P. W. Bridgman

“ When one thinks of an atom as a thing with any geometrical properties at all, I believe he will find that what he essentially does is to imagine a model, multiplying all the hypothetical dimensions by a factor large enough to bring it to a magnitude of ordinary experience. This large scale model is given properties corresponding to those of the physical thing. For example, the model of the atom which was accepted in the fall of 1925 contains electrons rotating in orbits, and every now and then an electron jumps from one orbit to another, and simultaneously energy is radiated from the atom. ”

“ If we attach the most fundamental significance to the behavior of material bodies, we shall do well to adopt one of the alternative definitions of velocity. If, on the other hand, we regard the phenomena of light as the most fundamental, we shall endeavor to form our definition so that the properties of light are simple. This was precisely the point of view of Einstein; it is characteristic of his entire scheme of restricted relativity that light is the fundamental thing, and this influenced him in adopting the first definition of velocity. ”

“ An example of a construct involving a greater amount of invention is the stress in an elastic body. A stress is by definition a property of the interior points of a body which is connected mathematically in a simple way with the forces acting across the free surface of the body. A stress is then, by its very nature, forever beyond the reach of direct experience, and it is therefore a construct. The entire structure of a stress corresponds to nothing in direct experience; it is related to force, but is itself a six-fold magnitude, whereas a force is only three-fold. ”

“ 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. ”

“ There is no physical phenomenon, whatever by which light may be detected apart from the phenomena of the source and the sink (understanding that a mirror is included in the idea of, sink) ; that is, no phenomenon exists independent of the phenomenon which led us to the invention of a thing travelling. Hence from the point of view of operations it is meaningless or trivial to ascribe physical reality to light in intermediate space, and light as a thing travelling must be recognized to be a pure invention. ”

“ Here as always, when our range of experience is extended, we must be prepared at some future time to find that, by extending the ordinary concept of event to small-scale phenomena by the device of the mental model, we have by implication smuggled into our picture phenomena which do not exist, so that it will be necessary to revise our thinking, casting it into terms corresponding to direct experience. ”

“ With so many physicists working to devise new theories, the chances are high that many false theories will be found, in which a number of phenomena may apparently fit together into a new relation, but which eventually prove to be inconsistent with other phenomena, so that the proposed theory has to be abandoned. As physics advances and the number of investigators and the amount of physical material increases, one has to be more and more exacting in one's requirements of a new theory. ”

“ I cannot see that the operations which are equivalent to the energy concept justify us in saying more than that energy is a property of a material system; the operations do not seem to give any unique meaning to a location associated with energy.
We now ask what significance is to be ascribed to the sort of conservation that energy does have. We restrict ourselves first to mechanical systems. The motions of a mechanical system satisfy certain differential equations of the second order, and the actual motion is to be found by an integration of the equations. ”

“ We regard our acts as not determined by the external world, so that changes produced in the external world by acts of our wills are, to a certain degree of approximation, arbitrary. The system, then, on which we are experimenting, is one capable of isolation from us in that we may regard ourselves as outside the system, and having no connection with it. The system, furthermore, is capable of isolation from the rest of the physical universe, in that events taking place outside the system have no connection with those taking place inside. ”

“ WHATEVER may be one's opinion as to our permanent acceptance of the analytical details of Einstein's restricted and general theories of relativity, there can be no doubt that through these theories physics is permanently changed. It was a great shock to discover that classical concepts, accepted unquestioningly, were inadequate to meet the actual situation, and the shock of this discovery has resulted in a critical attitude toward our whole conceptual structure which must at least in part be permanent. ”

“ In particular, if we examine the definition of absolute time in the light of experiment, we find nothing in nature with such properties.
The new attitude toward a concept is entirely different. We may illustrate by considering the concept of length: what do we mean by the length of an object? We evidently know what we mean by length if we can tell what the length of any and every object is, and for the physicist nothing more is required. To find the length of an object, we have to perform certain physical operations. ”

“ The thing-travelling point of view, even as treated by Einstein, does not land us in a situation which is at all satisfying logically. We are familiar with only two kinds of thing travelling, a disturbance in a medium, and a ballistic thing like a projectile. But light is not like a disturbance in a medium, for otherwise we should find a different velocity when we move with respect to the medium, and no such phenomenon exists; neither is light like a projectile, because the velocity of light with respect to the observer is independent of the velocity of the source. ”

“ The invention of new concepts is certainly not an easy thing, and is something which physics has always deliberately, and perhaps justifiably, shirked, as shown by the persistent attempts to carry the notions of mechanics down into the finest structure of things. This shirking has not had bad results, but on the contrary good results, as long as physics has been primarily concerned with phenomena near the range of ordinary experience, but I believe that as we get farther and farther away from ordinary experience, the invention of new concepts will become an increasing necessity. ”

“ But in determining the force from the acceleration, we have to know the mass. This mass has to be independently measured with the original concept of force; otherwise we have no basis for such simple statements as that the force of gravity on a body is proportional to its mass. All this applies to the ordinary range of experiments with low velocities. If now we extend the range of measurements, we find phenomena which we had not expected; for example, there seem to be difficulties in the way of indefinitely increasing the velocity of a material body, as of a charged atom. ”

“ Having now fixed what we mean by the magnitude of a moving charge, we are ready to turn to the general problem of the behavior of any system of charged bodies in motion. For the present we consider only phenomena of the scale of everyday experience. The most general problem that has meaning here is to determine all measurable properties of the system in terms of those data which experiment shows can be arbitrarily specified. Now we have already emphasized that the electromagnetic field itself is an invention, and is never subject to direct observation. ”

“ Implied in this recognition of the possibility of new experience beyond our present range, is the recognition that no element of a physical situation, no matter how apparently irrelevant or trivial, may be dismissed as without effect on the final result until proved to be without effect by actual experiment.
The attitude of the physicist must therefore be one of pure empiricism. He recognizes no a priori principles which determine or limit the possibilities of new experience. Experience is determined only by experience. ”

“ We now see that the concept of event is only an approximate concept, as was also that of identity, and for the same reason, namely, there are no such things in experience as sharp discontinuities, but as our measurements become more refined, the edges of supposed discontinuities become blurred. As we go to smaller scales of magnitude this blurring becomes more important, until the physical possibility of performing those operations by which the discontinuities are detected entirely disappears, and the concept of event acquires, in terms of operations, an entirely different meaning. ”

“ But the "absolute" may usefully return with an altered meaning, and we may say that a thing has absolute properties if the numerical magnitude is the same when measured with the same formal procedure by all observers. Whether a given property is absolute or not can be determined only by experiment, landing us in the paradoxical position that the absolute is absolute only relative to experiment. In some cases, the most superficial observation shows that a property is not absolute, as, for example, it is at once obvious that measured velocity changes with the motion of the observer. ”

“ We may say in partial self-defense that all the discussion of this essay has been subject to one explicit assumption, namely, that the working of our minds is understood, which of course involves the assumption that our minds continue to function in the future in the same way as in the past. Even with this proviso we can not rigorously avoid the implications of the past, but there can be no practical question that we recognize certain assumptions about the behavior of nature to be so special as to limit seriously the physical possibilities, and other assumptions to be less restricting. ”

“ The first lesson of our recent experience with relativity is merely an intensification and emphasis of the lesson which all past experience has also taught, namely, that when experiment is pushed into new domains, we must be prepared for new facts, of an entirely different character from those of our former experience. This is taught not only by the discovery of those unsuspected properties of matter moving with high velocities, which inspired the theory of relativity, but also even more emphatically by the new facts in the quantum domain. ”

“ We still carry our ordinary mechanical notions down into the realm of small electric effects, and still talk, for instance, about non-electrical forces which hold an electron together. Nor are there experiments affording sufficient basis for believing that all the mass of a positive nucleus is electrical in character. We also think of electrical charges as having the property of identifiability, which involves the possession of sharp edges and a change in the law of force at small distances, and this is certainly a property carried over from our large scale experience. ”

“ Now in spite of the resemblances pointed out above, there is at least one universal and fundamental difference between a thing that travels and light. We have independent physical evidence of the continued existence of the ball, for example, at all intermediate points of space; we can see it, or hear it, or feel the wind in the air as it passes, or even touch it. All these phenomena are independent of the initial and terminal phenomena, and hence by our criterion for the physical reality of an invention, we are justified in ascribing physical reality to the ball in transit. ”

“ It seems to me that it is very questionable whether Einstein, and all the rest of modern physics, for that matter, have not paid too high a price for simplicity and mathematical tractability in choosing to treat light as a thing that travels. Physically it is the essence of light that it is not a thing that travels, and in choosing to treat it as a thing that does, I do not see how we can expect to avoid the most serious difficulties. ”

“ No one realizes more vividly than I that this is a most difficult thing to do. If we are ever successful in carrying through such a modified treatment, it is evident that not only will the structure of most of our physics be altered, but in particular the formal approach to those phenomena now treated by relativity theory must be changed, and therefore the appearance of the entire theory altered. I believe that it is a very serious question whether we shall not ultimately see such a change, and whether Einstein's whole formal structure is not a more or less temporary affair. ”