PRESENT TENDENCIES IN THEORETICAL PHYSICS1

AT a time like the present, when the minds of all of us are intent upon the war and the great issues which depend upon it, it seems almost an affectation to discuss before you a subject so remote from "the instant need of things" as the methods and outlook of theoretical physics. The custom of many years, however, constrains the sectional vice-president to deliver an address. The many questions raised by the war and the relation of science to war have been so thoroughly discussed that I should certainly not be justified in inflicting upon you at great length my own views. The only alternative, therefore, to an appearance of detachment, which I am far from feeling, would have been the abolition for this year of the vice-presidential address before Section B-a measure of war-economy which would have commanded my hearty and unqualified support.

When, however, we turn our minds to a consideration of the recent development of our science, we are confronted at once with the unmistakable fact that there has been little progress since August, 1914, in either theoretical or experimental physics. We had become accustomed to a steady succession, year by year, of important experimental discoveries and of ingenious and original theoretical discussions; we need mention only a few-the Stark Effect, the crystalline diffraction of X-rays, Onnes's

1 Address of the vice-president and chairman of Section B-Physics-American Association for the Advancement of Science, Pittsburgh, December,

1917.

superconductivity, Debye's theory of specific heats, the Rutherford nucleus atom, the existence of chemical isotopes, Bohr's theory, Moseley's law, Einstein's theory of gravitation. I do not recall anything comparable with these in interest and importance which has appeared during the past three years. Whatever services science may render to war, it is plain that a state of war is not favorable to the progress of science. Accordingly, the word "present" in my title must be interpreted with some latitude; it really applies to the state of things before the peaceful labor of physicists was interrupted by the duty of turning their attention to problems in applied science whose solution is of immediate urgency.

No one can doubt that there has been something very like a revolution in the ideas and methods of theoretical physics since the beginning of the twentieth century. Much recent work of undoubted significance would seem very strange to Helmholtz and Lord Kelvin; and even in some of our own contemporaries whose tastes are conservative,, it excites feelings similar to those experienced by a Royal Academician before a cubist painting. On the other hand, some of our younger and more enthusiastic colleagues are inclined to be impatient of what they call "classical" theories (some of which were perfected in the 1890's), and to regard them as examples of superstition and logical punctilio from which they have been happily freed. The truth is of course to be found between the two extreme views. We must recognize that this is not the first change in physical science which has seemed at the time to be revolutionary. In the past, these changes have never been so complete and overwhelming as was expected by their supporters, nor so abortive as hoped by their opponents. In science, as in art, pol

itics and religion, the radicals are always partly right and the conservatives never wholly wrong; and the interplay and conflict between the two is of the very essence of progress.

One of the most striking things about the modern beginnings of our science-the preliminary formulation of the principles of mechanics by Galileo, and their more complete development by Newton-was their almost immediate acceptance by all who were not blinded by theological prejudices. This can not have been because they were simple or easy to formulate, or the world would not have had to wait so many centuries for them. But the phenomena of mechanics are directly and explicitly presented to us from our earliest childhood, and have been so presented to our long line of ancestors, human and pre-human. Under given conditions, certain mechanical actions are almost as confidently expected (even by quite uninstructed persons) as if their knowledge was of the a priori character that is attributed by many philosophers to our mathematical and spatial concepts. Even animals share this mechanical knowledge. The instinctive movements of a cat, which enable it to land upon its feet, could scarcely be improved upon if it possessed a satisfactory knowledge of the conservation of angular momentum. The difficulty of formulation was doubtless due to the lack of recognition of the true character of frictional and dissipative forces, and to the obscuring of the idea of mass by the more conspicuous property of weight. At all events, when the principles are once presented to the normal, intelligent, observant mind, they are quickly recognized, and soon come to seem almost as axiomatic as the attributes of space and number. There can be little doubt of the reality of this mechanical "intuition," be its origin what it may. Whatever the philosophers

may think of it in their moments of sophisticated philosophizing, there can be no doubt that they, in common with less instructed people, have a feeling of satisfaction and intellectual rest when an adequate mechanical "explanation" is given of some natural phenomenon.

Newton, with the characteristic boldness of genius, extended the Galilean mechanics of earthly matter to the heavenly bodies, and (as often happens) found in the remoter phenomena better and more complete confirmation of his theory than in the nearer and more obvious manifestations. With the single additional assumption of the gravitational force, all the intricate wanderings of sun, moon and planets in the celestial sphere fell into a system -simple, orderly and in accord with our commonest experiences of every-day life. It is not surprising that to all minds capable of understanding it, Newton's theory carried instant conviction.

Nature and Nature's Laws were hid in night, God said, "Let Newton be," and all was light.

But the law of gravitation did not enjoy the same independent status in the minds of natural philosophers; from that day to this they have been under temptation to find what we all call an "explanation" of it, while few if any have ever felt the necessity for an explanation of the laws of motion. Newton himself, in the "Opticks," speculates as to a possible ethereal explanation of gravitation; and even in the celebrated passage at the end of the "Principia," in which he renounces hypotheses, the context shows, I think, that he felt strongly the desire for an explanation, but was compelled to forego it because "hitherto I have not been able to discover the causes of those properties of gravity from phenomena."

The century following Newton was de

voted to the development of mechanics and of gravitational astronomy and culminated in the great achievements of Lagrange and Laplace. There was some discussion as to the relative merits of action at a distance. and vis a tergo, and some direct attempts to account for gravitation on the latter basis-notably that of LeSage early in the nineteenth century. But, on the whole, the opinion gained strength that Newton had been right in his view that there was little hope of being able to test such theories by comparison with "phenomena."

The discovery by Coulomb that magnetic and electric forces conformed to the Newtonian law gave strength to the prevalent opinion that this law was fundamental in the constitution of the physical universe. The mathematical technique of the subject was highly developed and there was a growing tendency to explain observed phenomena by distance-forces between particles, rather than to seek a more strictly dynamical theory to account for such forces. This procedure was certainly defensible upon philosophical grounds, and proved its utility in many problems of mathematical physics. It was the prevailing fashion in the early part of the nineteenth century.

Thus it was entirely natural that Ampère, when he heard in 1820 of Oersted's discovery, should have based his investigation of electrodynamics upon the Newtonian model, by using current-elements acting upon each other by forces in the line joining them. Again the law proved to be that of the inverse square; but the fact that the attracting elements were directed quantities added many difficulties which, in the state of mathematical science at that time, gave ample scope to the "Newton of electricity" for the display of his genius. These vector relations involve an indeterminateness which later gave rise to many rivals to Ampère's theory; other expres

sions for the forces between elements gave the same results when integrated around closed circuits, and no one succeeded in devising experiments which would discriminate between them. Even Ampère, however (like the great predecessor whose name Maxwell connected with his), was not immune from the inherent desire of the physicist for "explanations" of distanceforces, though he was compelled to forego them because no way appeared for putting them to an experimental test. At the beginning of the memoir,2 in which he sums up his electrodynamic researches, after declaring his adherence to the Newtonian procedure and renouncing anything in the nature of Cartesian vortices which Oersted's discovery had in a measure revived, he says:

I have made no attempt to find the cause of these forces, well persuaded that any attempt of this kind ought to be preceded by the purely experimental knowledge of the laws and by the determination from these laws alone of the value of the elementary forces, whose direction is necessarily that of the straight line drawn through the material points between which the forces act.

Later in the same memoir3 he disclaims any intention to assert that his forces are to be regarded as "truly elementary" and calls attention to previous attempts of his own to "assign a cause for these forces in the reactions of the fluid filling all space whose vibrations produce the phenomena of light."

Simultaneously with these developments and partly in consequence of some of them, the employment of imponderable fluids became very general in theoretical physics. In electrostatics and magnetism, the gravitational analogy required some sort of attracting or repelling substance; 2 Mem. de l'Acad., VI., p. 177 (1825).

8 P. 294.

4Recueil d'observations electro-dynamiques,"

p. 215.

in the theory of heat, the calorimetrical experiments of Black and his clear discrimination between temperature and quantity of heat, led directly to a substantial theory of heat. There was no great encouragement for the attempt to apply the principles of mechanics to these imponderables; so far as experiment showed they lacked not only the conspicuous property of weight, but also the most essential dynamical characteristic of ordinary matter, viz., inertia. The natural and fertile method of dealing with them was to take some empirical relations, as simple and fundamental as possible, as postulates for the mathematical development of the subject. Some of the most epoch-making advances. in theoretical physics are instances of this method; as examples one needs only to recall Fourier's theory of heat conduction (afterwards applied by Ohm to the conduction of electricity), and Carnot's deduction of the theory of heat engines from the empirical principle which we now call the second law of thermodynamics. In fact, the great physicists who flourished during the first three or four decades of the nineteenth century seem to have felt that there was little hope of giving dynamical explanations of all physical phenomena. Thus Fourier, in the introduction of his great work, recounting the glorious achievements of Newton and his successors, says:

It is recognized that the same principles regulate all the movements of the stars, their form, the inequalities of their courses, the equilibrium and oscillations of the seas, the harmonic vibrations of air and sonorous bodies, the transmission of light, capillary action, the undulations of fluids, in fine the most complex effects of all the natural forces; and thus has the thought of Newton been confirmed; quod tam paucis tam multa præstet geometria gloriatur.

"But," continues Fourier, "whatever may be the range of mechanical theories, they do not apply to the effects of heat.

These make up a special order of phenomena which can not be explained by the principles of motion and equilibrium." His attitude may fairly be taken as, in general, characteristic of his time; there were sharp lines of demarkation between the different departments of natural philosophy which would doubtless cause feelings of surprise and discomfort to a modern physicist if he could suddenly find himself at a meeting of the Royal Society or of the Paris Academy in the year 1822. These barriers were to a considerable extent broken down in the forties by the discovery and development of the principle of the conservation of energy. It was not simply the quantitative relation which excited the enthusiasm of

the men of that time, but the knowledge that there was a "correlation of Physical Forces"; their reception of the discovery shows how much such a relation had been wanted.

The psychology of physicists made it inevitable that energy should be regarded as something more real than a mathematical expression which remains constant during various processes. It was given a quasi-substantial interpretation and localized in space; and it was most natural that its newly recognized forms should be identified as nearly as possible with the familiar energy of ordinary mechanics. Thus we had at once a mechanical theory of heat which led to a great extension of molecular hypotheses; and the desire to deduce the empirical second law from dynamical principles was the motive for the development of statistical mechanics through the successive stages shown in the work of Maxwell, Boltzmann and Gibbs.

This tendency toward dynamical explanations was strengthened by the progress of the wave-theory of light. After the brilliant experiments and interpretations

of Young and Fresnel it was impossible to doubt the kinematical similarity of light to a transverse wave motion. This made it necessary to postulate an ether and to give it suitable properties; the theory of waves in an ordinary material elastic solid was developed by Green, Cauchy, Thomson and others and compared with the phenomena of light. The lack of complete agreement was a stimulus to the investigation of other possible types of elastic substances conforming to the general laws of mechanics. In the hands of MacCullagh, Stokes, and especially of Kelvin, these investigations led to great advances in our knowledge of the properties of continuous media, and showed the dynamical possibility of the existence of media which were quite different in their elastic properties from ordinary

matter.

Another current of thought which influenced profoundly the complex development of theoretical physics in the nineteenth century was the strong prejudice of Faraday against action at a distance and his instinctive preference for a mode of representation which involved the transfer of forces from point to point by the interaction of contiguous parts of a continuous medium. The fertility and usefulness of this method in electromagnetism is attested not only by Faraday's unparalleled success as a discoverer (for genius choses the method best suited to itself), but also by the fact that it has held the field in elementary instruction as well as in the most complicated applications of electrical engineering. We all know how Maxwell deliberately submitted himself to the influence of this prejudice, and the epoch-making result which followed from its union with his mathematical skill. The inclusion in a single theory of two great bodies of phenomena, those of light and those of electricity, was an achievement of