The logic of modern physics

by P. W. Bridgman

An examination of many of the so-called "explanations" of quantum theory constitutes at once a justification of the definition of explanation given above, and of the statement that in quantum phenomena we are at an explanatory crisis. For the endeavor of all these quantum explanations is to find in every new or more complicated situation the same elements which have already been met in simpler situations, and which are therefore relatively more familiar. For example, many quantum phenomena are made to involve the emission of energy when an electron jumps from one orbit to another. But always the elements to which reduction is made are themselves quantum phenomena, and these are still so new and unfamiliar that we feel an instinctive need for explanation in other terms. We seek to understand why the electron emits when it jumps.

The explanatory crisis which now confronts us in relativity and quantum phenomena is but a repetition of what has occurred many time in the past. A similar crisis confronted Prometheus when he discovered fire, and the first man who observed a straw sticking to a piece of rubbed amber, or a suspended lodestone seeking the north star. Every kitten is confronted with such a crisis at the end of nine days. Whenever experience takes us into new and unfamiliar realms, we are to be at least prepared for a new crisis.

Now what are we to do in such a crisis? It seems to me that the only sensible course is to do exactly what the kitten does, namely, to wait until we have amassed so much experience of the new kind that it is perfectly familiar to us, and then to resume the process of explanation with elements from our new experience included in our list of axioms. Not only will observation show that this is what is now actually being done with respect to quantum and gravitational phenomena, but it is in harmony with the entire spirit of our outlook on nature. All our knowledge is in terms of experience; we should not expect or desire to erect an explanatory structure different in character from that of experience. Our experience is finite; on the confines of the experimentally attainable it becomes hazy, and the concepts in terms of which we describe it fuse together and lose independent meaning. Furthermore, at every extension of our experimental range we must be prepared to find, and as a matter of fact we have often found, that we encounter phenomena of an entirely novel character for which previous experience has given us no preparation. The explanatory structure proposed above has all these properties; it is finite, being terminated by the edge of experiment, the final stages of our explanations are hazy in that it becomes more and more difficult to distinguish elements of familiar experience, and every now and then we must admit new elements into our explanations.

The first step in resuming our explanatory progress, after we have been confronted with such a crisis, is to seek for various sorts of correlation between the elements of our new experience, in the confident expectation that these elements will eventually become so familiar to us that they may be used as the ultimates of a new explanation. This is exactly what is now happening in quantum theory.

Diametrically opposed to the views above, there is another ideal of the explanatory process which is held by many physicists, and which has been mentioned above as the third possible way in which the explanatory sequence may be terminated, namely, the endeavor to devise beyond the limit of present experiment a structure built of elements like some of those of our present experience, in the action of which we endeavor to find the explanation of phenomena in the present range. Now a program such as this, as a serious program for the final correlation of nature, is entirely opposed to the spirit of the considerations expounded here. There is no warrant whatever in experience for the conviction that as we penetrate deeper and deeper we shall find the elements of previous experience repeated, although sometimes we do find such repetitions, as in the behavior of gases. Yet this has been the attitude of many eminent physicists, for example, Faraday and Maxwell, in seeking to explain distant electrical action by the propagation through a medium of a mechanical push or pull, or by Hertz, who sought in all phenomena the effect of concealed masses with ordinary mechanical inertia. Although as a general principle this program seems to be absolutely without justification, nevertheless it may be justified if the specific character of the physical facts seems to indicate a repetition at lower levels of elements familiar higher up. Hertz undoubtedly had this justification, as did also Maxwell to a certain extent, in the discovery that the general equations of electrodynamics are of the same form as the generalized Lagrangean equations of mechanics. For Faraday, however, there seems no such justification; the urge to this sort of thing in Faraday came from an uncritical acceptance of his own temperamental reactions.

From a less serious point of view it may, however, be quite justified to make such a working hypothesis as that in the action of electrical forces may be discovered the same elements with which we are familiar in the everyday experiences of mechanics. For such a hypothesis often enables us to make partial correlations which suggest new experimental tests, and thus gives the stimulus to an extension of our experimental horizon. Many physicists recognize the tentative character of such attempted explanations, but others apparently take them more seriously, as for example Lord Kelvin in his continuous life-long attempts to find a mechanical explanation of all physical phenomena. This quotation from Kelvin is illuminating. "I never satisfy myself until I can make a mechanical model of a thing. If I can make a mechanical model, I can understand it. As long as I cannot make a mechanical model all the way through, I cannot understand it.... But I want to understand light as well as I can without introducing things that we understand even less of."

So much for general considerations on the nature of explanation. Coming now to greater detail, many explanations involve what may be described as a mechanism. It is difficult to characterize exactly what we mean by mechanism, but it seems to be associated with an attitude of mind that strives to realize the third of the possibilities mentioned above. As a matter of fact, the mechanism sought for is usually of a particular type, in that the ultimate elements selected are mechanical elements. This point of view is particularly characteristic of the English school of physicists. Although "mechanism" usually implies mechanical elements, we may show by specific examples that we do actually use the word in a broader significance. If, for example, we could devise within the core of an atom a revolving system of electrical charges, acting on each other with the ordinary inverse square forces of electrostatics, such that every now and then the system becomes unstable and breaks up, we should doubtless say that we had found a mechanism for explaining radioactive disintegration.

However, the formulation of a precise definition of mechanism is of secondary concern to us; we are primarily interested in understanding the attitude of mind that feels a mechanism is necessary. A typical example of such an urge to a mechanism is afforded by the gravitational action between distant bodies. To many minds the concept of action at a distance is absolutely abhorrent, not to be tolerated for an instant. Such an intolerable situation is avoided by the invention of a medium filling all space, which transmits a force from one body to the other through the successive action on each other of its contiguous parts. Or the dilemma of action at a distance may be avoided in other ways, as by Boscovitch in the eighteenth century, who, in order to explain gravitation, filled space with a triply infinite horde of infinitesimal projectiles. Now of course it is a matter for experiment to decide whether any physical reality can be ascribed to a medium which makes gravitation possible by the action of its adjacent parts, but I can see no justification whatever for the attitude which refuses on purely a priori grounds to accept action at a distance as a possible axiom or ultimate of explanation. It is difficult to conceive anything more scientifically bigoted than to postulate that all possible experience conforms to the same type as that with which we are already familiar, and therefore to demand that explanation use only elements familiar in everyday experience. Such an attitude bespeaks an unimaginativeness, a mental obtuseness and obstinacy, which might be expected to have exhausted their pragmatic justification at a lower plane of mental activity.

Although it will probably be fairly easy to give intellectual assent to the strictures of the last paragraph, I believe many will discover in themselves a longing for mechanical explanation which has all the tenacity of original sin. The discovery of such a desire need not occasion any particular alarm, because it is easy to see how the demand for this sort of explanation has had its origin in the enormous preponderance of the mechanical in our physical experience. But nevertheless, just as the old monks struggled to subdue the flesh, so must the physicist struggle to subdue this sometimes nearly irresistible, but perfectly unjustifiable desire. One of the large purposes of this exposition will be attained if it carries the conviction that this longing is unjustifiable, and is worth making the effort to subdue.

The situation with respect to action at a distance is typical of the general situation. I believe the essence of the explanatory process is such that we must be prepared to accept as an ultimate for our explanations the mere statement of a correlation between phenomena or situations with which we are sufficiently familiar. Thus, in quantum theory, there is no reason why we should not be willing to accept as an ultimate the fundamental fact that when an electron jumps radiation is emitted, provided always that we can give independent meaning in terms of operations to the jumping of an electron. If there is no experiment suggesting other and intermediate phenomena, we ought to be able to rest intellectually satisfied with this. Of course it is quite a different matter, and entirely justified, to imagine what the assumption of finer details in the process would involve experimentally, and then to seek for these possible new experimental facts.