Fundamental units of length and time

TL;DR

This paper explores the foundational concepts of length and time by defining ideal rods and clocks as infinitesimal spacetime symmetries, deriving all possible spacetime models without assuming a predefined geometry.

Contribution

It introduces a geometric approach to defining fundamental units of length and time based solely on spacetime symmetries, without prior geometric assumptions.

Findings

All possible spacetime models derived from infinitesimal symmetry principles

A unified framework for understanding length and time units

No reliance on predefined geometric structures

Abstract

Ideal rods and clocks are defined as an infinitesimal symmetry of the spacetime. Since no a priori geometric structure is considered, all the possible models of spacetime are obtained.