XI A CENTURY’S PROGRESS IN PHYSICS (continued 2)

Finally attention must be drawn to the fact that the discoveries of inductive science, embodied in the great generalization we have just been discussing, have led to a more intimate knowledge of the nature of time and space than twenty centuries of introspection on the part of professional philosophers. Minskowski, whose promise of greater achievement was cut off by an untimely death, has shown that four dimensional geometry makes possible the representation with beautiful simplicity of the time and space relationships of this theory. The one time and three space dimensions merge in such a manner as to form a single whole with not a vestige of differentiation between these fundamental quantities. Wilson and Lewis^[168] have made this representation familiar to American readers through their admirable translation of Minskowski’s work into the notation of Gibbs’s vector analysis.

Aberration, the Doppler effect, anomalous dispersion, —indeed all known phenomena,—are found to be in accord with the principle of relativity. It must be borne in mind, however, that this principle applies only to systems moving relative to one another in straight lines with constant velocities. That there is something absolute about rotation has been recognized since Foucault performed his famous pendulum experiment in 1851. This experiment (C. S. Lyman, 12, 251 and 398, 1851) consisted in setting a pendulum composed of a heavy-brass ball suspended by a long wire into oscillation in such a way as to avoid appreciable ellipticity in its motion. Observation of the rate at which the ground rotates relative to the plane of vibration of the pendulum furnished a method of measuring the rotation of the earth about its axis without reference to celestial bodies. The gyroscopic compass in use to-day provides yet another terrestrial method of detecting this rotation.

The Future of Physics.—At times during the history of physics it has seemed as if the fundamental laws of 380this science had been so completely formulated that nothing remained to future generations beyond the routine of deducing to the full the consequences of these laws, and increasing the precision of the methods used to measure the constants appearing in them. That Laplace held this view has already been pointed out, and Maxwell, in his introductory lecture at the opening of the Cavendish laboratory in 1871, said, “This characteristic of modern experiments—that they consist principally of measurements—is so prominent, that the opinion seems to have gotten abroad that in a few years all the great physical constants will have been approximately estimated, and that the only occupation which will then be left to men of science will be to carry on these measurements to another place of decimals.” That he himself did not entertain this view is made evident by a succeeding paragraph. “But we have no right to think thus of the unsearchable riches of creation, or of the untried fertility of those fresh minds into which these riches will continue to be poured. It may possibly be true that, in some of those fields of discovery which lie open to such rough observations as can be made without artificial methods, the great explorers of former times have appropriated most of what is valuable, and that the gleanings which remain are sought after rather for their abstruseness than for their intrinsic worth. But the history of science shows that even during that phase of her progress in which she devotes herself to improving the accuracy of the numerical measurement of quantities with which she has long been familiar, she is preparing the materials for the subjugation of new regions, which would have remained unknown if she had been contented with the rough methods of her early pioneers....”

That Maxwell’s forecast of the prospects of his science was no overestimate will be granted by those who have followed the progress of physics during the last twenty years. Yet the work accomplished in the past appears small compared to that which is left to the future. Many of the unsolved problems are matters of fitting together puzzling details, but there is at least one whose solution appears to demand a radical modification in our fundamental physical conceptions. This is the formulation of 381the laws which govern the motions of electrons and positively charged particles inside the atom.

Black Radiation.—The significance of the problem was first brought to light through the study of black radiation. By a black body is meant one whose distinguishing characteristic is that it emits and absorbs radiation of all frequencies, and black radiation is that which will exist in thermal equilibrium with such a body. The interest of this type of radiation lies in the fact, demonstrated by Kirchhoff, that its nature depends only upon the temperature of the black body with which it is in equilibrium, and on none of this body’s physical or chemical characteristics. Thus we may speak of the “temperature” of the radiation itself, meaning by this the temperature of the material body with which it would be in equilibrium.

The problem of black radiation is to find the distribution of energy among the waves of different frequencies at any given temperature. The first step toward a solution was made when Stefan showed experimentally, and Boltzmann as a deduction from thermodynamics and electrodynamics, that the total energy density summed up over all wave lengths varies with the fourth power of the absolute temperature. If the energy density is plotted as ordinate against the wave length as abscissa, the experimental curve for any one temperature rises from the axis of abscissas at the origin, reaches a maximum, and falls to zero again as the wave length becomes infinitely great. Now Wien’s displacement law, the second important step toward the determination of the form of this curve, shows that as the temperature is raised the wave length to which its highest point corresponds becomes shorter,—in fact this particular wave length varies inversely with the absolute temperature. This theoretical conclusion is entirely confirmed by experiment. (J. W. Draper, 4, 388, 1847.)

Farther than this general thermodynamical principles are unable to go. Statistical mechanics, however, asserts that when a large number of like elements are in thermal equilibrium, the average kinetic energy associated with each degree of freedom is equal to a universal constant multiplied by the absolute temperature. This “principle of equi-partition of energy” has been applied 382in various ways to obtain a radiation law. The most straightforward method is based on the equilibrium which must ensue between radiation field and material oscillators when the latter emit, on the average, as much energy as they absorb. From whatever aspect the problem is treated, however, the radiation law obtained from the application of the equi-partition principle is the same. And while this law agrees well with the experimental curve for long wave lengths, it shows an energy density that becomes indefinitely great for extremely short waves, which is not only at variance with the facts, but actually leads to an infinite value of this quantity when integrated over the entire spectrum.

The Energy Quantum.—Now the principle of equi-partition of energy rests securely on most general dynamical principles. That these dynamical laws are inexact to any such extent as the divergence between theory and experiment would indicate, is inconceivable; that they are insufficient when applied to motions of electrons in such intense fields as occur within the atom seems no longer open to doubt. In order to obtain a radiation formula in accord with experiment Planck has found it necessary to extend the atomic idea to energy, which he conceives to exist in multiples of a fundamental quantum hν, ν being the frequency and h Planck’s constant. That some such hypothesis of discontinuity is essential in order to obtain any law that will even approximately fit the experimental facts has been proved by Poincaré. But the precise spot at which the quantum is introduced differs for every new derivation of Planck’s law. As deduced most recently by Planck himself, the quantum shows itself in connection with the emission of energy by the material oscillators with which the radiation field is in equilibrium. These oscillators are supposed to act quite normally in every respect except emission; here the radiation demanded by the electrodynamic equations is cast aside, and an oscillator is supposed to emit at once all its energy after it has accumulated an amount equal to some integral multiple of hν. A form of the theory which does not contain this improbable contradiction of the firmly established facts of electrodynamics introduces the quantum into the specification 383of the energy of vibration which is permitted to each oscillator. Here both emission and absorption follow the classical theory, but the motion of an emitting and absorbing linear oscillator of frequency ν is supposed to be stable only for those amplitudes for which the energy of its oscillations is an integral multiple of hν. In order to maintain the energy at these particular values, the oscillator may draw energy from, or deposit surplus energy with, other degrees of freedom which partake neither in emission nor absorption, but act merely as storehouses.

Photoelectric Effect.—When investigating the production of electromagnetic waves, Hertz had noticed that a spark passed more readily between the terminals of his oscillator when the negative electrode was illuminated by light from another spark. Further investigation by Hallwachs, Elster and Geitel, and others showed that this effect was due to the emission of electrons by a metal exposed to the influence of ultra-violet light. Lenard discovered that the energy with which a negatively charged particle is ejected is entirely independent of the intensity of the light, and further investigation showed it to depend only on the frequency. Einstein suggested that the electrons appearing in this so-called photo-electric effect start from within the metal with an initial energy hν. In passing through the surface a resistance is encountered, however, so he concluded that the energy with which the fastest moving electrons appear outside the metal should be equal to hν less the work done in overcoming this resistance. Recent experiments not only confirm this relation, but provide a most satisfactory method of determining the value of h. Millikan^[169] finds it to be 6·57(10)^–27 ergs sec., which gives the quantum for yellow light a value sixty times as great as the heat energy of a monatomic gas molecule at O°C. That this large amount of energy can be transferred from the incident light to the ejected electron is quite out of the question; it must come from within the atom. In this way some indication is obtained of how vast intra-atomic energies must be.

Structure of the Atom.—The generally accepted model of the atom is that due chiefly to Rutherford.^[170] He considers 384it to be constituted of electrons revolving about a positive nucleus either singly or grouped in concentric rings, in much the same manner as the planets revolve around the sun. Experiments on the scattering of alpha rays, however, show that the nucleus, while it must have a positive charge sufficient to neutralize the charges of all the electrons moving around it, cannot have a volume of an order of magnitude greater than that of the electron. The number of unit charges residing on it, except in the case of hydrogen, which is supposed to consist of a singly charged nucleus and only one electron, is found to be approximately half the atomic weight. Thus helium, with an atomic weight of about four, has a doubly charged nucleus with two electrons revolving about it, and lithium a triply charged nucleus and three electrons. The number of unit charges on the nucleus is supposed to correspond with the atomic number used by Moseley in interpreting the results of his experiment on the X-ray spectra of the elements.

Now the electron which is revolving around the positive nucleus of a hydrogen atom, must, according to electrodynamic laws, radiate energy. This radiation will act as a resistance to its motion, causing its orbit to become smaller and its frequency to increase. Hence luminous hydrogen would be expected to give off a continuous spectrum. The very fine lines actually found seem inexplicable on the classical dynamical and electrodynamical theories. These lines, and those of many other spectra, may even be grouped into series, and the relations between them expressed in mathematical form. Formulæ have been proposed by Balmer, Rydberg, Ritz and others, all of which contain a universal constant N as well as certain parameters which must be varied by unity in passing from one line of a series to the next.

In 1913 Bohr^[171] proposed anatomic theory which brings to light a remarkable numerical relationship between this quantity N and Planck’s constant h. He postulated that the electron in the hydrogen atom, for instance, cannot revolve in a circle of any arbitrary radius, but is confined to those orbits for which its kinetic energy is an integral multiple of ½hn, n being its orbital frequency. Now at times this electron is supposed to jump from an 385outer to an inner orbit, when the excess energy of the first orbit over the second is radiated away. But the energy emitted is also taken to be equal to hν, where ν is the frequency of the radiation. Hence ν can be determined, and the expression obtained for it is exactly that given long before by Balmer as an empirical law. The most remarkable thing about it, however, is that Bohr’s result contains a constant involving h and the electronic charge and mass which has precisely the value of the universal constant N of Balmer’s and Rydberg’s formulæ. In all, the theory accounts for three series of hydrogen, and yields satisfactory results for helium atoms which have lost an electron, or lithium atoms which have a double positive charge. But for atoms which retain more than a single electron it seems no longer to hold.

The three mentioned are only the most clearly defined of a growing group of phenomena in which the quantum manifests itself. Its significance and the alteration in our fundamental conceptions to which it seems to be leading is for the future to make clear. That it presents the most important and interesting problem as yet unsolved few physicists would deny.

American Physicists.—In attempting to cover the progress of physics during the last hundred years in the space of a few pages, many important developments of the subject have of necessity remained untouched, and the treatment of many others has been entirely inadequate. Among those appearing in the Journal of which no mention has been made are LeConte’s (25, 62, 1858) discovery of the sensitive flame and Rood’s (46, 173, 1893) invention of the flicker photometer. However, enough has been recounted to indicate the preeminent position in the history of physics in America occupied by four men: Joseph Henry, of the Albany Academy, Princeton, and the Smithsonian Institution; Henry Augustus Rowland, of Johns Hopkins University; Josiah Willard Gibbs, of Yale; and Albert Abraham Michelson, of the United States Naval Academy, Case School of Applied Science, Clark University, and the University of Chicago. Of these, the last named has the distinction of being the only American physicist to have received the Nobel prize, though there is little doubt that 386the other three would have been similarly honored had not their important work been published prior to the institution of this award. All four occupy high places in the ranks of the world’s great men of science, and the investigations carried out by them and their fellow workers in America have given to their country a position in the annals of physics which is by no means insignificant.