The logic of modern physics

by P. W. Bridgman

[17]This phenomenon is discussed at length in the book by J. Perrin, Brownian Movement and Molecular Reality, translated by F. Soddy, Taylor and Francis, London, 1909.

It is evident that we here go beyond any possible experience, at least for the present, and that experience has again become poorer and our concepts fewer in number. All that we can now demand is that certain combinations of numbers, some of which represent mechanical mass and others electrical charge, have proper relations to each other when integrated throughout the entire body of the electron. Similar questions confront us when we ask what are the forces which the parts of the electron exert on each other. We return to this question in considering the nature of the electrical concepts. In any event, the concepts of both force and mass are entirely altered in this domain.

It is interesting to note, in passing, that present electrical theory gives no meaning to the mass of the elements of the electron, since the total electromagnetic mass of the electron is built up from the mutual terms in the action of the elements—the total mass is not a linear resultant of the action of the elements.

THE CONCEPT OF ENERGY

In examining the concept of energy, we start with purely mechanical energy. In isolated mechanical systems, in which there are only conservative forces, the sum of kinetic and potential energy is constant. The kinetic energy may be defined as ∑ ½ mv², formed for all parts of the body. The potential energy is determined by the position of the parts of the system, and has physical significance only with reference to a datum position, that is, only changes of potential energy have meaning in terms of operations. The total energy ascribed to the system has therefore an element of arbitrariness in that the datum position may be chosen at random, and energy acquires meaning only on tracing the history back to the epoch of the datum position.

The concept of energy may be extended from mechanical systems to all systems with which we are acquainted; the operations by which meaning is given to the extended energy concept involve the generalized conservation principle, or the first law of thermodynamics. The extension to thermal systems is immediate; the inclusion of optical and electrical systems in the scheme was a most important physical step, which of course required careful experimental justification. Because of its wide range of application, the energy concept has now come to be regarded as one of the most important in physics; this idea was held by Ostwald[18] twenty and more years ago, and is now much to the front because of the connection between mass and energy indicated by the theory of relativity, and the important rôle assigned to energy levels in spectrum analysis.

[18]W. Ostwald, Die Energie, Barth, Leipzig, 1908.

What now is the precise nature and significance of the general energy concept? In the first place the conservation property of energy is one of the simplest and most obvious of the properties of matter, so that in this property of energy is seen a reason for ascribing to it certain of the properties of matter, in particular and most important, that of localization in space. We must recognize, however, that this idea of a location in space is injected into the situation entirely by ourselves, and corresponds to nothing directly given by the operations of experiment. The idea has had a most important effect, however. Witness, for instance, the importance ascribed to the discovery by Kelvin of a function by which the total energy of an electric field can be represented as distributed through space;[19] this was one of the most important props of the medium point of view.

[19]This function is ⅛π times the scalar product of electric force and displacement. If Maxwell's definition of displacement is adopted, the factor ⅛π is replaced by ½, and an accurate analogy results between the energy stored in the ether and the elastic energy stored in a bent spring.

A more critical examination is likely to diminish considerably our satisfaction with this naive analogy drawn between matter and energy. With regard to matter, we may still be tolerably satisfied with our ascription to matter of location in space, but it is quite different with regard to conservation of matter. In just what sense is matter conserved? Certainly not in terms of mass, as we at one time thought. Nevertheless we undeniably have a feeling that there is some sort of conservation property here, and are driven to formulate it badly in terms of a hypothetically constant number of protons and electrons. I have long thought that Newton was groping after some very similar idea when he so far forgot himself as to define mass as quantity of matter, a definition perfectly meaningless to a rigorous and unsympathetic interpretation. On the other hand, whatever meaning may reside in our idea of conservation of matter, it certainly is not, in at least one important respect, like the conservation of energy. For the energy of an isolated mechanical system is a function of the frame of reference in which it is described; merely by giving velocity to the reference frame and altering in no way the mechanical system we may change its kinetic, and so its total, energy by any direct amount. This does not even remotely resemble ordinary matter. I cannot see that the operations which are equivalent to the energy concept justify us in saying more than that energy is a property of a material system; the operations do not seem to give any unique meaning to a location associated with energy.