Philosophy

by Bertrand Russell

[CHAPTER XIV]
PERCEPTION AND PHYSICAL CAUSAL LAWS

In an earlier chapter we saw the inadequacy of the traditional notion of cause, without adequately explaining the causal laws which are a substitute in the practice of science. The time has now come when it is possible to remedy this defect, and, in so doing, to fit perception into its place in the chain of physical causation and recapitulate the main points of previous arguments.

The old view was that an event A will always be followed by a certain event B, and that the problem of discovering causal laws is the problem, given an event B, of finding that event A which is its invariable antecedent or vice versa. At an early stage of a science this point of view is useful; it gives laws which are true usually, though probably not always, and it affords the basis for more exact laws. But it has no philosophical validity, and is superseded in science as soon as we arrive at genuine laws. Genuine laws, in advanced sciences, are practically always quantitative laws of tendency. I will try to illustrate by taking the simplest possible case in physics.

Imagine a hydrogen atom, in which the electron is revolving not in the minimum orbit, but in the next, which has four times the minimum radius. So long as this state continues, the atom has no external effects, apart from its infinitesimal gravitational action; we cannot, therefore, obtain any evidence of its existence except when it changes its state. In fact, our knowledge of atoms is like that which a ticket collector has of the population of his town: he knows nothing of those who stay quietly at home. Now at some moment, according to laws of which we have only statistical knowledge, the electron in our atom jumps to a smaller orbit, and the energy lost to the atom travels outward in a light-wave. We know no causal law as to when the electron will jump, though we know how far it will jump and exactly what will happen in the neighbourhood when it does. At least, when I say we know exactly what will happen, I ought to say that we know exactly the mathematical laws of what will happen. A series of events, having quantitative characteristics which obey certain equations, will travel outward in all directions from the electron, and will proceed quite regularly, like ripples on a pool, until other matter is encountered. We have here one important and apparently fundamental kind of causal law, the kind regulating the propagation of light in vacuo. This is summed up in Maxwell’s equations, which enable us to calculate the diffusion of an electro-magnetic disturbance starting from a source. So long as two such disturbances do not meet, the matter is exceedingly simple; but the equations also tell us what happens when they do meet. We then have, as always in traditional physics, two separate tendencies, which have a resultant compounded according to mathematical laws, of which the parallelogram law is the oldest and simplest. That is to say, each previous circumstance in the space-time neighbourhood contributes a tendency, and the resulting event is obtained by compounding these tendencies according to a mathematical law.

So far, we have been considering only electro-magnetic phenomena in empty space. We have another set of facts about empty space, namely those upon which gravitation depends. These have to do with the structure of space-time, and show that this structure has singularities in the regions where there is matter, which spread with diminishing intensity as we get away from these regions. You may conceive the structure of space-time on the analogy of a pond with a fountain playing in it, so that wherever a spray falls from the fountain there is a little hill of water which flattens quickly as you get away from the spot where the spray falls. Here again the same sort of thing applies: to infer the structure in a small region of space-time from that in the neighbourhood, it will be necessary to superpose a number of tendencies according to mathematical rules. Thus philosophically this introduces no novelty.

But now consider what happens when the wave of light which started from our hydrogen atom comes in contact with matter. Various things may happen. The matter may absorb all or some of the energy of the light-ray; this is the interesting case from our point of view. The absorption may take the form of causing the electrons to move in larger orbits, in which case, later, when they return to their previous orbits, we get the phenomenon of fluorescence. Or the body may become heated; or it may visibly move, like a radiometer. The effects upon bodies depend upon the bodies as well as the light. Some of them can be individually predicted, others can only be calculated in statistical averages; this depends upon whether quantum considerations come in or not. Where they do, we can enumerate possibilities, and state the relative frequencies with which they will be realised, but we cannot tell which will be realised in any given case.

So far, we have considered the radiation of energy from matter into empty space, its propagation in empty space and its impact on matter from empty space. We have not considered the history of a given piece of matter, or the distinction between matter and empty space.

The essence of matter appears to be this: We can distinguish series of events in space-time which have a certain kind of close resemblance to each other, such that common sense regards them as manifestations of one “thing”. But when we look closely at the question, it turns out that what physics offers is something more abstract than this. Take, e. g. the continued existence of a certain electron. This means to say that events in a certain neighbourhood will be such as can be calculated on the assumption that there is an electric charge of a certain standard magnitude in the middle of that neighbourhood; and that the neighbourhoods of which this is true form a tube in space-time.

So long as we stick to the standpoint of pure physics there is a certain air of taking in each other’s washing about the whole business. Events in empty space are only known as regards their abstract mathematical characteristics; matter is only an abstract mathematical characteristic of events in empty space. This seems rather a cold world. But as a matter of fact we know some things that are a little more concrete. We know, e.g. what it feels like when we see things. From the point of view of physics, when our light-wave starts out through empty space, if it presently reaches our eye we know one link in the causal chain, namely the visual sensation, otherwise than as a term in an abstract mathematical formula. And it is this one term which forms the basis for our belief in all the rest. Seeing is believing.

At this point I propose to make a brief digression on the subject of our evidence for causal laws. The laws for which we first get evidence are such as do not hold always, but only as a general rule. As a rule, when you decide to move your arm, it moves: but sometimes it is paralysed and remains motionless. As a rule, when you say how-do-you-do to an old friend, he says the same to you; but he may have grown blind and deaf since you last saw him, and not notice your words or gesture. As a rule, if you put a match to gunpowder, it explodes; but it may have got damp. It is such common but not invariable rules of sequence that we notice first. But science is always seeking to replace them by laws that may have no exceptions. We notice first that heavy bodies fall, then that some bodies do not fall. Then we generalise both sets of facts into the law of gravitation and the laws of resistance of the air. These more general laws do not state that anything will actually happen: they state a tendency, and lead to the conclusion that what actually happens is the resultant of a number of tendencies. We cannot know what the resultant will be unless we know a great deal about the neighbourhood concerned. For example, I might, within the next few seconds be hit on the head by a meteorite; to know whether this is going to happen, I must know what matter is to be found in the neighbourhood of the earth. This illustrates that actual predictions based upon laws which are perfectly valid may always be falsified by some unknown fact of what we may call geography. Moreover, we can never be sure that our scientific laws are quite right; of this the Einsteinian modification of the law of gravitation has afforded a notable instance.