The evolution of scientific thought from Newton to Einstein

by A. D'Abro

and

the space and time separations, as measured from the embankment and the train, respectively, we should have found that

Here, then, was the expression of the space-time distance between the two events, or rather of its square. It is the fact that our measurements would have verified the invariance of this distance, which permits us to consider space and time as amalgamated. It cannot be too strongly emphasised that our clocks and rods would have been the ordinary clocks and rods of classical science. They would not have been adjusted so as to force relativistic results, as is often erroneously supposed; for had this been the case the theory would have been artificial and worthless. All that the theory suggests, therefore, is that our ordinary rods and clocks do not behave quite as we used to believe they did.[159]

We see, then, that the juxtaposition of space and time in classical science was just as artificial as a juxtaposition of space and temperature would have been. In short, the reality of space-time arises from Minkowski’s discovery that it was possible to define an invariant distance between two points in space-time, holding for all observers; and that it was impossible to define any such invariant distance in space alone or in time alone, showing that space and time by themselves were phantoms. These last two concepts must henceforth be considered jointly, and no longer as separate entities.

Now it is apparent that if the model of space-time is to spare us from a conflict with certain fundamental facts of consciousness it is imperative that some kind of mathematical difference should distinguish time directions from space directions. However, we need not anticipate any difficulties from the space-time model on this score; for we know that, owing to the heterogeneity which exists between time directions and space directions, space-time is anisotropic. Bearing this peculiarity in mind, we see that space-time around any point-event can be split up into a bundle of time directions and into bundles of space directions; these, however, can never overlap with the time-bundle. Then, from this bundle of possible time directions, every observer will select that particular line which constitutes his world-line through space-time. As for the flow of psychological time, or the duration between two psychological events measured by a clock at our side, it will be given by the space-time length of our world-line limited by those two events. Thus, two world-lines of equal length will always correspond to the same duration of time lived by the observers who follow these world-lines. For instance, of two identical sodium atoms, one near the sun and one far away, the solar atom will beat a slower time; but with both atoms the segments of the world-lines limited by successive vibrations will be the same in length. The existence of the Einstein shift-effect has verified this fact, and it is equivalent to stating that the atoms behave like perfect clocks.

So far as an observer’s three space directions are concerned, they will be perpendicular to his world-line or time direction. If his time direction is curved owing to his acceleration or to the intrinsic curvature of space-time due to matter, the space and time directions will be properly determined as perpendicular to one another only in the immediate vicinity of the observer. Elsewhere a definition of orthogonality, or perpendicularity will be impossible; as a result the very concepts of time and space become blurred in the general theory, and we have to content ourselves with co-ordinate systems which constitute measurements neither in space nor in time. We cannot dwell on this type of difficulty because it necessitates explanations of too technical a nature; suffice it to say that it is this complication that causes all problems connected with rotating disks and gravitational fields to suffer from a certain measure of obscurity when we attempt to interpret them in terms of space and time. We may also add that when large masses are moving about, the concept of simultaneity throughout space even for a given observer loses all precise significance.

The great difference between our present views and those of classical science is that whereas in classical science our lines of time-reckoning and of space-reckoning were unique, they now offer an indefinite number of possible alternatives, because of the plurality of time and space directions present in space-time. It is as though the flow of time were represented no longer by a single stream, but by a number of branches radiating from every point in different directions. In spite of this ambiguity in the possible space and time directions, we have seen that to each and every observer a definite space and time separation will correspond; so that all ambiguity disappears[160] as soon as we have defined the observer.

The strange results and concepts which the theory of relativity has disclosed have been appealed to by a number of writers in order to justify an ultra-idealistic philosophy of nature. These men have concluded that the real objective universe about which scientists were never weary of talking had been dashed to the ground and that realistic science had finally surrendered to the idealistic school of philosophy. This expression of opinion results from a confusion between the point of view of science and that of the metaphysical realist.