2006/06/27 by Yves Pierseaux, Dr Yves Pierseaux, Pierseaux, Dr Yves
Mathematics · Physics and Astronomy · #FOS: Physical sciences #General Physics (physics.gen-ph) #History and Theory of Mathematics #Mathematics and Applications #Relativity and Gravitational Theory #physics.gen-ph
paper · pdf · doi:10.48550/arxiv.physics/0606233
5 pages with 3 figures. Submitted to American Journal of Physics
arxiv created 2006/06/27 · openalex publication_date 2006/06/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The relativity of simultaneity implies that the image of a Lorentz transformed (LT) spherical (circular) wavefront is not a spherical (circular) wavefront (Einstein 1905) but an ellipsoidal (elliptical) wavefront (Moreau, Am.J.of Phys).We show firstly that the relativity of simultaneity leads to the consequence that the image of a Lorentz transformed plane wavefront is a tangent plane to an ellipsoid and not a tangent plane to a sphere (Einstein 1905). We deduce then a longitudinal component of the tangent vector to Poincare's ellipse which is directly connected to the relativity of simultaneity. We suggest finally that this violation of relativity of simultaneity is related to Einstein's implicit choice of the (non relativistic) transverse gauge in his theory of (rigid) wavefronts.