many of the technical results
concerning these reductions pertain also more generally to the bare,
uninterpreted formalism of quantum theory.
