Caspar Jacobs (Merton College): How (Not) to Define Inertial Frames

#SigmaClub​​​ | 30 January 2023
It is nearly impossible to open a textbook on Newtonian mechanics without encountering the concept of inertial frames: frames which are uniquely privileged by the theory’s dynamics. In this paper, I argue that extant definitions of inertial frames are unsatisfactory. I criticise two common definitions of inertial frames: law-based definitions, according to which inertial frames are simply those in which the laws are true (in their simplest form), and structure-based definitions, according to which inertial frames are those that are `adapted’ to spacetime structure. Both definitions misclassify certain non-Newtonian worlds as Newtonian. I then offer a new, symmetry-based definition of inertial frames. This definition follows from the dynamical symmetries of Newtonian mechanics, and so offers a non-conventional way of specifying the dynamically privileged frames. This result clarifies the foundations of Newtonian mechanics and accounts for the empirical success of coordinate-dependent formulations of it.
Caspar Jacobs is a junior research fellow at Merton College, University of Oxford. His main research areas are philosophy of physics and philosophy of science. He’s also interested in the metaphysics of quantities, and in Early Modern history and philosophy of science.