Special Relativity: Einstein's Spherical Waves versus Poincare's Ellipsoidal Waves

摘要

We show that the image by the Lorentz transformation of a spherical(circular) light wave, emitted by a moving source, is not a spherical(circular) light wave but an ellipsoidal (elliptical) light wave. Poincare'sellipsoid (ellipse) is the direct geometrical representation of Poincare'srelativity of simultaneity. Einstein's spheres (circles) are the directgeometrical representation of Einstein's convention of synchronisation.Poincare adopts another convention for the definition of space-time unitsinvolving that the Lorentz transformation of an unit of length is directlyproportional to Lorentz transformation of an unit of time. Poincare'srelativistic kinematics predicts both a dilation of time and an expansion ofspace as well.