Page:Eddington A. Space Time and Gravitation. 1920.djvu/103

V] further test must be applied—whether the law is confirmed by observation.

The irrelevance of the mesh-system to the laws of nature is sometimes expressed in a slightly different way. There is one type of observation which, we can scarcely doubt, must be independent of any possible circumstances of the observer, namely a complete coincidence in space and time. The track of a particle through four-dimensional space-time is called its world-line. Now, the world-lines of two particles either intersect or they do not intersect; the standpoint of the observer is not involved. In so far as our knowledge of nature is a knowledge of intersections of world-lines, it is absolute knowledge independent of the observer. If we examine the nature of our observations, distinguishing what is actually seen from what is merely inferred, we find that, at least in all exact measurements, our knowledge is primarily built up of intersections of world-lines of two or more entities, that is to say their coincidences. For example, an electrician states that he has observed a current of 5 milliamperes. This is his inference: his actual observation was a coincidence of the image of a wire in his galvanometer with a division of a scale. A meteorologist finds that the temperature of the air is 75°; his observation was the coincidence of the top of the mercury-thread with division 75 on the scale of his thermometer. It would be extremely clumsy to describe the results of the simplest physical experiment entirely in terms of coincidence. The absolute observation is, whether or not the coincidence exists, not when or where or under what circumstances the coincidence exists; unless we are to resort to relative knowledge, the place, time and other circumstances must in their turn be described by reference to other coincidences. But it seems clear that if we could draw all the world-lines so as to show all the intersections in their proper order, but otherwise arbitrary, this would contain a complete history of the world, and nothing within reach of observation would be omitted.

Let us draw such a picture, and imagine it embedded in a jelly. If we deform the jelly in any way, the intersections will still occur in the same order along each world-line and no additional intersections will be created. The deformed jelly will represent a history of the world, just as accurate as the one