The Euclid space-time diagram of the theory of relativity

TL;DR

This paper introduces an Euclid space-time diagram for relativity that aligns with Euclidean geometry, making relativistic effects more intuitive and providing a new way to analyze phenomena like clock dilation and length contraction.

Contribution

It proposes a novel Euclid-based space-time diagram that accurately represents relativistic effects and offers improved intuition over traditional Minkowski diagrams.

Findings

Euclid space-time diagram accurately models relativistic effects

The diagram simplifies understanding of clock dilation and length contraction

Application to satellite clocks demonstrates practical utility

Abstract

A conventional space-time diagram is $r-ct$ one, which satisfies the Minkowski geometry. This geometry conflict the intuition from the Euclid geometry. In this work an Euclid space-time diagram is proposed to describe relativistic world lines with an exact Euclid geometry. The relativistic effects such as the dilation of moving clocks, the contraction of moving length, and the twin paradox can be geometrically expressed in the Euclid space-time diagram. It is applied to the case of a satellite clock to correct the gravitational effect. It is found that this Euclid space-time diagram is much more intuitive than the conventional space-time diagram.