Inter-Theory Relations in Physics: Case Studies from Quantum Mechanics and Quantum Field Theory

Abstract: 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 I argue that one traditional approach to theory reduction in physics, founded on the notion that a superseded theory should simply be a mathematical limit of the theory that supersedes it, is misleading as a general picture of the relationship whereby one theory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.