Timeless Relativistic Approach to Classical Mechanics

TL;DR

This paper introduces a timeless relativistic reformulation of classical mechanics using binate frames, providing a new perspective that unifies classical and relativistic descriptions without clocks, and offers novel solutions for mass-spring systems.

Contribution

It presents a new class of inertial reference frames called binate frames, enabling a timeless relativistic approach to classical mechanics applicable at all energy levels.

Findings

Binate frames are inertial and adaptable to relative motions.

The approach yields harmonic solutions for mass-spring systems at rest, contrasting with traditional anharmonic predictions.

The reformulation unifies classical and relativistic mechanics without reliance on clocks.

Abstract

We reformulate Classical Mechanics as a timeless relativistic theory. Readers are introduced to a new class of reference systems, the binate frames, where physical events are identified with four position-coordinates -- no clocks are used. The binate frames are inertial and adaptable to relative motions. Analyses that use binate frames are valid at all energy levels. When desirable to do so, the results are easily expressed as in special relativity, in terms of space and time coordinates of inertial observers. Given the importance of mass-and-spring systems to theoretical physics, we analyzed such a system. Published special relativistic solutions predict anharmonic oscillations, but in the inertial frame where the mass-and-spring system (as a whole) is at rest, our solution is harmonic with energy-dependent angular frequency.