Abstract

Einstein's transformation equations are believed to be mathematically correct in part due to the Spherical Wave Proof that Einstein offers in each of his derivations. Einstein asserts that if an electromagnetic wave is propagated as a Sphere in system K that the wave will also be represented as a Sphere in system K', where the values of the Sphere in K' are determined using the transformation equations. The proof asserts a one-to-one mapping between the points representing the Sphere in K and the points representing the Sphere in K'. Here we find that Einstein's proof shows that the transformed values conform to the general equation of a Sphere in K', but that his proof does not validate that all of the transformed points are part of the same Sphere in K'. We then show that the proof fails because the transformed K' values have different radii and represent points on multiple spheres in K', instead of on a single sphere.