The logic of modern physics

by P. W. Bridgman

IN this last chapter we propose to discuss certain special hypotheses about the structure of nature, and certain other matters that could best be left until we had examined our fundamental concepts.

We have seen that in setting up the general rules which are to guide us in describing and correlating nature, we have to take extreme care to allow no special hypotheses to creep in, as otherwise we might be restraining possible future experience. Even here there is no hard and fast line of separation of the general from the special, and one might entangle himself in inextricable difficulties if his ideals were too meticulous. How for example is the critic to be answered who says: "Your very endeavor to formulate principles so broad as not to restrict future experience means, when examined in the light of operations, that you are seeking for principles which past experience suggests will not limit the future. It is in the very nature of things impossible to escape all the implications of past experience and therefore to find any completely general principle." I believe that we must admit the critic is right, and that rigorously our goal is impossible of attainment. 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. In the previous discussion we had to make assumptions, but I hope these assumptions will be recognized by all with physical experience to be so broad as not to restrict us seriously. More special assumptions or hypotheses have their very great use, however, when we attempt to push forward the domains of experimental knowledge, because they may suggest new experiments or aid in correlating information already obtained. These special hypotheses may cover a very wide range of generality; some of them are general enough in character to be discussed here.

Among these special hypotheses there is a group which play an important part in the speculation of most physicists, and which have features in common. These are: the hypotheses of the simplicity of nature, of the finiteness of nature in the direction of the very small, and of the determinateness of the future in terms of the present. That these views have points of similarity is obvious if we consider a hypothetical special case. Suppose that no physical structure beyond the electrons and protons can be discovered, or is even suggested by any known phenomenon, so that the entire future behavior of a system can be determined by a specification of the present relations of all its protons and electrons; in this case nature would be both simple and finite and the future determined by the present.

THE SIMPLICITY OF NATURE

Of these hypotheses, perhaps the most important is that of the simplicity of nature, because of its wide spread diffusion and the effect it has had on physical thought. The hypothesis of simplicity assumes several forms; some physicists are convinced that the laws which govern nature are simple, others that the ultimate stuff of which nature is composed is simple (perhaps protons and electrons and energy), or there may be a combination of both views into the belief that ultimately we shall find simple ultimate elements behaving according to simple laws. In one respect it is obvious that nature is not simple, namely numerically—try counting the electrons or atoms or stars!

Consider now the first of these aspects of the thesis of simplicity, which may be expressed as the conviction that the behavior of the entire universe can be comprehended in a few principles of great breadth and simplicity, such as the inverse square law of force, or the second law of thermodynamics, or perhaps still better the equality of the elementary positive and negative charges, which apparently holds to an enormous degree of precision. In explanation of a view like this there is in the first place the mental urge, because we can take a satisfaction almost æsthetic in contemplating such a universe, and there is in the second place a strong suggestion from experience. Practically all the history of physics is a history of the reduction of the complicated to the simpler. For example, the behavior of a large part of the world of immediate experience can be reduced to the simple laws of mechanics. The behavior of another very large group of natural phenomena can be reduced to thermodynamics. The behavior of the heavenly bodies, which at first was described in a rather complicated way in the Ptolemaic system of astronomy, can be reduced to those same laws of mechanics which we find in our immediate neighborhood, with the one addition of the universal law of gravitation, which later refined experiment discloses is really active in our immediate surroundings. Similarly the laws of thermodynamics (except that part dealing with radiation) are reduced to the ordinary laws of mechanics through the additional assumption of the atomic structure of matter. Truly a stupendous accomplishment that may well color our whole future outlook. One may find great justification here for the belief that all nature will ultimately be reduced to a similar simplicity, and, in particular, justification for the attempt to find the explanation of all nature in the action of mechanical laws. Now, of course, as a matter of physical and historical fact, this program could not be carried through, but obdurate physical phenomena were discovered. Electric phenomena, which at first seemed so promising, refused to fit into the scheme, and the converse attempt, to explain mechanical effects in terms of electrical effects, also failed. 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.

It seems fairly evident then that the laws of nature cannot be reduced to either those of mechanics or of electricity, nor probably, as is suggested by quantum phenomena, to a combination of both. This of course does not preclude the possibility that the laws still may be simple when expressed in other forms. An example of such a broad general law that goes deeper than mechanics or electrodynamics is probably afforded by the second law of thermodynamics when extended to include radiation phenomena.

Examples of attempts to find other such simple laws are Tolman's Principle of Similitude,[33] and Lewis's theory of Ultimate Rational Units,[34] and his recently enunciated principle of Complete Reversibility.[35] The first two of these attempts I do not believe are successful, for reasons I have stated elsewhere,[36] the third also seems somewhat doubtful.

[33]R. C. Tolman, Phys. Rev. 3, 244-255, 1914; 6, 219-233, 1915; 15, 521, 1920; Jour. Amer. Chem. Soc., 43, 866-875, 1921.

[34]G. N. Lewis. Vol. 15, 1921 of the Contributions from the Jefferson Physical Laboratory, dedicated to Professor Hall, Cambridge, Mass.; Phil. Mag., 49, 739-750, 1925.