Viewing the question in another way, we should notice that as a matter of fact the Newtonian principle of relativity merely states that velocity of matter with respect to matter alone has physical significance. Velocity of matter through empty space is physically meaningless. It is the same in Einstein’s special principle. Einstein’s theory proves (see next chapter) that molar matter can never move with the absolute speed of light. We are therefore perfectly justified in saying that the velocity of matter remains essentially relative, since it can never attain that critical velocity (i.e. that of light) which is absolute. [Pg 156] CHAPTER XIV RELATIVISTIC MECHANICS WE saw in the preceding chapter that the time and space variables which entered into the Lorentz-Einstein transformations should be considered of absolutely general validity. They were assumed to represent the duration actually sensed and lived by the observer and the spatial measurements actually determined by his rigid rods in his Galilean frame. It was no longer a case, as in Lorentz’s theory, of supposing that these space and time variables applied only in certain electromagnetic cases and not in others. They were now of absolutely general application, and in particular should hold for all mechanical phenomena. But this realisation brought us face to face with a peculiar difficulty. Einstein’s fundamental postulate was that Galilean motion was meaningless, or at least could never be detected by experiment—whether of a mechanical or electromagnetic nature. Now the complete relativity of Galilean motion is expressed mathematically by the invariance of form of the laws of nature for transformations corresponding to that type of motion. The classical laws of mechanics satisfied this requirement in classical science, since they remained invariant when submitted to the classical transformations. But if we accept Einstein’s views, these laws must remain invariant no longer to the classical transformations but to the Lorentz-Einstein ones. The classical laws of mechanics did not fulfil this new condition of invariance. From this it would appear that the relativity of Galilean motion which Einstein had succeeded in establishing for electrodynamic and optical experiments could be maintained only at the price of abandoning this same relativity for mechanical ones. What had been gained on one side had been lost on the other. Inasmuch as the laws of mechanics would certainly have to remain invariant to the Lorentz-Einstein transformations if absolute velocity were to remain meaningless, and inasmuch as the classical laws did not satisfy this condition, there was only one way out of the difficulty. It was necessary to assume that the classical laws were incorrect.