Smoothing the Speed of Light
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| Format: | Recurso digital |
| Sprache: | Englisch |
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2025
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| _version_ | 1866901038204715008 |
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| 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 |