Page:Russell - An outline of philosophy.pdf/134

122 Common sense says: thunder follows lightning, waves at sea follow wind, and so on. Rules of this sort are indispensable in practical life, but in science they are all only approximate. If there is any finite interval of time, however short, between the cause and the effect, something may happen to prevent the effect from occurring. Scientific laws can only be expressed in differential equations. This means that, although you cannot tell what may happen after a finite time, you can say that, if you make the time shorter and shorter, what will happen will be more and more nearly according to such-and-such a rule. To take a very simple case: I am now in this room; you cannot tell where I shall be in another second, because a bomb may explode and blow me sky-high, but if you take any two small fragments of my body which are now very close together, you can be sure that, after some very short finite time, they will still be very close together. If a second is not short enough, you must take a shorter time; you cannot tell in advance how short a time you may have to take, but you may feel fairly certain that there is a short enough time.

The laws of sequence in physics, apart from quantum phenomena, are of two sorts, which appeared in traditional dynamics as laws of velocity and laws of acceleration. In a very short time, the velocity of a body alters very little, and if the time is taken short enough, the change of velocity diminishes without limit. This is what, in the last chapter, we called an "intrinsic" causal law. Then there is the effect of the outer world, as it appeared in traditional dynamics, which is shown in acceleration. The small change which does occur in the velocity in a short time is attributed to surrounding bodies, because it is found to vary as they vary, and to vary according to ascertained laws. Thus we think of surrounding bodies as exerting an influence, which we call "force", though this remains as mysterious as the influence of the stars in astrology.

Einstein's theory of gravitation has done away with this conception in so far as gravitational forces are concerned. In this theory, a planet moving round the sun is moving in