No one, so far as I know, has ventured to suggest what may be termed a molecular theory of energy, a somewhat remarkable fact when we consider the control now exercised over all thought in physics by molecular theories of matter. While we now believe, for instance, that a material body, say a crystal, can by no possibility increase continuously in mass, but must do so step by step, the minimum mass of matter that can be added being the molecule, we believe on the contrary that the energy possessed by the same body can and may increase with absolutely perfect continuity, being hampered by no such restriction.
It is not the purpose of this paper to discuss whether we have grounds for belief that there is such a thing as a minimum quantity, or atom, of energy, that does not separate into smaller parts, no matter what changes it undergoes. Suffice it to say that there appears to be no a priori absurdity in such an idea. At first sight both matter and energy appear non-molecular in structure. But we have been forced to look upon the gradual growth of a crystal as a step-by-step process, and we may some day, by equally cogent considerations, be forced to regard the gradual increase of energy of an accelerating body as also a step-by-step process, although the discontinuity is as invisible to the eye in the latter case as in the former.
Without following this out any farther, however, the point may be here emphasized that it is hardly possible for one who, like the majority of physicists, regards matter as molecular and energy as a continuum, to hold the same ideas regarding the identity of the two. Efforts to show that definite portions of energy, like definite portions of matter, retain their identity have hitherto been made chiefly on the lines of a demonstration that energy travels by definite and continuous paths in space just as matter does. This is very well, but it would appear to be necessary to supplement it with evidence to show that the lines representing these paths do not form at their intersections continuous blurs that not only forbid any practical attempt at identification on emergence, but make it doubtful whether we can in any true sense call the issuing path identical with the entering one. Otherwise the identity of energy can be admitted to be only that kind of identity that could be preserved by matter if its molecular structure did not exist. One who can admit that this sort of identity is the same sort that can be preserved by molecular matter may be able to hold the identity of energy in the present state of the evidence, but the present attitude of physicists would seem to show that, whether they realize the connection of the two subjects or not, they cannot take this view. In other words, modern views of the identity of matter seem closely connected with modern views of its structure, and the same connection will doubtless hold good for energy.
Regarding the probable success of an attempt to prove that energy has a “structure” analogous to the molecular structure of matter, any prediction would doubtless be rash just now. The writer has been unable, up to the present time, to disprove the proposition, but the subject is one of corresponding importance to that of the whole molecular theory of matter and should not be entered upon lightly.
The writer freely acknowledges at present that the illustrations in the foregoing are badly chosen and some of the statements are too strong, but it still represents essentially his ideas on the subject. No reputable scientific journal would undertake to publish it. The paper was then sent to Prof. J. Willard Gibbs of Yale, and elicited the following letter from him:
“New Haven, June 2, 1897.
“My Dear Mr. Bostwick:
“I regret that I have allowed your letter to lie so long unanswered. It was in fact not very easy to answer, and when one lays a letter aside to answer, the weeks slip away very fast.
“I do not think that you state the matter quite right in regard to the mixture of fluids if they were continuous. The mixing of water as I regard it would be like this, if it were continuous and not molecular. Suppose you should take strips of white and red glass and heat them until soft and twist them together. Keep on drawing them out and doubling them up and twisting them together. It would soon require a microscope to distinguish the red and white glass, which would be drawn out into thinner and thinner filaments if the matter were continuous. But it would be always only a matter of optical power to distinguish perfectly the portion of red and white glass. The stirring up of water from two pails would not really mix them but only entangle filaments from the pails.
“To come to the case of energy. All our ideas concerning energy seem to require that it is capable of gradual increase. Thus the energy due to velocity can increase continuously if velocity can. Since the energy is as the square of the velocity, if the velocity can only increase discontinuously by equal increments, the energy of the body will increase by unequal increments in such a way as to make the exchange of energy between bodies a very awkward matter to adjust.
“But apart from the question of the increase of energy by discontinuous increments, the question of relative and absolute motion makes it very hard to give a particular position to energy, since the ‘energy’ we speak of in any case is not one quantity but may be interpreted in a great many ways. Take the important case of two equal elastic balls. One, moving, strikes the other at rest, we say, and gives it nearly all its energy. But we have no right to call one ball at rest and we can not say (as anything absolute) which of the balls has lost and which has gained energy. If there is such a thing as absolute energy of motion it is something entirely unknowable to us. Take the solar system, supposed isolated. We may take as our origin of coordinates the center of gravity of the system. Or we may take an origin with respect to which the center of gravity of the solar system has any (constant) velocity. The kinetic energy of the earth, for example, may have any value whatever, and the principle of the conservation of energy will hold in any case for the whole solar system. But the shifting of energy from one planet to another will take place entirely differently when we estimate the energies with reference to different origins.
“It does not seem to me that your ideas fit in with what we know about nature. If you ask my advice, I should not advise you to try to publish them.
“At best you would be entering into a discussion (perhaps not in bad company) in which words would play a greater part than precise ideas.
“This is the way I feel about it.
“I remain,
“Yours faithfully,
“J.W. Gibbs.”
Professor Gibbs’s criticism of the illustration of water-mixture is evidently just. Another might well have been used where the things mixed are not material—for instance, the value of money deposited in a bank. If A and B each deposits $100 to C’s credit and C then draws $10, there is evidently no way of determining what part of it came from A and what from B. The structure of “value”, in other words, is perfectly continuous. Professor Gibbs’s objections to an “atomic” theory of the structure of energy are most interesting. The difficulties that it involves are not overstated. In 1897 they made it unnecessary, but since that time considerations have been brought forward, and generally recognized, which may make it necessary to brave those difficulties.
Planck’s theory was suggested by the apparent necessity of modifying the generally accepted theory of statistical equilibrium involving the so called “law of equipartition,” enunciated first for gases and extended to liquids and solids.
In the first place the kinetic theory fixes the number of degrees of freedom of each gaseous molecule, which would be three for argon, for instance, and five for oxygen. But what prevents either from having the six degrees to which ordinary mechanical theory entitles it? Furthermore, the oxygen spectrum has more than five lines, and the molecule must therefore vibrate in more than five modes. “Why,” asks Poincaré, “do certain degrees of freedom appear to play no part here; why are they, so to speak, ‘ankylosed’?” Again, suppose a system in statistical equilibrium, each part gaining on an average, in a short time, exactly as much as it loses. If the system consists of molecules and ether, as the former have a finite number of degrees of freedom and the latter an infinite number, the unmodified law of equipartition would require that the ether should finally appropriate all energy, leaving none of it to the matter. To escape this conclusion we have Rayleigh’s law that the radiated energy, for a given wave length, is proportional to the absolute temperature, and for a given temperature is in inverse ratio to the fourth power of the wave-length. This is found by Planck to be experimentally unverifiable, the radiation being less for small wave-lengths and low temperatures, than the law requires.