We have now to consider a number of difficulties that arise from Newton’s conception of absolute space. In the first place, although Newton had postulated absolute space and motion, the fact remained that of all the absolute motions, absolute acceleration and rotation were the only ones that had ever been detected, at least by mechanical means. It seemed strange, if absolute velocity were to have a meaning, as indeed it must if space were absolute, that it should be so obstinate in refusing to reveal itself. We could not hold that our inability to discover which one of the Galilean frames was truly at rest was due to the crudeness of our mechanical experiments; for the entire structure of Newtonian mechanics would have come crashing down had any such suggestion been proved correct. The reason for this statement is easily understood. The fundamental law of Newtonian mechanics states that the force acting on a body is equal to the mass of the body (an invariant) multiplied by the acceleration. Now, the acceleration of a body as computed in any Galilean frame is always the same; for the various Galilean frames differ only in their velocity through absolute space, and a velocity added to or subtracted from an acceleration can never modify an acceleration. The mass of the body being an invariant according to classical mechanics, the force must also measure out the same in all Galilean frames. In other words, it was essential to classical science that the fundamental law of mechanics should remain the same in all Galilean frames, and similar conclusions would have to apply to all the mechanical laws. But then no mechanical experiment, however precise, executed in one Galilean frame or another, could ever yield varying results; so that absolute velocity could never be known. In short, if Newtonian science were to stand, the failure of mechanical experiments to detect the absolute velocity of our Galilean frame through space could never be attributed to their lack of refinement, since any positive results would have overthrown the entire structure of Newtonian dynamics. Here, then, was an absolute velocity which was a reality since space was absolute, but which on no account could ever manifest itself! It was, of course, possible to suggest that space had a dual structure, partly absolute and partly relative; absolute for rotation and acceleration, but relative for velocity. But this intrinsic duality in the nature of space and motion was hard to accept; it seemed as though space and motion should be one thing or the other: either entirely absolute or else entirely relative. Moreover, it was extremely difficult to conceive of a duality in the structure of space, so the [Pg 114] entire situation was most mysterious.