, whereas the light waves radiated by it will still possess a velocity
in all directions in our frame. It will then appear to us that the light waves are speeding away from the sphere in the direction of its motion with a velocity
while they are traveling with a speed
in the opposite direction. The conditions of light pressure will no longer be symmetrical, and calculation shows that the motion of the sphere should gradually slow down under the action of this resistance. Now this is impossible; for if the sphere appeared to us to be slowing down, it could never remain attached to its evenly moving Galilean frame, and we should be faced with a contradiction. As soon, however, as we recognise that the incandescent sphere by radiating light is losing energy and hence mass, the principle of the conservation of momentum shows that this gradual loss of mass would have for effect an increase in the velocity of the sphere and would thus compensate exactly the loss of velocity generated by the unsymmetrical light pressure. In this way the paradox is explained very simply.
[51] A further verification was afforded when the mechanism of Bohr’s atom was studied by Sommerfeld. In Bohr’s atom the electrons revolve round the central nucleus in certain stable orbits. Sommerfeld, by taking into consideration the variations in mass of the electrons due to their motions as necessitated by Einstein’s theory, proved that in place of the sharp spectral lines which had always been observed it was legitimate to expect that more accurate observation would prove these sharp lines to be bundles of very fine ones closely huddled together. These anticipations were confirmed by experiment both qualitatively and quantitatively.
[52] Whenever we refer to “another Galilean frame,” we invariably mean one in motion with respect to the first. Were it not in a state of relative motion, it would constitute the same frame.