Rethinking Newton's $\textit{Principia}$

TL;DR

This paper challenges the traditional view by arguing that Newton's Principia does not require inertial frames, but only the concept of parallelism of spatial directions over time, redefining the underlying space-time structure.

Contribution

It proposes a new interpretation of Newton's Principia, removing the necessity of inertial frames and emphasizing parallelism as the core structural concept.

Findings

Inertial frames are not essential in Newton's theory of motion.

The appropriate space-time structure relies solely on parallelism of spatial directions.

This reinterpretation simplifies the conceptual foundations of Newtonian mechanics.

Abstract

It is widely accepted that the notion of an inertial frame is central to Newtonian mechanics and that the correct space-time structure underlying $\text{Newton's}$ methods in $\textit{Principia}$ is neo-Newtonian or Galilean space-time. I argue to the contrary that inertial frames are not needed in $\text{Newton's}$ theory of motion, and that the right space-time structure for $\text{Newton's}$ $\textit{Principia}$ requires the notion of parallelism of spatial directions at different times and nothing more.