Possibility of a Fully Satisfactory Spacetime Structure Weaker Than Galilean Spacetime

Determine whether Newtonian dynamics can be formulated in a fully satisfactory way using a spacetime structure weaker than Galilean spacetime, particularly one invariant under transformations that map between unaccelerated and uniformly accelerated trajectories.

Background

The paper compares its geometrical reconstruction of the gauge argument with the Weyl-Stein argument that Newtonian dynamics requires Galilean spacetime rather than Newtonian spacetime. Galilean spacetime retains a compatible derivative operator while dispensing with Newtonian spacetime’s preferred standard of rest.

The authors note that Newtonian dynamics is invariant under additional transformations associated with uniformly accelerated trajectories, raising the possibility that an even weaker spacetime structure might suffice. They identify as unresolved whether such a reduction can be achieved in a fully satisfactory manner, while observing that structures with too little geometric content, such as Leibnizian spacetime, fail to support the dynamics.