Page:The principle of relativity (1920).djvu/75



At the present time, different opinions are being held about the fundamental equations of Electro-dynamics for moving bodies. The Hertzian forms must be given up, for it has appeared that they are contrary to many experimental results.

In 1895 H. A. Lorentz published his theory of optical and electrical phenomena in moving bodies; this theory was based upon the atomistic conception (vorstellung) of electricity, and on account of its great success appears to have justified the bold hypotheses, by which it has been ushered into existence. In his theory, Lorentz proceeds from certain equations, which must hold at every point of "Äther"; then by forming the average values over "Physically infinitely small" regions, which however contain large numbers of electrons, the equations for electro-magnetic processes in moving bodies can be successfully built up.

In particular, Lorentz's theory gives a good account of the non-existence of relative motion of the earth and the luminiferous "Äther"; it shows that this fact is intimately connected with the covariance of the original equation, when certain simultaneous transformations of the space and time co-ordinates are effected; these transformations have therefore obtained from H. Poincare the name of Lorentz-transformations. The covariance of these fundamental equations, when subjected to the Lorentz-transformation is a purely mathematical fact i.e. not based on any physical considerations; I will call this the Theorem of Relativity; this theorem rests essentially on the form of the