Fundamental and emergent geometry in Newtonian physics

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Wallace, David
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Using as a starting point recent and apparently incompatible conclusions by Simon Saunders (Philosophy of Science 80 (2013) pp.22-48) and Eleanor Knox (British Journal for the Philosophy of Science 65 (2014) pp.863-880), I revisit the question of the correct spacetime setting for Newtonian physics. I argue that understood correctly, these two theories make the same claims both about the background geometry required to define the theory, and about the inertial structure of the theory. In doing so I illustrate and explore in detail the view --- espoused by Knox, and also by Harvey Brown (Physical Relativity, OUP 2005) --- that inertial structure is defined by the dynamics governing subsystems of a larger system. This clarifies some interesting features of Newtonian physics, notably (i) the distinction between using the theory to model subsystems of a larger whole and using it to model complete Universes, and (ii) the scale-relativity of spacetime structure.