The logic of modern physics

by P. W. Bridgman

We may now go still further. Operations themselves are, of course, derived from experience, and would be expected also to have a nebulous edge of uncertainty. We have to ask such questions as whether the operations of arithmetic are clean-cut things. Is the operation of multiplying 2 objects by 2 a definite operation, with no enveloping haze? All our physical experience convinces us that if there is a penumbra about the concept of operations of this sort it is so tenuous as to be negligible, at least for the present; but the question affords an interesting topic for speculation. We also have to ask whether mental operations may similarly be enveloped in a haze.

EXPLANATIONS AND MECHANISMS

Perhaps the climax of our task of interpreting and correlating nature is reached when we are able to find an explanation of phenomena; with the finding of the explanation we are inclined to feel that our understanding of the situation is complete. We now have to ask what is the nature of the explanation which we set as the goal of our efforts. The answer is not easy to give, and there may be difference of opinion about it. We shall get the best answer to this, as to so many other questions, by adopting the operational point of view, and examining what we do in giving an explanation. I believe that examination will show that the essence of an explanation consists in reducing a situation to elements with which we are so familiar that we accept them as a matter of course, so that our curiosity rests.[5] "Reducing a situation to elements" means, from the operational point of view, discovering familiar correlations between the phenomena of which the situation is composed.

[5]The ultimate elements of explanation are analogous to the axioms of formal mathematics.

There is involved here the thesis that it is possible to analyze nature into correlations, without, however, any assumption whatever as to the character of these correlations. It seems to me that such a thesis is the most general that can be made if nature is to be intelligible at all. This thesis underlies all the considerations of this essay, and we shall not try to find anything more general. We shall, however, recognize that any assumption as to the character of the correlations constitutes a special hypothesis which may restrict the future, and that therefore these special hypotheses are to be subjected to special examination. We return to this matter in more detail in discussing the causality concept, which is closely related to the concept of explanation.

In this view of explanation there is no implication that the "element" is either a smaller or a larger scale thing than the phenomenon being explained; thus we may explain the properties of a gas in terms of its constituent molecules, or perhaps some day we shall become so familiar with the idea of a non-Euclidean space that we shall explain (instead of describe) the gravitational attraction of a stone by the earth in terms of a space-time curvature imposed by all the rest of the matter in the universe.

If this is accepted as the true nature of explanation, we see that an explanation is not an absolute sort of thing, but what is satisfactory for one man will not be for another. The savage is satisfied by explaining the thunderstorm as the capricious act of an angry god. The physicist demands more, and requires that the familiar elements to which we reduce a situation be such that we can intuitively predict their behavior. Thus even if the physicist believed in the existence of the angry god, he would not be satisfied with this explanation of the thunderstorm because he is not so well acquainted with angry gods as to be able to predict when anger is followed by a storm. He would have to know why the god had become angry, and why making a thunderstorm eased his ire. But even with this additional qualification, scientific explanation is obviously still a relative affair—relative to the elements or axioms to which we make reduction and which we accept as ultimate. These elements depend to a certain extent on the purpose in view, and also on the range of our previous physical experience. If we are explaining the action of a machine, we are satisfied to reduce the action to the push and pull of the various members of the machine, it being accepted as an ultimate that these members transmit pushes or pulls. But the physicist who has extended his experimental knowledge further, may want to explain how the members transmit pushes or pulls in terms of the action on each other of the electrons in their orbits in the atoms. The character of our explanatory structure will depend on the character of our experimental knowledge, and will change as this changes.

Formally, there is no limit to the process of explanation, because we can always ask what is the explanation of the elements in terms of which we have given the last explanation. But the point of view of operations shows that this is mere formalism which ends only in meaningless jargon, for we soon arrive at the limit of our experimental knowledge, and beyond this the operations involved in the concepts of our explanations become impossible and the concepts become meaningless.

As we extend experimental knowledge and push our explanations further and further, we see that the explanatory sequence may be terminated in several possible ways. In the first place, we may never push our experiments beyond a stage into which the elements with which we are already familiar do not enter. In this case explanation is very simple: it involves nothing essentially new, but merely the disentanglement of complexities. The kinetic theory of gases, in explaining the thermal properties of a gas in terms of ordinary mechanical properties of the molecules, suggests such a situation. Or, secondly, our experiments may bring us into contact with situations novel to us, in which we can recognize no familiar elements, or at least must recognize that there is something in addition to the familiar elements. Such a situation constitutes an explanatory crisis and explanation has to stop by definition. Or thirdly, we may try to force our explanations into a predetermined mold, by formally erecting or inventing beyond the range of present experiment ultimates more or less like elements already familiar to us, and seek to explain all present experience in terms of these chosen ultimates.

Leaving for the present the third possibility, which is within our control to accept or reject, and is a formal matter, it is merely a question of experimental fact which of the first two possibilities corresponds to the actual state of affairs. The most perfunctory examination of the present state of physics shows that we are now facing the second of these possibilities, and that in the new experimental facts of relativity, and in all quantum phenomena, we are confronted with an explanatory crisis. It has often been emphasized that Einstein's theory of gravitation does not seek at all to give an explanation of gravitational phenomena, but merely describes and correlates these phenomena in comparatively simple mathematical language. No more attempt is made to reduce the gravitational attraction between the earth and the sun to simple terms than was made by Newton. In the realm of quantum phenomena it is of course the merest commonplace that our old ideas of mechanics and electrodynamics have failed, so that it is a matter of the greatest concern to find how many, or indeed whether any, elements of the old situations can be carried over into the new.