The Relations of Physics of Electrons to Other Branches of Science

Front matter

SECTION C—PHYSICS OF THE ELECTRON

(Hall 5, September 22, 3 p. m.)

Chairman: Professor A.G. Webster, Clark University.

I. The Electromagnetic Ether

(1) Fields and Charges. One can say that the combined efforts of Faraday, Maxwell, and Hertz have resulted in giving us a precise knowledge of the properties of the electromagnetic ether, and of light; of a medium, homogeneous and void of matter, whose state is completely defined, with the exception of gravitation, when we know at any point the direction and magnitude of the electric and magnetic fields.

I insist, for the present, on the possibility of arriving at a conception of fields of force, as well as the related idea of electric charges, independently of all dynamics; I wish by this to imply only a knowledge of the laws of motion and of matter. The two fields possess this property, that their divergence is zero in all parts of the ether; that is to say, the flux of electric and magnetic force is rigorously zero across a closed surface which does not contain any matter in its interior. It is in fact always matter in the ordinary sense of the word which contains and can furnish the electric charges around which the divergence of field exists whose direction varies with the sign of the charges.

In extreme cases where the electric charges appear to be most completely separated from their material support, as in the case of the cathode rays for example, the experimental fact of the granular structure of these rays and the complete indestructibility of their charge, the fact finally that cathodic particles are charges possessing the fundamental property of matter, inertia, and experiencing acceleration in the electromagnetic field, these facts do not allow us to distinguish their charge from the so-called free charge of ordinary electrified matter.

Furthermore, we shall come to the idea not only that there can be no electric charge without matter, but that, in fact, there can be no matter without electricity, an aggregation of electrical centres of the two kinds. Electrons, analogous to the cathode particles, possess almost all the known properties of matter by the fact alone that these centres are electrified. We shall see within what limits this conception can be considered sufficiently known, and if it is necessary to superimpose other properties on those which result from electrically charged centres in order to obtain a satisfactory representation of matter; the ether alone, on the contrary, never contains any electricity. If experiment obliges us to admit the existence of electric charges, positive and negative, from the flux of electric force different from zero across a closed surface drawn entirely in the ether and containing matter, it is otherwise for the magnetic field. Experiment has never furnished an instance where a closed surface drawn in the ether was traversed by a magnetic field different from zero. One interesting phenomenon observed recently by P. Villard in the effect of an intense magnetic field on the production of the cathode rays, appears to receive a simple explanation in the hypothesis of free magnetic charges; but it is not certain that this hypothesis is necessary.

(2) The Equations of Hertz. The two fields, electric and magnetic, of which the ether can be the seat, are related to one another in such a manner that one of them can exist only on the condition that the other varies; all variations of an electric field produce a magnetic field; it is the displacement current of Maxwell: and all variations of the magnetic field produce an electric field; this is the phenomenon of induction discovered by Faraday. These two relations are expressed by Hertz's equations; they sum up completely our knowledge of the electromagnetic medium, and from these it results that all disturbances of this medium are propagated with the velocity of light. Hertz had the glory of proving this fact experimentally.

(3) Energy. We can now say that the ether is the seat of two distinct forms of energy, the electric and the magnetic, capable of transformation from the one into the other, but only through matter as an intermediary, that is to say, by means of the electrified centres which it contains.

In the ether alone, in fact, in the free radiation which it propagates, the electric and magnetic fields, transverse with respect to the direction of propagation, represent always equal energies in each element of volume, without oscillation of the energy from one form to the other. In the presence of matter, on the other hand, the electric energy can exist alone, and it is the motion of electrified centres which allows the transformation into magnetic energy, and vice versa. Matter only can be the source of radiation.

It is necessary, to the two preceding forms of energy, to add gravitation, which corresponds probably to a third mode of activity of the ether, whose connection with the two others is still obscure.

I insist here on the point that the principle of equivalence of various forms of energy, as far as the process allows of measurement, can be attained independently of all dynamical notions, by the process of using solely material systems in equilibrium.

One can find some information on this subject in a recent exposition by M. Perrin.

(4) The Theory of Lorentz. The ether being thus completely known to us from the electromagnetic and optical point of view, the problem which follows as a continuation of the work of Maxwell and of Hertz is that of the connection between ether and matter, inert matter, the source and recipient of the radiations which the ether transmits. The connection sought for is furnished us by the electron or corpuscle, an electrical centre movable with respect to the ether, and carrying with it its divergent electric field.

This was the fundamental idea which caused Lorentz to conceive of the possibility of a relative displacement of electrified centres of divergence of the electric field, and of the ether considered as immovable. This displacement takes place without any change in the amount of the charge, that is to say, that the surface which is displaced in the ether with the electron is crossed by an electric flux which is completely invariable. It is the fundamental principle of the conservation of electricity, which will perhaps absorb the principle of the conservation of matter, as we cannot have matter without electricity. It is, however, probable that electricity alone is not sufficient to constitute matter.

We have actually no very precise information of the relative displacement of charges and of the ether, of electrified centres in an immovable medium, no tangible form under which we can conceive it. The attempts which have thus far been made to obtain a concrete representation, in order to give a material structure to the ether, have all been sterile of results. Perhaps there is a difficulty which belongs to the actual constitution of our minds, habituated by our secular evolution to think through matter, unable to form a concrete representation which is not material; also it seems scarcely reasonable to seek to construct a simple medium such as the ether by considering it to spring from a complex and various medium like matter. I believe it will be necessary to think ether, to conceive of it independently of all material representations, by means of those electromagnetic properties which put us in contact with it. I will return to this point later in reference to the mechanical theories of the ether.

If the electric charge is assumed to have a volume distribution in a portion of the medium, the principle of the conservation of electricity, and also the possibility of relative displacement of electricity and ether, makes it necessary for us, in this portion of space, to modify the equations of Hertz relative to the displacement current by the addition of a convection current, a necessary consequence of the existence of a displacement current connected with a motion of charges, and implying the production of a magnetic field by the motion of electrified bodies across the medium. This consequence of Hertz's equations has now received complete experimental confirmation.

Moreover, the experimental facts impose on these movable charges a discontinuous, granular structure, and lead to the idea of the electron as a singular region of the ether, carrying a charge equal to that of the hydrogen atom in electrolysis, but of different sign, and distributed on the surface or in the volume of the electron according as the intensity of the electric field is supposed to present, or not, a discontinuity when it crosses the surface which limits the volume occupied by the electron. Inertia, of electromagnetic origin, which we are about to refer to a similar centre, is opposed also, under the difficulty of its becoming infinite, to the hypothesis of a finite electric charge condensed in a point without extension.

The various considerations, more and more precise, all converging toward this notion of the atomic structure of charges, form the starting-point of all recent works on electricity.

II. The Atom of Electricity

(6) The Electron. The remarkable laws of electrolysis discovered by Faraday establish an intimate and necessary connection between the atomic structure of matter and that of electricity. They were sufficient to lead Helmholtz to conceive the latter as constituted of distinct, indivisible portions, elements of charge, all identical from the point of view of the quantity of electricity which they carry, and differing only in the sign. This elementary charge is equal to that carried by a monovalent atom or radical in electrolysis; a polyvalent atom or radical carries an equivalent number of such charges.

It was Johnstone Stoney who first used the word electron to designate atoms of electricity as distinct from matter, with which they combine to furnish the electrolytic ions. The presence of similar electrons combined with material atoms allows us to represent certain peculiarities of the spectrum, the existence of doublets of like frequencies; the electron, in motion, is thus considered as the origin of the emission of all luminous rays.

(7) Gaseous Conductors. But there are the researches on the electrical conductivity of gases, which have presented to us in a forcible manner the idea of electrical atoms, which have made this notion more tangible by allowing us to count these electric centres, to lay hold of them individually, and to measure for the first time the charge of each of them in absolute value.

As early as 1882, Giese, in observing the peculiarities of the conductivity of gases escaping from flames, the departure from Ohm's law, the impossibility of drawing from the gas, whatever might be the electric field employed, more than a limited amount of electricity of each kind, the progressive recombination of the free charges in the gas, had expressed in a precise manner the idea, that as in electrolytes the free electric charges in a gas are carried by distinct positive and negative centres in limited numbers, capable of moving in opposite directions under the action of an external electric field in order to discharge the electrified body which produces the field.

It is difficult, in fact, to conceive how, on the hypothesis that the charges are distributed in a continuous manner in space, a mass of gas electrically neutral could furnish a limited quantity of electricity of each kind, decreasing with the time by progressive recombination if one delays the establishment of the electric field in the gas.

It is indeed necessary to admit, for the two electricities, a discontinuous structure in order to allow their coexistence without completely neutralizing one another. The progressive recombination of the charged particles or ions of two kinds would produce this neutralization at the moment of their mutual collisions.

The phenomena of the saturation current, of the limited quantity of free electricity in a gas, were obtained under conditions most favorable to experimental study, when, immediately after the discovery of Roentgen rays and like radiations, one had recognized their property of making the gas they traversed a conductor of electricity. The limited charge which we can extract from a gas thus modified, the velocity, finite and easily measured, with which they move under the action of an electric field, their progressive recombination, are interpreted in an admirable manner on the hypothesis that the radiations, as well as the intense heat agitations in a flame, dissociate a certain number of the molecules of the gas into electrified parts carrying charges of opposite kinds.

(8) The Phenomena of Condensation. We know how the phenomena of condensation of supersaturated water vapor in the presence of a conducting gas, already referred by H. von Helmholtz to the presence of ions, has given the preceding hypothesis a brilliant confirmation. As a result of the researches of J. J. Thomson, Townsend, C. T. R. Wilson, and H. A. Wilson, these droplets of visible water, each formed by condensation around an electrified centre, bring forward a tangible witness to the existence of these centres, and furnish a means of measuring the individual charge, present on each drop of water formed, and equal to about 3.4 x 10-10 electrostatic units of electricity according to the recent measurements of J. J. Thomson and H. A. Wilson.

The fundamental idea in these kinds of measurements, applied for the first time by Townsend to the charged drops which are produced in the presence of saturated water vapor in recently prepared gases, consists in deducing the mass of each drop from its velocity of fall under the action of gravity by means of Stokes's formula, which gives the frictional resistance of a sphere moving through a viscous medium, and which expresses the velocity of fall in terms of the radius of the drop and consequently of its mass. We can obtain from this the electric charge carried by each drop if we know the ratio of this charge to the mass.

This ratio can be obtained, as was done by Townsend and J. J. Thomson, by measuring or calculating the total mass of water carried by the droplets, considered as uniform, as well as the total quantity of electricity carried by the ions which have served as centres for the formation of the drops. The charge thus obtained by Townsend was found to be 3 × 10-10 electrostatic units for each centre in the case of gases of electrolysis, and to 6.5 × 10-10 by J. J. Thomson from the first series of measurement on gases ionized by Roentgen rays.

H. A. Wilson obtained the ratio of charge to the mass of a drop more simply by comparing the velocity of fall under the action of gravity alone with the velocity of fall in a vertical electric field. He obtained thus directly the ratio sought for. This method has the advantage of showing that the electric charges are really carried by the drops, and of separating those drops which carry a single elementary charge from those which, by diffusion of the ions toward one another, carry a double or triple charge.

Wilson gives as the mean result of his measurements 3.1 × 10-10, a value very near to that of Townsend.

A second series of experiments by Professor J. J. Thomson, in which he used radioactive substances as sources of ionization more constant than the Crookes tube, and in which he took care to cause the drops to form on all the ions present in the gas, by producing a supersaturation of the water vapor by a rapid expansion of sufficient magnitude to cause the condensation on the ions of both kinds, gave as a mean result 3.4 × 10-10, a value in complete agreement with the other two experimenters. The principles of thermodynamics account perfectly for the influence of electrified centres on the condensation of water vapor: the electric charge of a drop in fact diminishes the pressure of water vapor in equilibrium with it. Moreover, the least supersaturation found necessary, by C. T. R. Wilson, for the formation of drops of water on the ions, which are the same whatever may be the means of producing them (Roentgen rays, Becquerel rays, brush discharge, action of ultra-violet light on metal negatively charged), allows us by purely thermodynamical reasoning to calculate approximately the charge carried by each of the ions, and this calculation, entirely distinct from direct measurement, gives in the case of the positive centres a value of 4 × 10-10 E. S. units.

(9) The Radiation Integral. More surprising still is the result recently obtained by H. A. Lorentz, who succeeded in basing a precise measurement of the elementary charges carried by the electrified centres present in metals on the experimental study of the radiation integral or black body radiation.

We will see how the emission and absorption of heat- and lightwaves by matter are dependent on the presence in it of electrons in motion. The ratio, for a radiation of given wave-length, between the emissive and absorptive power, a ratio independent of the nature of the substance, represents the emissive power of the radiation integral, which bolometric measurements give directly.

Now this ratio can be calculated, as Lorentz has shown, for wavelengths which are long in comparison with the mean path of free electrons in the metal, as a function of the charge carried by each of them. The comparison of these results with those of Kurlbaum furnishes an entirely new method of obtaining this charge, and gives 3.7 × 10-10 E. S. units.

(10) The Kinetic Theory. Finally, the last confirmation, which states more precisely still our knowledge of the electric atom, and our confidence in this fundamental idea, Townsend, through comparing by the simple reasoning of the kinetic theory the velocities of ions in a gas under the action of an electric field with their coefficient of diffusion through the interior of the gas, two quantities directly measurable by experiment, has been able to demonstrate the identity of the charge of one of these gaseous ions with the electric atom of Helmholtz, the charge of a monovalent atom in electrolysis.

From this comes directly a new confirmation of the values previously obtained, for it allows us to know, owing to Townsend's results, the charge on an atom in electrolysis, and from it to deduce immediately the constant of Avogadro, the number of molecules contained in a given volume of a gas. The results are well in agreement with the values of this constant (in general a little greater), which we can directly deduce from the kinetic theory of gases.

Here is an important group of concordant indications, all of absolutely distinct origin, which show without doubt the granular structure of electric charges, and consequently the atomic structure of matter itself. The measurements which I have just enumerated allow us to establish, in great security, the hypothesis of the existence of molecular masses.

I seek to point out here this extremely remarkable result, which belongs without doubt to some fundamental property of the ether and of the electrons, that all these electrified centres, whatever may be their origin, are now identical from the point of view of the charge which they carry.

It is necessary for us to penetrate further into their properties, into their relations with material atoms, to determine their relative sizes, in order to add among others to the more exact ideas which we possess in this field, that the electrons, or negative cathode corpuscles, are all identical not only from the point of view of their charge, but also from the point of view of their dynamic properties and of their masses. We are unhappily not so well informed in regard to the positive centres.

III. Inertia and Radiation

(11) The Electromagnetic Wake. Before going farther it is important to point out what we can draw from the point of view to which we have now come. Electrified centres, whose existence is experimentally proven, whose charge we know in absolute units, are movable with respect to a fixed ether defined according to the equations of Hertz, without its having been necessary for us to have recourse to dynamic principles to arrive at this point of view.

To what extent can the known properties of matter be deduced from these two ideas of the electron and the ether, and is it necessary to add something to them in order to build up a synthesis? We are going to see rapidly and definitely from our idea of the electron, how it is sufficient to represent at the same time the inertia of matter, its dynamic properties, also how it can emit and absorb the radiations which the ether transmits.

The possibility of conceiving of inertia, mass, not as a fundamental idea, but as a consequence of the laws of electromagnetism, is a conception which owes its origin to an important memoir published in 1881 by Professor J. J. Thomson. He studies there, basing his assumptions on the existence of the displacement currents of Maxwell, the electromagnetic field accompanying an electrified sphere in motion. This motion implies a change in the electric field at a point fixed with respect to the medium, and this displacement current immediately produces a magnetic field according to the ideas of Maxwell. The necessity of a convection current is pointed out later. The magnetic field thus produced, identical with that of an element of current parallel to the velocity of the moving charge, is proportional at each point to that velocity, at least, if it does not approach too nearly to that of light.

The creation of a magnetic field at the time of setting the charged centre in motion implies an expenditure of energy, energy of selfinduction of the convection current, proportional to a first approximation to the square of the velocity, for those velocities which are small compared to the velocity of light. It is thus an expression of the same form as that of ordinary kinetic energy. A part, at least, of the inertia of an electrified body, of its capacity for kinetic energy, is thus a consequence of its electric charge.

Moreover, the magnetic field thus produced, and the electric field as well, modified by the velocity as it approaches more nearly to that of light, constitute around the electrified centre in translation a wake which accompanies it in its translation through the ether without change so long as the velocity remains constant. It is besides necessary that an external action should intervene in order to modify the energy of this wake and consequently to increase or diminish the velocity. This implies, in the absence of all other kinetic energy than this of electromagnetic origin, corresponding to the production of the wake, by the law of Galileo on the conservation of the velocity acquired, in the absence of action of all external fields of force, that an electrified centre possesses inertia by the fact alone that it is electrified.

It is the immovable ether, the electromagnetic medium, which serves as a fixed support for the axes with respect to which the principle of inertia is applicable, and of which the ordinary mechanics limits itself in affirming the existence by saying: there exists a system of axes, determined by a nearly uniform translation with respect to which the principle of Galileo is exactly verified.

(12) The Absolute Motion. If we are able, from the actual point of view, to conceive of the ether as supporting these Galilean axes, it does not necessarily follow that the electromagnetic phenomena enable us to arrive at this absolute motion. It seems, on the contrary, so far, that static experiments, carried on in a material system by an observer carried along with it with a uniform motion of translation, do not allow, whatever may be the degree of accuracy of observation, the detection of a relative motion of the ether with respect to matter.

Larmor, and more completely Lorentz, have shown that there exist in the system actions of electromagnetic origin; it is possible to establish in a complete manner a static correspondence (relating to the positions of equilibrium or to the black fringes in optics) between the system in motion and a system fixed with respect to the ether, by means of a change of variables which preserves for the equations of the medium for a moving system the exact form which they possess for a system at rest.

The two systems differ from one another in that the moving system is slightly contracted compared with the fixed system in the direction of the resultant motion by an amount always very small, proportional to the square of the ratio of the velocity of motion to the velocity of light. This contraction affects equally all the elements of the moving system, i. e. the electrons themselves, if we admit with Lorentz that the interior actions of these electrons are solely electromagnetic actions or are modified in the same manner by the translation, - with the result that observation cannot prove this contraction any more than it can prove the general dragging of the ether. These elements behave as though they belonged to a corresponding fixed system. Thus is found an explanation of the negative results of experiments undertaken to show the absolute motion of the earth, by Michelson and Morley, Lord Rayleigh, Brace, Trouton, and Noble, if one admits that all the internal forces of matter are of electromagnetic origin, and that the energy is entirely divided between the two fields, electric and magnetic.

We shall see, however, farther on that it Is difficult to eliminate in this way all other forms of energy, all other forces, such as gravitation; and it would then be necessary to admit with Lorentz, in order that the correspondence between the two systems should actually subsist, that in the moved system the forces and masses of different origins are modified exactly as the electromagnetic forces and masses, an hypothesis too complicated and arbitrary in the actual state of the question.

But this does not seem to be a necessary consequence: it appears probable that these actions, foreign to electromagnetism, and necessary at the interior of the electron in order to give stability and in order to represent gravitation, and which are probably connected with one another, do not intervene in a sensible manner in the negative experiments referred to above, and that everything transpires as if the electromagnetic forces alone played a role, alone existed.

We shall see farther on that perhaps experiments of another kind than those referred to here, for example, some dynamic measurements bringing in a relative motion of the system moved, or some static experiments bringing in gravitation, would enable us to understand the absolute motion, the axes bound to the ether, instead of conceiving simply of their existence.

(13) Electromagnetic Inertia. The problem of the electromagnetic wake accompanying an electrified sphere or ellipsoid in the ether has been taken up since J. J. Thomson by Heaviside and Searle.

Max Abraham has shown their results to consist approximately of a numerical factor when, instead of supposing the body to be a conductor having a surface charge, we suppose its charge to have a uniform volume distribution.

Among the more important results contained in this solution of J. J. Thomson's problem, I will point out these: that in the case of a conducting sphere, the charge remains uniformly distributed on the surface whatever may be the velocity, and that in all cases the electric field at a distance tends to become more and more concentrated in the equatorial plane with respect to the direction of the velocity in proportion as this velocity approaches that of light.

Moreover the kinetic energy which it is necessary to expend at the moment of putting it in motion in order to create the electromagnetic wake ceases to be proportional to the square of the velocity, and increases indefinitely as the velocity approaches the velocity of lightwaves; the law of the increase of this kinetic energy with the velocity, the energy of self-induction of the current to which the charged body in motion is equal, may be easily deduced by Searle's solution.

Without any other hypothesis than that of its electric charge, the electron is found to have inertia defined as capacity for kinetic energy, but with a particular law of variation of this as a function of the velocity, and this inertia appears to approach infinity as the velocity approaches that of light.

The behavior of this law depends very little on the hypothesis made as to the form of the electron and the distribution of the electric charge which it carries. In all cases it is found to be impossible to give the electron a velocity equal to that of light, at least permanently.

Instead of considering with Max Abraham the electron to be spherical at all velocities, Lorentz admits it to be spherical when at rest and to have a uniform distribution of charge; but if all internal forces are solely electromagnetic or act as such, we have the view that the electron is flattened in the direction of motion by a quantity proportional to the square of the ratio (β=v/V). of its velocity to that of light, becoming an ellipsoid of revolution, the equatorial diameter remaining equal to that of the original. This leads, as we shall see, to a law of inertia different from that of an invariable sphere.

We shall likewise see that it does not appear to be necessary to assign to the electrons, the negative ones at least, any other inertia than this in order to account for the dynamic properties of the cathode rays; however, experiments are not yet sufficiently exact to allow us to infer the form of the electron itself, which depends on the law of the variation of the kinetic energy with the velocity.

(14) Two Problems. We have examined, so far, only the case of an electron in uniform motion in the absence of any external electromagnetic field capable of modifying the motion of the electron by giving it an acceleration.

The general problem of the connection between the ether and the electron, which probably represents the most important of the connections between ether and matter, is double.