Smoothing the Speed of Light

Fuente: Zenodo
Gespeichert in:
Bibliographische Detailangaben
1. Verfasser: Hall, Matthew
Format: Recurso digital
Sprache:Englisch
Veröffentlicht: Zenodo 2025
Schlagworte:
Online-Zugang:
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
_version_ 1866901038204715008
author Hall, Matthew
author_facet Hall, Matthew
contents <p>This paper addresses a long-standing misconception in the teaching of relativity: the apparent “break” at the speed of light. Traditional presentations emphasize the divergence of the Lorentz factor and the vanishing of proper time as velocity approaches <span><span>cc</span><span><span><span>c</span></span></span></span>, leading to the impression that light’s motion is discontinuous. This work shows that such a break is not physical, but a result of parametrization choices. Using rapidity for timelike motion and affine parameters for null motion, the discontinuity is removed and trajectories become smooth. The analysis is carried out entirely within established relativity and electrodynamics, without introducing new fields. The geometric-optics limit of Maxwell’s theory yields the eikonal equation, identifying light rays as null geodesics, while the Gordon optical metric extends this result to refractive media and curved spacetime. The paper demonstrates that the speed-of-light limit reflects a coordinate artifact, not a breakdown of physics. This clarification reinforces the geometric continuity of light’s path and strengthens the pedagogical and conceptual foundations of relativity. Artificial intelligence tools were used to assist with algebraic checks and drafting, while all scientific interpretations and conclusions remain the responsibility of the author.</p>
format Recurso digital
id zenodo_https___doi_org_10_5281_zenodo_17081378
institution Zenodo
language eng
publishDate 2025
publisher Zenodo
record_format zenodo
spellingShingle Smoothing the Speed of Light
Hall, Matthew
special relativity
null geodesics
rapidity
affine parameter
eikonal approximation
Maxwell equations
Gordon metric
optical metric
pedagogy in physics
<p>This paper addresses a long-standing misconception in the teaching of relativity: the apparent “break” at the speed of light. Traditional presentations emphasize the divergence of the Lorentz factor and the vanishing of proper time as velocity approaches <span><span>cc</span><span><span><span>c</span></span></span></span>, leading to the impression that light’s motion is discontinuous. This work shows that such a break is not physical, but a result of parametrization choices. Using rapidity for timelike motion and affine parameters for null motion, the discontinuity is removed and trajectories become smooth. The analysis is carried out entirely within established relativity and electrodynamics, without introducing new fields. The geometric-optics limit of Maxwell’s theory yields the eikonal equation, identifying light rays as null geodesics, while the Gordon optical metric extends this result to refractive media and curved spacetime. The paper demonstrates that the speed-of-light limit reflects a coordinate artifact, not a breakdown of physics. This clarification reinforces the geometric continuity of light’s path and strengthens the pedagogical and conceptual foundations of relativity. Artificial intelligence tools were used to assist with algebraic checks and drafting, while all scientific interpretations and conclusions remain the responsibility of the author.</p>
title Smoothing the Speed of Light
topic special relativity
null geodesics
rapidity
affine parameter
eikonal approximation
Maxwell equations
Gordon metric
optical metric
pedagogy in physics
url https://doi.org/10.5281/zenodo.17081378