Authors
Joshua Rosaler
Oxford University
Abstract
I defend three general claims concerning inter-theoretic reduction in physics. First, the popular notion that a superseded theory in physics is generally a simple limit of the theory that supersedes it paints an oversimplified picture of reductive relations in physics. Second, where reduction specifically between two dynamical systems models of a single system is concerned, reduction requires the existence of a particular sort of function from the state space of the low-level model to that of the high-level model that approximately commutes, in a specific sense, with the rules of dynamical evolution prescribed by the models. The third point addresses a tension between, on the one hand, the frequent need to take into account system-specific details in providing a full derivation of the high-level theory’s success in a particular context, and, on the other hand, a desire to understand the general mechanisms and results that under- write reduction between two theories across a wide and disparate range of different systems; I suggest a reconciliation based on the use of partial proofs of reduction, designed to reveal these general mechanisms of reduction at work across a range of systems, while leaving certain gaps to be filled in on the basis of system-specific details. After discussing these points of general methodology, I go on to demonstrate their application 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. I approach these reductions from a realist perspective, and for this reason consider two realist interpretations of quantum theory - the Everett and Bohm theories - as potential bases for these reductions. Nevertheless, many of the technical results concerning these reductions pertain also more generally to the bare, uninterpreted formalism of quantum theory. Throughout my analysis, I make the application of the general methodological claims of the thesis explicit, so as to provide concrete illustration of their validity.
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References found in this work BETA

Is Classical Electrodynamics an Inconsistent Theory?Gordon Belot - 2007 - Canadian Journal of Philosophy 37 (2):263-282.
Bohmian Trajectories Post-Decoherence.D. M. Appleby - 1999 - Foundations of Physics 29 (12):1885-1916.
On the Classical Limit in Bohm’s Theory.Gary E. Bowman - 2005 - Foundations of Physics 35 (4):605-625.
Generic Bohmian Trajectories of an Isolated Particle.D. M. Appleby - 1999 - Foundations of Physics 29 (12):1863-1883.

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Citations of this work BETA

Interpretation Neutrality in the Classical Domain of Quantum Theory.Joshua Rosaler - 2016 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 53:54-72.
Reduction as an a Posteriori Relation.Joshua Rosaler - 2019 - British Journal for the Philosophy of Science 70 (1):269-299.
Lost horizon? – modeling black holes in string theory.Nick Huggett & Keizo Matsubara - 2021 - European Journal for Philosophy of Science 11 (3):1-19.
The Homunculus Brain and Categorical Logic.Steve Awodey & Michał Heller - 2020 - Philosophical Problems in Science 69:253-280.

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