Attempt of a Theory of Electrical and Optical Phenomena in Moving Bodies/Introduction
|Attempt of a Theory of Electrical and Optical Phenomena in Moving Bodies by
§ 1. The question as to whether the aether shares the motion of ponderable bodies or not, has still found no answer that satisfies all physicists. For the decision, primarily the aberration of light and related phenomena could be used, but so far none of the two contested theories, neither that of Fresnel, nor that of Stokes, were fully confirmed with respect to all observations, so concerning the choice between the two views we can only weigh against each other the remaining problems for both of them. By that I was long ago led to believe that with Fresnel's view, i.e. with the assumption of a stationary aether, we are on the right way. While against the view of Stokes there is hardly more than one objection, i.e. the doubt that his assumptions regarding the aether-motion in the vicinity of Earth are contradictory, but this objection is of great weight, and I can't see at all how it could be eliminated.
The difficulties for Fresnel's theory stem from the known interference experiment of Michelson and, as some think, from the experiments, by which Des Coudres in vain sought to find an influence of Earth's motion on the induction of two circuits. The results of the American scientist, however, allow of an interpretation by an auxiliary hypotheses, and the findings of Des Coudres can easily be explained without such one.
Concerning the observations of Fizeau on the rotation of polarization in glass columns, the matter is as follows. At first glance, the result is decidedly against Stokes' view. Yet when I tried to improve Fresnel's theory, the explanation of Fizeau's experiments was not quite successful, so I gradually suspected that this result had been obtained by observational error, or at least it had not met the theoretical considerations which formed the basis of the experiments. And Fizeau was so friendly to tell my colleague van de Sande Bakhuijzen after his request, that at present he himself doesn't see his observations as crucial.
In the further course of this work, I will come back in more detail to some of the issues raised at this place. Here I was concerned only with the preliminary justification of the standpoint I have taken.
In favor of Fresnel's theory several well-known reasons can be cited. Especially the impossibility of locking the aether between solid or liquid walls. As far as we know, a space devoid of air behaves (in the mechanical sense) like a real vacuum, when ponderable bodies are in motion. When we see how the mercury of a barometer rises to the top when the tube is inclined, or how easily a closed metal shell can be compressed, one can not avoid the idea, that solid and liquid bodies let the aether pass through without hindrance. One hardly will assume, that this medium could suffer a compression, without giving resistance to it.
That transparent bodies can move, without communicating their full velocity to the contained aether, was proven by Fizeau's famous interference experiment with streaming water. This experiment, that later was repeated by Michelson and Morley on a larger scale, could impossibly have had the observed success, when everything within the tube would possess a common velocity. By that, only the behavior of nontransparent substances and very extended bodies remains questionable.
It should be noted, moreover, that we can imagine the permeability of a body in two ways. First, this property might not be present in individual atoms, yet when the atoms were very small compared to the gaps between them, it might be present in matter of greater extension; but secondly, it may be assumed - and this hypothesis I will use in the following - that ponderable matter is absolutely permeable, namely that at the location of an atom, also the aether exists at the same time, which would be understandable if we were allowed to see the atoms as local modifications of the aether.
It is not my intention to enter into such speculations more closely, or to express assumptions about the nature of the aether. I only wish to keep myself as free as possible from preconceived opinions about that substance, and I won't, for example, attribute to it the properties of ordinary liquids and gases. If it is the case, that a representation of the phenomena would succeed best under the condition of absolute permeability, then one should admit of such an assumption for the time being, and leave it to the subsequent research, to give us a deeper understanding.
That we cannot speak about an absolute rest of the aether, is self-evident; this expression would not even make sense. When I say for the sake of brevity, that the aether would be at rest, then this only means that one part of this medium does not move against the other one and that all perceptible motions are relative motions of the celestial bodies in relation to the aether.
§ 2. Since Maxwell's views became more and more accepted, the question of the properties of the aether became highly important also for the theory of elasticity. Strictly speaking, not a single experiment in which a charged body or a current conductor moves, can be handled carefully, if the state of motion of the aether is not considered at the same time. In any phenomenon of electricity, the question arises whether an influence of the earth's motion is to be expected; and regarding the consequences of the latter for optical phenomena, we have to demand from the electro-magnetic theory of light that it can account for the already established facts. Namely, the aberration theory isn't one of those parts of optics, for which treatment the general principles of wave theory are sufficient. Once a telescope comes into play, one can not help but to apply Fresnel's dragging coefficient to the lenses, yet its value can only be derived from special assumptions about the nature of light vibrations.
The fact that the electro-magnetic theory of light really leads to that coefficient assumed by Fresnel, was shown by me two years ago. Since then I have greatly simplified the theory and extended it also to the processes involved in reflection and refraction, as well as birefringent bodies. It may be permitted for me, to come back to this matter.
To come to the basic equations for the phenomena of electricity in moving bodies, I joined an opinion that has been represented in recent years by several physicists; I have indeed assumed that small electrically charged molecules exist in all bodies, and that all electric processes are based on the location and motion of these "ions". As regards the electrolytes, this view is widely recognized as the only possible one, and Giese, Schuster, Arrhenius, Elster and Geitel have defended the view, that also as regards the electricity conduction in gases, we are dealing with a convection by ions. It seems to me, that nothing prevents us to believe that the molecules of ponderable dielectric bodies contain such particles, which are connected to certain equilibrium positions and are moved only by external electric forces thereof; just herein the "dielectric polarization" of such bodies would consist.
The periodically changing polarization, which forms a light ray according to Maxwell's theory, become vibrations of the ions in this conception. It is well known that many researchers, who stood on the basis of the older theory of light, considered the resonance of ponderable matter as the cause of color dispersion, and this explanation can in the main also included into the electro-magnetic theory of light, for which it is only necessary to ascribe to the ions a certain mass. This I have shown in a previous paper, in which I admittedly have derived the equations of motion from actions at a distance, and not, what I now consider to be much easier, from Maxwell's expressions. Later, von Helmholtz in his electromagnetic theory of color dispersion started from the same point of view.
Giese has applied to various cases the hypothesis, that electricity is connected to ions in metallic conductors as well; but the picture which he gives of the processes in these bodies is at one point substantially different from the idea that we have on the conduction in electrolytes. While the particles of dissolved salt, however often they may be stopped by the water molecules, eventually might travel over large distances, the ions in a copper wire will hardly have such a great mobility. We can however be satisfied with forward and backward motion at molecular distances, if we only assume that one ion often transfers its charge to another, or that two oppositely charged ions, if they meet, or after they were "connected" with one another, exchange their charges against each other. In any case, such processes must take place at the boundary of two bodies, when a current flows from one to the other. If for example positively charged copper atoms are separated at a copper plate, and we also want for the latter all the electricity be connected to ions, then we have to assume that the charges are transferred to atoms in the plate, or that of the deposited particles exchange their charges with negatively charged copper atoms, which were already in the electrode.
Thus, if the adoption of this transition or exchange of the ionic charges - one of course still very dark process - is the essential complement to any theory that requires an entrainment of electricity by ions, then a persistent electric current never consists of a convection alone, at least not when the centers of two touching or interconnected particles are in some distance from each other. Then the electricity motion happens without convection over a distance of order , and only if this is very small in proportion to the distance over which a convection takes place, we on the whole are dealing almost exclusively with this latter phenomenon.
Giese is of the opinion that in metals a real convection was not at all in play. But since it does not seem possible to include the "jumping" of the charges into the theory, then one would excuse, that for my part I totally disregard such a process, and that I interpret a current in a metal wire simply as a motion of charged particles.
Further research will have to decide whether the results of the theory remains at a different view.
§ 3. The theory of ions was very suitable for my purpose, because it makes it possible to introduce the permeability of the aether in a rather satisfactory way in the equations. Of course, these were decomposed into two groups. First, we have to express as to how the state of the aether by charge, position and motion of the ions is determined; then, secondly, we have to indicate by which forces the aether is acting on the charged particles. In my paper already cited I have derived the formulas by means of d'Alembert's principle from certain assumptions and therefore selected a path, that has much resemblance with Maxwell's application of Lagrange's equations. Now I prefer for the sake of brevity, to introduce the basic equations themselves as hypotheses.
The formulas for the aether are in agreement, regarding the space between the ions, with the known equations of Maxwell's theory, and generally express that any change that was caused by an ion in the aether, propagates with the velocity of light. But we regard the force exerted by the aether on a charged particle, as a function of the state of that medium at the point where the particle is located. The adopted fundamental law differs in a major point from the laws, that were introduced by Weber and Clausius. The influence that was suffered by a particle B due to the vicinity of a second one A, indeed depends on the motion of the latter, but not on its instantaneous motion. Much more relevant is the motion of A some time earlier, and the adopted law corresponds to the requirement for the theory of electrodynamics, that was presented by Gauss in 1845 in his known letter to Weber
In general, the assumptions that I introduce represent in a certain sense a return to the earlier theories of electricity. The core of Maxwell's views is therefore not lost, but it cannot be denied that with the adoption of ions we are not far away from the electric particles, which were used earlier. In some simple cases, this occurs particularly clear. Since the essence of electric charge is seen by us in the accumulation of positive or negative charged particles, and since the basic formulas for stationary ions give Coulomb's law, therefore, for example, the entire electrostatics can be brought into the earlier form.
- Lorentz. De l’influence du mouvement de la terre sur les phénomènes lumineux. Arch. néerl., T. 21, p. 103, 1887; Lodge. Aberration problems. London Phil. Trans., Vol. 184. A, p. 727, 1893; Lorentz. De aberratietheorie van Stokes. Zittingsverslagen der Akad. v. Wet. te Amsterdam, 1892—93, p. 97.
- Michelson. American Journal of Science, 3d. Ser., Vol. 22, p. 120; Vol. 34, p. 333, 1887; Phil. Mag., 5th. Ser., Vol. 24, p. 449, 1887.
- Des Coudres. Wied. Ann., Bd. 38, p. 71, 1889.
- Fizeau. Ann. de chim. et de phys., 3e sér., T. 58, p. 129, 1860; Pogg. Ann., Bd. 114, p. 554, 1861.
- Fizeau. Ann. de chim. et de phys., 3e sér. T. 57, p. 385, 1859; Pogg. Ann., Erg. 3, p. 457, 1853.
- Michelson and Morley. American Journal of Science, 3d. ser., Vol. 31, p. 377, 1886.
- Lorentz. La théorie électromagnétique de Maxwell et son application aux corps mouvants. Leide, E. J. Brill, 1892. (Also published in Arch, néerl., T. 25).
- A preliminary report about that was published in Zittingsverslagen der Akad. v. Wet. te Amsterdam, 1892—93, pp. 28 and 149.
- Giese. Wied. Ann., Bd. 17, p. 538, 1882.
- Schuster. Proc. Roy. Soc., Vol. 37, p. 317, 1884.
- Arrhenius. Wied. Ann., Bd. 32, p. 565, 1887; Bd. 33, p. 638, 1888.
- Elster and Geitel. Wiener Sitz.-Ber., Bd. 97, Abth. 2, p. 1255, 1888.
- Lorentz. Over net vorband tusschen de voortplantingssnelheid van het licht en de dichtheid en samenstelling der middenstoffen. Verhandelingen der Akad. van Wet. te Amsterdam, Deel 18, 1878; Wied. Ann., Bd. 9, p. 641, 1880.
- v. Helmholtz. Wied. Ann., Bd. 48, p. 389, 1893.
- Also Koláček (Wied. Ann., Bd. 32, pp. 224 and 429, 1887) attempted to explain (albeit in a different manner) dispersion by electrical vibrations in the molecules.
Also the theory of Goldhammer (Wied. Ann., Bd. 47, p. 93, 1892) has to be mentioned.
- Giese. Wied. Ann., Bd. 37, p. 576, 1889.
- Lorentz. La théorie électromagnétique de Maxwell et son application aux corps mouvants.
- Gauss. Werke, Bd. 5, p. 629.