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Attempt=20
of a Theory of Electrical and Optical Phenomena in Moving=20
Bodies by Introduction |
Definitions=E2=86=92= |
=C2=A7 1. The question as to whether the aether shares the motion of = ponderable=20 bodies or not, has still found no answer that satisfies all physicists. = For the=20 decision, primarily the aberration of light and related phenomena could = be used,=20 but so far none of the two contested theories, neither that of Fresnel, nor that of Stokes, were fully confirmed = with=20 respect to all observations, so concerning the choice between the two = views we=20 can only weigh against each other the remaining problems for both of = them. By=20 that I was long ago led to believe that with Fresnel's view, i.e. = with the=20 assumption of a stationary aether, we are on the right way. While = against the=20 view of Stokes there is = hardly=20 more than one objection, i.e. the doubt that his assumptions = regarding=20 the aether-motion in the vicinity of Earth are contradictory[1]= SUP>,=20 but this objection is of great weight, and I can't see at all how it = could be=20 eliminated.
The difficulties for Fresnel's=20 theory stem from the known interference experiment of Michelson[2]= SUP>=20 and, as some think, from the experiments, by which Des Coudres in vain sought to = find an=20 influence of Earth's motion on the induction=20 of two circuits[3]= SUP>.=20 The results of the American scientist, however, allow of an = interpretation by an=20 auxiliary hypotheses, and the findings of Des Coudres can easily be = explained=20 without such one.
Concerning the observations of Fizeau[4]= SUP>=20 on the rotation of polarization in glass columns, the matter is as = follows. At=20 first glance, the result is decidedly against Stokes' view. Yet when I tried = to=20 improve Fresnel's = theory, the=20 explanation of Fizeau's=20 experiments was not quite successful, so I gradually suspected that this = result=20 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=20 colleague van de Sande = Bakhuijzen=20 after his request, that at present he himself doesn't see his = observations as=20 crucial.
In the further course of this work, I will come back in more detail = to some=20 of the issues raised at this place. Here I was concerned only with the=20 preliminary justification of the standpoint I have taken.
In favor of Fresnel's = theory=20 several well-known reasons can be cited. Especially the impossibility of = locking=20 the aether between solid or liquid walls. As far as we know, a space = devoid of=20 air behaves (in the mechanical sense) like a real vacuum, when = ponderable bodies=20 are in motion. When we see how the mercury of a barometer rises to the = top when=20 the tube is inclined, or how easily a closed metal shell can be = compressed, one=20 can not avoid the idea, that solid and liquid bodies let the aether pass = through=20 without hindrance. One hardly will assume,=20 that this medium could suffer a compression, without giving resistance = to=20 it.
That transparent bodies can move, without communicating their = full=20 velocity to the contained aether, was proven by Fizeau's famous interference = experiment=20 with streaming water[5]= SUP>.=20 This experiment, that later was repeated by Michelson and Morley[6]= SUP>=20 on a larger scale, could impossibly have had the observed success, when=20 everything within the tube would possess a common velocity. By = that, only=20 the behavior of nontransparent substances and very extended bodies = remains=20 questionable.
It should be noted, moreover, that we can imagine the permeability of = a body=20 in two ways. First, this property might not be present in individual = atoms, yet=20 when the atoms were very small compared to the gaps between them, it = might be=20 present in matter of greater extension; but secondly, it may be assumed = - and=20 this hypothesis I will use in the following - that ponderable matter is=20 absolutely permeable, namely that at the location of an atom, = also the=20 aether exists at the same time, which would be understandable if we were = allowed=20 to see the atoms as local modifications of the aether.
It is not my intention to enter into such speculations more closely, = or to=20 express assumptions about the nature of the aether. I only wish to keep = me as=20 free as possible from preconceived opinions about that substance, and I = won't,=20 for example, attribute to it the properties of ordinary liquids and = gases. If it=20 is the case, that a representation of the phenomena would succeed best = under the=20 condition of absolute permeability, then one should admit of such an = assumption=20 for the time being, and leave it to the subsequent research, to give us = a deeper=20 understanding.
That=20 we cannot speak about an absolute rest of the aether, is = self-evident;=20 this expression would not even make sense. When I say for the sake of = brevity,=20 that the aether would be at rest, then this only means that one part of = this=20 medium does not move against the other one and that all perceptible = motions are=20 relative motions of the celestial bodies in relation to the aether.
=C2=A7 2. Since Maxwell's views=20 became more and more accepted, the question of the properties of the = aether=20 became highly important also for the theory of elasticity. Strictly = speaking,=20 not a single experiment in which a charged body or a current conductor = moves,=20 can be handled carefully, if the state of motion of the aether is not = considered=20 at the same time. In any phenomenon of electricity, the question arises = whether=20 an influence of the earth's motion is to be expected; and regarding the=20 consequences of the latter for optical phenomena, we have to demand from = the=20 electro-magnetic theory of light that it can account for the already = established=20 facts. Namely, the aberration theory isn't one of those parts of optics, = for=20 which treatment the general principles of wave theory are sufficient. = Once a=20 telescope comes into play, one can not help but to apply Fresnel's dragging coefficient = to the=20 lenses, yet its value can only be derived from special assumptions about = the=20 nature of light vibrations.
The fact that the electro-magnetic theory of light really leads to = that=20 coefficient assumed by Fresnel,=20 was shown by me two years ago[7]= SUP>.=20 Since then I have greatly simplified the theory and extended it also to = the=20 processes involved in reflection and refraction, as well as birefringent = bodies[8]= SUP>.=20 It may be permitted for me, to come back to this matter.
To=20 come to the basic equations for the phenomena of electricity in moving = bodies, I=20 joined an opinion that has been represented in recent years by several=20 physicists; I have indeed assumed that small electrically charged = molecules=20 exist in all bodies, and that all electric processes are based on the = location=20 and motion of these "ions". As regards the electrolytes, this view is = widely=20 recognized as the only possible one, and Giese[9]= SUP>,=20 Schuster[10]<= /SUP>,=20 Arrhenius[11]= ,=20 Elster and Geitel[12]= =20 have defended the view, that also as regards the electricity conduction = in=20 gases, we are dealing with a convection by ions. It seems to me, that = nothing=20 prevents us to believe that the molecules of ponderable dielectric = bodies=20 contain such particles, which are connected to certain equilibrium = positions and=20 are moved only by external electric forces thereof; just herein the = "dielectric=20 polarization" of such bodies would consist.
The periodically changing polarization, which forms a light ray = according to=20 Maxwell's theory, become = vibrations of the ions in this conception. It is well known that many=20 researchers, who stood on the basis of the older theory of light, = considered the=20 resonance of ponderable matter as the cause of color dispersion, and = this=20 explanation can in the main also included into the electro-magnetic = theory of=20 light, for which it is only necessary to ascribe to the ions a certain = mass.=20 This I have shown in a previous paper[13]= ,=20 in which I admittedly have derived the equations of motion from actions = at a=20 distance, and not, what I now consider to be much easier, from Maxwell's expressions. = Later,=20 von Helmholtz[14]= =20 in his electromagnetic theory of color dispersion started from the same = point of=20 view[15]= .
Giese[16]= =20 has applied to various cases the hypothesis, that electricity is = connected to=20 ions in metallic conductors as well; but the picture which he gives of = the=20 processes in these bodies is at one point substantially different = from=20 the idea that we have on the conduction in electrolytes. While the = particles of=20 dissolved salt, however often they may be stopped by the water = molecules,=20 eventually might travel over large distances, the ions in a copper wire = will=20 hardly have such a great mobility. We can however be satisfied with = forward and=20 backward motion at molecular distances, if we only assume that one ion = often=20 transfers its charge to another, or that two oppositely charged ions, if = they=20 meet, or after they were "connected" with one another, exchange their = charges=20 against each other. In any case, such processes must take place at the = boundary=20 of two bodies, when a current flows from one to the other. If for = example n positively charged copper = atoms are=20 separated at a copper plate, and we also want for the latter all the = electricity=20 be connected to ions, then we have to assume that the charges are = transferred to=20 n atoms in the plate, or = that =20 of the deposited particles exchange their charges with =20 negatively charged copper atoms, which were already in the = electrode.
Thus, if the adoption of this transition or exchange of the ionic = charges -=20 one of course still very dark process - is the essential complement to = any=20 theory that requires=20 an entrainment of electricity by ions, then a persistent electric = current never=20 consists of a convection alone, at least not when the centers of = two=20 touching or interconnected particles are in some distance l from each other. Then the electricity = motion=20 happens without convection over a distance of order l, and only if this is very small in = proportion to=20 the distance over which a convection takes place, we on the whole are = dealing=20 almost exclusively with this latter phenomenon.
Giese is of the = opinion that in=20 metals a real convection was not at all in play. But since it does not = seem=20 possible to include the "jumping" of the charges into the theory, then = one would=20 excuse, that for my part I totally disregard such a process, and that I=20 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=20 remains at a different view.
=C2=A7 3. The theory of ions was very suitable for my purpose, = because it makes it=20 possible to introduce the permeability of the aether in a rather = satisfactory=20 way in the equations. Of course, these were decomposed into two groups. = First,=20 we have to express as to how the state of the aether by charge, position = and=20 motion of the ions is determined; then, secondly, we have to indicate by = which=20 forces the aether is acting on the charged particles. In my paper = already=20 cited[17]= =20 I have derived the formulas by means of d'Alembert's principle from = certain=20 assumptions and therefore selected a path, that has much resemblance = with Maxwell's application of Lagrange's equations. Now I = prefer for=20 the sake of brevity, to introduce the basic equations themselves as=20 hypotheses.
The formulas for the aether are in agreement, regarding the space = between=20 the=20 ions, with the known equations of Maxwell's theory, and = generally express=20 that any change that was caused by an ion in the aether, propagates with = the=20 velocity of light. But we regard the force exerted by the aether on a = charged=20 particle, as a function of the state of that medium at the point where = the=20 particle is located. The adopted fundamental law differs in a major = point from=20 the laws, that were introduced by Weber and Clausius. The influence that = was=20 suffered by a particle B due to the vicinity of a second one A, indeed = depends=20 on the motion of the latter, but not on its instantaneous motion. = Much=20 more relevant is the motion of A some time earlier, and the adopted law=20 corresponds to the requirement for the theory of electrodynamics, that = was=20 presented by Gauss in = 1845 in his=20 known letter to Weber[18]=
In general, the assumptions that I introduce represent in a certain = sense a=20 return to the earlier theories of electricity. The core of Maxwell's views is therefore = not lost,=20 but it cannot be denied that with the adoption of ions we are not far = away from=20 the electric particles, which were used earlier. In some simple cases, = this=20 occurs particularly clear. Since the essence of electric charge is seen = by us in=20 the accumulation of positive or negative charged particles, and since = the basic=20 formulas for stationary ions give Coulomb's law, therefore, for = example,=20 the entire electrostatics can be brought into the earlier form.