This rearrangement of the basic words has not, however, altered the feeling that a world-force with its substratum does exist. The motion-problem is as insoluble as ever. All that has happened on the way from Newton to Faraday—or from Berkeley to Mill—is that the religious deed-idea has been replaced by the irreligious work-idea.[[521]] In the Nature-picture of Bruno, Newton and Goethe something divine is working itself out in acts, in that of modern physics Nature is doing work; for every “process” within the meaning of the First Law of Thermodynamics is or should be measurable by the expenditure of energy to which a quantity of work corresponds in the form of “bound energy.”
Naturally, therefore, we find the decisive discovery of J. R. Mayer coinciding in time with the birth of the Socialist theory. Even economic systems wield the same concepts; the value-problem has been in relation with quantity of work[[522]]] ever since Adam Smith, who vis-à-vis Quesney and Turgot marks the change from an organic to a mechanical structure of the economic field. The “work” which is the foundation of modern economic theory has purely dynamic meaning, and phrases could be found in the language of economists which correspond exactly to the physical propositions of conservation of energy, entropy and least action.
If, then, we review the successive stages through which the central idea of force has passed since its birth in the Baroque, and its intimate relations with the form-worlds of the great arts and of mathematics, we find that (1) in the 17th Century (Galileo, Newton, Leibniz) it is pictorially formed and in unison with the great art of oil-painting that died out about 1630; (2) in the 18th Century (the “classical” mechanics of Laplace and Lagrange) it acquires the abstract character of the fugue-style and is in unison with Bach; and (3) with the Culture at its end and the civilized intelligence victorious over the spiritual, it appears in the domain of pure analysis, and in particular in the theory of functions of several complex variables, without which it is, in its most modern form, scarcely understandable.
XIII
But with this, it cannot be denied, the Western physics is drawing near to the limit of its possibilities. At bottom, its mission as a historical phenomenon has been to transform the Faustian Nature-feeling into an intellectual knowledge, the faith-forms of springtime into the machine-forms of exact science. And, though for the time being it will continue to quarry more and more practical and even “purely theoretical” results, results as such, whatever their kind, belong to the superficial history of a science. To its deeps belong only the history of its symbolism and its style, and it is almost too evident to be worth the saying that in those deeps the essence and nucleus of our science is in rapid disintegration. Up to the end of the 19th Century every step was in the direction of an inward fulfilment, an increasing purity, rigour and fullness of the dynamic Nature-picture—and then, that which has brought it to an optimum of theoretical clarity, suddenly becomes a solvent. This is not happening intentionally—the high intelligences of modern physics are, in fact, unconscious that it is happening at all—but from an inherent historic necessity. Just so, at the same relative stage, the Classical science inwardly fulfilled itself about 200 B.C. Analysis reached its goal with Gauss, Cauchy and Riemann, and to-day it is only filling up the gaps in its structure.
This is the origin of the sudden and annihilating doubt that has arisen about things that even yesterday were the unchallenged foundation of physical theory, about the meaning of the energy-principle, the concepts of mass, space, absolute time, and causality-laws generally. This doubt is no longer the fruitful doubt of the Baroque, which brought the knower and the object of his knowledge together; it is a doubt affecting the very possibility of a Nature-science. To take one instance alone, what a depth of unconscious Skepsis there is in the rapidly-increasing use of enumerative and statistical methods, which aim only at probability of results and forgo in advance the absolute scientific exactitude that was a creed to the hopeful earlier generations.
The moment is at hand now, when the possibility of a self-contained and self-consistent mechanics will be given up for good. Every physics, as I have shown, must break down over the motion-problem, in which the living person of the knower methodically intrudes into the inorganic form-world of the known. But to-day, not only is this dilemma still inherent in all the newest theories but three centuries of intellectual work have brought it so sharply to focus that there is no possibility more of ignoring it. The theory of gravitation, which since Newton has been an impregnable truth, has now been recognized as a temporally limited and shaky hypothesis. The principle of the Conservation of Energy has no meaning if energy is supposed to be infinite in an infinite space. The acceptance of the principle is incompatible with any three-dimensional structure of space, whether infinite or Euclidean or (as the Non-Euclidean geometries present it) spherical and of “finite, yet unbounded” volume. Its validity therefore is restricted to “a system of bodies self-contained and not externally influenced” and such a limitation does not and cannot exist in actuality. But symbolic infinity was just what the Faustian world-feeling had meant to express in this basic idea, which was simply the mechanical and extensional re-ideation of the idea of immortality and world-soul. In fact it was a feeling out of which knowledge could never succeed in forming a pure system. The luminiferous æther, again, was an ideal postulate of modern dynamics whereby every motion required a something-to-be-moved, but every conceivable hypothesis concerning the constitution of this æther has broken down under inner contradictions; more, Lord Kelvin has proved mathematically that there can be no structure of this light-transmitter that is not open to objections. As, according to the interpretation of Fresnel’s experiments, the light-waves are transversal, the æther would have to be a rigid body (with truly quaint properties), but then the laws of elasticity would have to apply to it and in that case the waves would be longitudinal. The Maxwell-Hertz equations of the Electro-magnetic Theory of Light, which in fact are pure nameless numbers of indubitable validity, exclude the explanation of the æther by any mechanics whatsoever. Therefore, and having regard also to the consequences of the Relativity theory, physicists now regard the æther as pure vacuum. But that, after all, is not very different from demolishing the dynamic picture itself.
Since Newton, the assumption of constant mass—the counterpart of constant force—has had uncontested validity. But the Quantum theory of Planck, and the conclusions of Niels Bohr therefrom as to the fine structure of atoms, which experimental experience had rendered necessary, have destroyed this assumption. Every self-contained system possesses, besides kinetic energy, an energy of radiant heat which is inseparable from it and therefore cannot be represented purely by the concept of mass. For if mass is defined by living energy it is ipso facto no longer constant with reference to thermodynamic state. Nevertheless, it is impossible to fit the theory of quanta into the group of hypotheses constituting the “classical” mechanics of the Baroque; moreover, along with the principle of causal continuity, the basis of the Infinitesimal Calculus founded by Newton and Leibniz is threatened.[[523]] But, if these are serious enough doubts, the ruthlessly cynical hypothesis of the Relativity theory strikes to the very heart of dynamics. Supported by the experiments of A. A. Michelson, which showed that the velocity of light remains unaffected by the motion of the medium, and prepared mathematically by Lorentz and Minkowski, its specific tendency is to destroy the notion of absolute time. Astronomical discoveries (and here present-day scientists are seriously deceiving themselves) can neither establish nor refute it. “Correct” and “incorrect” are not the criteria whereby such assumptions are to be tested; the question is whether, in the chaos of involved and artificial ideas that has been produced by the innumerable hypotheses of Radioactivity and Thermodynamics, it can hold its own as a useable hypothesis or not. But however this may be, it has abolished the constancy of those physical quantities into the definition of which time has entered, and unlike the antique statics, the Western dynamics knows only such quantities. Absolute measures of length and rigid bodies are no more. And with this the possibility of absolute quantitative delimitations and therefore the “classical” concept of mass as the constant ratio between force and acceleration fall to the ground—just after the quantum of action, a product of energy and time, had been set up as a new constant.
If we make it clear to ourselves that the atomic ideas of Rutherford and Bohr[[524]] signify nothing but this, that the numerical results of observations have suddenly been provided with a picture of a planetary world within the atom, instead of that of atom-swarms hitherto favoured; if we observe how rapidly card-houses of hypothesis are run up nowadays, every contradiction being immediately covered up by a new hurried hypothesis; if we reflect on how little heed is paid to the fact that these images contradict one another and the “classical” Baroque mechanics alike, we cannot but realize that the great style of ideation is at an end and that, as in architecture and the arts of form, a sort of craft-art of hypothesis-building has taken its place. Only our extreme maestria in experimental technique—true child of its century—hides the collapse of the symbolism.