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Fundamental and Emergent Geometry in Newtonian Physics

Using as a starting point recent and apparently incompatible conclusions by Saunders ([2013]) and Knox ([2014]), I revisit the question of the correct spacetime setting for Newtonian physics. I argue that understood correctly, these two versions of Newtonian physics 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 Brown ([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. 1 Introduction 2 Newtonian Mechanics and Galilean Spacetime 3 Vector Relationism and Maxwellian Spacetime 4 Recovering the Galilei Group: Dynamics of Subsystems 5 Knox on Inertial Structure 6 Connections on Maxwellian Spacetime 7 Knox on Newtonian Gravity 8 Vector Relationism and Newton–Cartan Theory 9 Inertial Structure in Newton–Cartan Gravity 10 Reconciling Knox and Saunders 11 Conclusions 1 Introduction 2 Newtonian Mechanics and Galilean Spacetime 3 Vector Relationism and Maxwellian Spacetime 4 Recovering the Galilei Group: Dynamics of Subsystems 5 Knox on Inertial Structure 6 Connections on Maxwellian Spacetime 7 Knox on Newtonian Gravity 8 Vector Relationism and Newton–Cartan Theory 9 Inertial Structure in Newton–Cartan Gravity 10 Reconciling Knox and Saunders 11 Conclusions