Extending the abilities of the Minkowski spacetime diagram

TL;DR

This paper introduces a method to extend Minkowski spacetime diagrams so that Euclidean lengths on the diagram accurately represent physical quantities across all inertial frames, enabling easier visualization of relativistic effects.

Contribution

The paper derives a factor to convert Euclidean lengths on the diagram into true physical values for any inertial observer, enhancing the diagram's utility.

Findings

Allows inference of Lorentz contraction and time dilation from diagrams

Enables use of simple trigonometry to understand relativistic effects

Provides a unified method for visualizing spacetime transformations

Abstract

A two-dimensional Minkowski spacetime diagram is neatly represented on a Euclidean ordinary plane. However the Euclidean lengths of the lines on the diagram do not correspond to the true values of physical quantities in spacetime, except for those referring to the stationary reference frame. In order to extend its abilities to other inertial reference frames, we derive a factor which, multiplied by the magnitude of the actually displayed values (on the diagram), leads to the corresponding true measured values by any other inertial observers. Doing so, the student can infer from the Euclidean diagram plot the expressions that account for Lorentz length contraction, time dilation and also Lorentz Transformations just by using regular trigonometry.