When, however, we consider the problem of motion, we shall find that in contradistinction to what holds for mathematical space, motion in physical space appears to be absolute. While it is true that from a purely visual standpoint the motion of a body will depend essentially on the frame of reference we select, and will vary when we change our frame from the earth to, say, the moon or the sun, yet owing to the generation of dynamical effects it is possible to decide in an absolute way whether the body is rotating or not. This is due to the fact that these telltale dynamical effects are present just the same regardless of our choice of a frame of reference. It was owing to these empirically discovered dynamical facts that Newton felt compelled to accept the absolute significance of motion, hence of space. We may gather from what has been said that we may not extend lightly to the physical space of experience the conclusions derived from conceptual mathematical space. We now come to a last point. Suppose that in mathematical space we wish to measure the distance between two objects moving in various ways through our frame. For our measurements to have any significance, we must of course specify that the positions of the two objects correspond to the same instant of time. If, therefore, a change in the relative motion of our frame of reference were assumed to cause a modification in our understanding of the sameness of a time at two different places, the distance between the two objects would vary with the frame in which we were reckoning it. But here we are discussing pure mathematical space, which we may always conceive of as divorced from time. Hence we may assume that the sameness of a time at two different places remains unaffected by any alteration in the choice of our frame. Classical science believed that the space of experience would also satisfy these conditions. It thought that time was absolute, that its rate of flow was ever the same, and that the concept of the sameness of a time at two different places was an absolute and unambiguous one. This assumption was tantamount to divorcing space from time and regarding them as two essentially different categories. It has been one of the triumphs of the relativity theory to disprove this fundamental thesis, and to show that in the real world of experience a continuum of space by itself is but a shadow. Henceforth the continuum of reality is space-time, a four-dimensional continuum of events, and no longer, as in classical science, a three-dimensional one of points, coupled with a one-dimensional continuum of instants. But inasmuch as the necessity for these new conceptions will be justified at length in future chapters, we shall refrain from discussing them at this stage. [Pg 47] CHAPTER IV THE PROBLEM OF PHYSICAL SPACE