A theory involving some sort of a discrete or discontinuous structure of energy has been put forward by Prof. Max Planck of the University of Berlin. The various aspects of this theory are discussed and elaborated by the late M. Henri Poincaré in a paper entitled “L’Hypothèse des Quanta,” published in the Revue Scientifique (Paris, Feb. 21, 1912).
A paper in which a discontinuous or “atomic” structure of energy was suggested was prepared by the present writer fifteen years ago but remains unpublished for reasons that will appear later. Although he has no desire to put in a claim of priority and is well aware that failure to publish would put any such claim out of court, it seems to him that in connection with present radical developments in physical theory the paper, together with some correspondence relating thereto, has historical interest. Planck’s theory was suggested by thermodynamical considerations. In the paper now to be quoted the matter was approached from the standpoint of a criterion for determining the identity of two portions of matter or of energy. The paper is as follows:
Some Consideration on the Identity of Definite Portions of Energy
It has been remarked recently that physicists are now divided into two opposing schools according to the way in which they view the subject of energy, some regarding it as a mere mathematical abstraction and others looking upon it as a physical entity, filling space and continuously migrating by definite paths from one place to another. It may be added that there are numerous factions within these two parties; for instance, not all of those who consider energy to be something more than a mere mathematical expression would maintain that a given quantity of it retains its identity just as a given quantity of matter does. In fact a close analysis would possibly show that opinions are graded very closely and continuously from a view hardly differing from that of Lagrange, who clearly saw and freely used the mathematical considerations involving energy before the word had been invented or its physical meaning developed, up to that stated recently in its extreme form by Professor Ostwald, who would replace what he terms a mechanical theory of the universe by an “energetical” theory, and would dwell exclusively on energy as opposed to its vehicles.
Differences of opinion of this sort very frequently reduce to differences of definition, and in this case the meaning of the word “identity” or some similar word or phrase has undoubtedly much to do with the view that is taken of the matter. It may be interesting, for instance, to look for a moment at our ideas of the identity of matter and the extent to which they are influenced by the accepted theory of its constitution.
Very few persons would hesitate to admit that the matter that now constitutes the universe is identical in amount with that which constituted it one million years ago, and that any given portion of that matter is identical with an equal amount of matter that then existed, although the situations of the parts of that portion might be and probably were widely different in the two classes. To assert this is of course a very different thing from asserting that the identity of the two portions or any parts thereof could have been practically shown by following them during all their changes of location or state. That cannot be done even in the case of some simple changes that are effected in a fraction of a second. For instance, if water from the pail A be mixed with water from the pail B there is no possible way of telling which pail any given portion of the mixture came from or in what proportions, yet it is certain that such portion is identical with a portion of equal mass that recently occupied part of one or both pails.
How far our certainty as to this is influenced by our ideas regarding the ultimate constitution of the water is worthy of investigation. All who accept the molecular theory, for instance, will regard our inability to trace the elements of a mixture as due to purely physical limitations. A set of Maxwell’s “demons” if bidden to watch the molecules of the water in pail A, one demon being assigned to each molecule, would be able to tell us at any time the precise proportions of any given part of the mixture. But if we should not accept the molecular theory and believe for instance, that water is a continuum, absolutely homogeneous, no matter how small portions of it be selected, then our demons would be as powerless as we ourselves now are to trace the constituents in the mixture.
We are now in a position to ask the question: Is the matter in a mixture of two continua identical with that of its constituents? The identity certainly seems of a different kind or degree from that which obtains in the first case, for there is no part, however small, that was derived from one pail alone. The mixture is something more than a mere juxtaposition of elements each of which has retained its identity; it is now of such nature that no part of it is identical with any part of A alone or of B alone, nor of A+B, where the sign + denotes simple juxtaposition. It is identical, to be sure, with a perfect mixture of certain parts of A and B, but this is simply saying that it is identical with what it is now, that is, with itself, not with something that went before.
Probably no one now believes that water or any other kind of matter is a continuum, but the bearing of what has been said may be seen when we remember that this is precisely the present stage of our belief regarding energy.