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A Case-by-case Derivation of the Lorentz Transformation Equations

Author:

Giesecke, Gerald L

Category:

Research Papers

Sub-Category:

Relativity Theory

Language:

English

Date Published:

May 11, 2026

File:

/Research Papers-Relativity Theory/Download/10546

Downloads:

Keywords:

Special Relativity, Lorentz Transformation Equations, Minkowski Diagrams

Abstract:

This derivation considers a train moving to the right with two unidirectional flashes of light: one originating on the train and one originating on the stationary platform. Both flashes move perpendicularly to the path of the train. Using this setup, the derivation shows that the Lorentz transformation equations are valid for all finite values of time and position. The paper also represents each of the transformation equations as a plane in a 3-dimentional space. This makes it easier to see how the times in both reference frames can be initialized to zero, even though the Lorenz transformation equations allow only one event to have a time of zero in both inertial reference frames. The 3-dimensional representations of the transformation equations can also be used to construct 2-dimensional Minkowski diagrams.

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