1911 Encyclopædia Britannica/Aether
AETHER, or Ether (Gr. αἰθήρ, probably from αἴθω, burn, though Plato in his Cratylus (410 B) derives the name from its perpetual motion—ὅτι ἀεὶ θεῖ περὶ τὸν ἀέρα ῥέων, ἀειθεῂρ δικαίως ἄν καλοῖτο), a material substance of a more subtle kind than visible bodies, supposed to exist in those parts of space which are apparently empty.
“The hypothesis of an aether has been maintained by different speculators for very different reasons. To those who maintained the existence of a plenum as a philosophical principle, nature’s abhorrence of a vacuum was a sufficient reason for imagining an all-surrounding aether, even though every other argument should be against it. To Descartes, who made extension the sole essential property of matter, and matter a necessary condition of extension, the bare existence of bodies apparently at a distance was a proof of the existence of a continuous medium between them. But besides these high metaphysical necessities for a medium, there were more mundane uses to be fulfilled by aethers. Aethers were invented for the planets to swim in, to constitute electric atmospheres and magnetic effluvia, to convey sensations from one part of our bodies to another, and so on, till all space had been filled three or four times over with aethers. It is only when we remember the extensive and mischievous influence on science which hypotheses about aethers used formerly to exercise, that we can appreciate the horror of aethers which sober-minded men had during the 18th century, and which, probably as a sort of hereditary prejudice, descended even to John Stuart Mill. The disciples of Newton maintained that in the fact of the mutual gravitation of the heavenly bodies, according to Newton’s law, they had a complete quantitative account of their motions; and they endeavoured to follow out the path which Newton had opened up by investigating and measuring the attractions and repulsions of electrified and magnetic bodies, and the cohesive forces in the interior of bodies, without attempting to account for these forces. Newton himself, however, endeavoured to account for gravitation by differences of pressure in an aether; but he did not publish his theory, ‘because he was not able from experiment and observation to give a satisfactory account of this medium, and the manner of its operation in producing the chief phenomena of nature.’ On the other hand, those who imagined aethers in order to explain phenomena could not specify the nature of the motion of these media, and could not prove that the media, as imagined by them, would produce the effects they were meant to explain. The only aether which has survived is that which was invented by Huygens to explain the propagation of light. The evidence for the existence of the luminiferous aether has accumulated as additional phenomena of light and other radiations have been discovered; and the properties of this medium, as deduced from the phenomena of light, have been found to be precisely those required to explain electromagnetic phenomena.”
This description, quoted from James Clerk Maxwell’s article in the 9th edition of the Encyclopaedia Britannica, represents the historical position of the subject up till about 1860, when Maxwell began those constructive speculations in electrical theory, based on the influence of the physical views of Faraday and Lord Kelvin, which have in their subsequent development largely transformed theoretical physics into the science of the aether.
In the remainder of the article referred to, Maxwell reviews the evidence for the necessity of an aether, from the fact that light takes time to travel, while it cannot travel as a substance, for if so two interfering lights could not mask each other in the dark fringes (see Interference of Light.) Light is therefore an influence propagated as wave-motion, and moreover by transverse undulations, for the reasons brought out by Thomas Young and Augustin Fresnel; so that the aether is a medium which possesses elasticity of a type analogous to rigidity. It must be very different from ordinary matter as we know it, for waves travelling in matter constitute sound, which is propagated hundreds of thousands of times slower than light.
If we suppose that the aether differs from ordinary matter in degree but not in kind, we can obtain some idea of its quality from a knowledge of the velocity of radiation and of its possible intensity near the sun, in a manner applied long ago by Lord Kelvin (Trans. R. S. Edin. xxi. 1854). According to modern measurements the solar radiation imparts almost 3 gramme-calories of energy per minute per square centimetre at the distance of the earth, which is about 1.3×106 ergs per sec. per cm.2 The energy in sunlight per cubic cm. just outside the earth’s atmosphere is therefore about 4×10−5 ergs; applying the law of inverse squares the value near the sun’s surface would be 1.8 ergs. Let E be the effective elasticity of the aether; then E=ρc2, where ρ is its density, and c the velocity of light which is 3×1010 cm./sec. If ξ=A cosn (t−x/c) is the linear vibration, the stress is E dξ/dx; and the total energy, which is twice the kinetic energy 1⁄2 ρ(dξ/dt)2dx, is 1⁄2 ρn2 A2 per cm., which is thus equal to 1.8 ergs as above. Now λ=2πc/n, so that if A/λ=k, we have 1⁄2 ρ(2πck)2= 1.8, giving ρ=10−22k−2 and E=10−1k−2. Lord Kelvin assumed as a superior limit of k, the ratio of amplitude to wave-length, the value 10−2, which is a very safe limit. It follows that the density of the aether must exceed 10−18, and its elastic modulus must exceed 103, which is only about 10−8 of the modulus of rigidity of glass. It thus appears that if the amplitude of vibration could be as much as 10−2 of the wave-length, the aether would be an excessively rare medium with very slight elasticity; and yet it would be capable of transmitting the supply of solar energy on which all terrestrial activity depends. But on the modern theory, which includes the play of electrical phenomena as a function of the aether, there are other considerations which show that this number 10−2 is really an enormous overestimate; and it is not impossible that the co-efficient of ultimate inertia of the aether is greater than the co-efficient of inertia (of different kind) of any existing material substance.
The question of whether the aether is carried along by the earth’s motion has been considered from the early days of the undulatory theory of light. In reviving that theory at the beginning of the 19th century, Thomas Young stated his conviction that material media offered an open structure to the substance called aether, which passed through them without hindrance "like the wind through a grove of trees." Any convection of that medium could be tested by the change of effective velocity of light, which would be revealed by a prism as was suggested by F. J. D. Arago. Before 1868 Maxwell conducted the experiment by sending light from the illuminated cross-wires of an observing telescope forward through the object-glass, and through a train of prisms, and then reflecting it back along the same path; any influence of convection would conspire in altering both refractions, but yet no displacement of the image depending on the earth's motion was detected. As will be seen later, modern experiments have confirmed the entire absence of any effect, such as convection would produce, to very high precision. It has further been verified by Sir Oliver Lodge that even in very narrow spaces the aether is not entrained by its surroundings when they are put into rapid motion.
A train of ideas which strongly impressed itself on Clerk Maxwell's mind, in the early stages of his theoretical views, was put forward by Lord Kelvin in 1858; he showed that the special characteristics of the rotation of the plane of polarization, discovered by Faraday in light propagated along a magnetic field, viz. that it is doubled instead of being undone when the light retraces its path, requires the operation of some directed agency of a rotational kind, which must be related to the magnetic field. Lord Kelvin was thereby induced to identify magnetic force with rotation, involving, therefore, angular momentum in the aether. Modern theory accepts the deduction, but ascribes the momentum to the revolving ions in the molecules of matter traversed by the light; for the magneto-optic effect is present only in material media. Long previously Lord Kelvin himself came nearer this view, in offering the opinion that magnetism consisted, in some way, in the angular momentum of the material molecules, of which the energy of irregular translations constitutes heat; but the essential idea of moving electric ions of both kinds, positive and negative, in the molecules had still to be introduced.
The question of the transparency of the celestial spaces presents itself in the present connexion. Light from stars at unfathomable distances reaches us in such quantity as to suggest that space itself is absolutely transparent, leaving open the question as to whether there is enough matter scattered through it to absorb a sensible part of the light in its journey of years from the luminous body. If the aether were itself constituted of discrete molecules, on the model of material bodies, such transparency would not be conceivable. We must be content to treat the aether as a plenum, which places it in a class by itself; and we can thus recognize that it may behave very differently from matter, though in some manner consistent with itself—a remark which is fundamental in the modern theory.
Action across a Distance contrasted with Transmitted Action.—In the mechanical processes which we can experimentally modify at will, and which therefore we learn to apprehend with greatest fulness, whenever an effect on a body, B, is in causal connexion with a process instituted in another body, A, it is usually possible to discover a mechanical connexion between the two bodies which allows the influence of A to be traced all the way across the intervening region. The question thus arises whether, in electric attractions across apparently empty space and in gravitational attraction across the celestial regions, we are invited or required to make search for some similar method of continuous transmission of the physical effect, or whether we should rest content with an exact knowledge of the laws according to which one body affects mechanically another body at a distance. The view that our knowledge in such cases may be completely represented by means of laws of action at a distance, expressible in terms of the positions (and possibly motions) of the interacting bodies without taking any heed of the intervening space, belongs to modern times. It could hardly have been thought of before Sir Isaac Newton's discovery of the actual facts regarding universal gravitation. Although, however, gravitation has formed the most perfect instance of an influence completely expressible, up to the most extreme refinement of accuracy, in terms of laws of direct action across space, yet, as is well known, the author of this ideally simple and perfect theory held the view that it is not possible to conceive of direct mechanical action independent of means of transmission. In this belief he differed from his pupil, Roger Cotes, and from most of the great mathematical astronomers of the 18th century, who worked out in detail the task sketched by the genius of Newton. They were content with a knowledge of the truth of the principle of gravitation; instead of essaying to explain it further by the properties of a transmitting medium, they in fact modelled the whole of their natural philosophy on that principle, and tried to express all kinds of material interaction in terms of laws of direct mechanical attraction across space. If material systems are constituted of discrete atoms, separated from each other by many times the diameter of any of them, this simple plan of exhibiting their interactions in terms of direct forces between them would indeed be exact enough to apply to a wide range of questions, provided we could be certain that the laws of the forces depended only on the positions and not also on the motions of the atoms. The most important example of its successful application has been the theory of capillary action elaborated by P. S. Laplace; though even here it appeared, in the hands of Young, and in complete fulness afterwards in those of C. F. Gauss, that the definite results attainable by the hypothesis of mutual atomic attractions really reposed on much wider and less special principles—those, namely, connected with the modern doctrine of energy.
Idea of an Aether.—The wider view, according to which the hypothesis of direct transmission of physical influences expresses only part of the facts, is that all space is filled with physical activity, and that while an influence is passing across from a body, A, to another body, B, there is some dynamical process in action in the intervening region, though it appears to the senses to be mere empty space. The problem is whether we can represent the facts more simply by supposing the intervening space to be occupied by a medium which transmits physical actions, after the manner that a continuous material medium, solid or liquid, transmits mechanical disturbance. Various analogies of this sort are open to us to follow up: for example, the way in which a fluid medium transmits pressure from one immersed solid to another—or from one vortex ring belonging to the fluid to another, which is a much wider and more suggestive case; or the way in which an elastic fluid like the atmosphere transmits sound; or the way in which an elastic solid transmits waves of transverse as well as longitudinal displacement. It is on our familiarity with modes of transmission such as these, and with the exact analyses of them which the science of mathematical physics has been able to make, that our predilection for filling space with an aethereal transmitting medium, constituting a universal connexion between material bodies, largely depends; perhaps ultimately it depends most of all, like all our physical conceptions, on the intimate knowledge that we can ourselves exert mechanical effect on outside bodies only through the agencies of our limbs and sinews. The problem thus arises: Can we form a consistent notion of such a connecting medium? It must be a medium which can be effective for transmitting all the types of physical action known to us; it would be worse than no solution to have one medium to transmit gravitation, another to transmit electric effects, another to transmit light, and so on. Thus the attempt to find out a constitution for the aether will involve a synthesis of intimate correlation of the various types of physical agencies, which appear so different to us mainly because we perceive them through different senses. The evidence for this view, that all these agencies are at bottom connected together and parts of the same scheme, was enormously strengthened during the latter half of the 19th century by the development of a relation of simple quantitative equivalence between them; it has been found that we can define quantities relating to them, under the names of mechanical energy, electric energy, thermal energy, and so on, so that when one of them disappears, it is replaced by the others to exactly equal amount. This single principle of energy has transformed physical science by making possible the construction of a network of ramifying connexions between its various departments; it thus stimulates the belief that these constitute a single whole, and encourages the search for the complete scheme of interconnexion of which the principle of energy and the links which it suggests form only a single feature.
In carrying out this scientific procedure false steps will from time to time be made, which will have to be retraced, or rather amended; but the combination of experimental science with theory has elevated our presumption of the rationality of all natural processes, so far as we can apprehend them at all, into practical certainty; so that, though the mode of presentation of the results may vary from age to age, it is hardly conceivable that the essentials of the method are not of permanent validity.
Atomic Structure of Matter.—The greatest obstacle to such a search for the fundamental medium is the illimitable complexity of matter, as contrasted with the theoretical simplicity and uniformity of the physical agencies which connect together its different parts. It has been maintained since the times of the early Greek philosophers, and possibly even more remote ages, that matter is constituted of independent indestructible units, which cannot ever become divided by means of any mutual actions they can exert. Since the period, a century ago, when Dalton and his contemporaries constructed from this idea a scientific basis for chemistry, the progress of that subject has been wonderful beyond any conception that could previously have been entertained; and the atomic theory in some form appears to be an indispensable part of the framework of physical science. Now this doctrine of material atoms is an almost necessary corollary to the doctrine of a universal aether. For if we held that matter is continuous, one of two alternatives would be open. We might consider that matter and aether can coexist in the same space; this would involve the co-existence and interaction of a double set of properties, introducing great complication, which would place any coherent scheme of physical action probably beyond the powers of human analysis. Or we might consider that aether exists only where matter is not, thus making it a very rare and subtle and elastic kind of matter; then we should have to assign these very properties to the matter itself where it replaces aether, in addition to its more familiar properties, and the complication would remain. The other course is to consider matter as formed of ultimate atoms, each the nucleus or core of an intrinsic modification impressed on the siurounding region of the aether; this might conceivably be of the nature of vortical motion of a liquid round a ring-core, thus giving a vortex atom, or of an intrinsic strain of some sort radiating from a core, which would give an electric atom. We recognize an atom only through its physical activities, as manifested in its interactions with other atoms at a distance from it; this field of physical activity would be identical with the surrounding field of aethereal motion or strain that is inseparably associated with the nucleus, and is carried on along with it as it moves. Here then we have the basis of a view in which there are not two media to be considered, but one medium, homogeneous in essence and differentiated as regards its parts only by the presence of nuclei of intrinsic strain or motion—in which the physical activities of matter are identified with those arising from the atmospheres of modified aether which thus belong to its atoms. As regards laws of general physical interactions, the atom is fully represented by the constitution of this atmosphere, and its nucleus may be left out of our discussions; but in the problems of biology great tracts of invariable correlations have to be dealt with, which seem hopelessly more complex than any known or humanly possible physical scheme. To make room for these we have to remember that the atomic nucleus has remained entirely undefined and beyond our problem; so that what may occur, say when two molecules come into close relations, is outside physical science—not, however, altogether outside, for we know that when the vital nexus in any portion of matter is dissolved, the atoms will remain, in their number, and their atmospheres, and all inorganic relations, as they were before vitality supervened.
Nature of Properties of Material Bodies.—It thus appears that the doctrine of atomic material constitution and the doctrine of a universal aether stand to each other in a relation of mutual support; if the scheme of physical laws is to be as precise as observation and measurement appear to make it, both doctrines are required in our efforts towards synthesis. Our direct knowledge of matter can, however, never be more than a rough knowledge of the general average behaviour of its molecules; for the smallest material speck that is sensible to our coarse perceptions contains myriads of atoms. The properties of the most minute portion of matter which we can examine are thus of the nature of averages. We may gradually invent means of tracing more and more closely the average drifts of translation or orientation, or of changes of arrangement, of the atoms; but there will always remain an unaveraged residue devoid of any recognized regularity, which we can only estimate by its total amount. Thus, if we are treating of energy, we can separate out mechanical and electric and other constituents in it; and there will be a residue of which we know nothing except its quantity, and which we call thermal. This merely thermal energy—which is gradually but very slowly being restricted in amount as new subsidiary organized types become recognized in it—though transmutable in equivalent quantities with the other kinds, yet is so only to a limited extent; the tracing out of the laws of this limitation belongs to the science of thermodynamics. It is the business of that science to find out what is the greatest amount of thermal energy that can possibly be recoverable into organized kinds under given circumstances. The discovery of definite laws in this region might at first sight seem hopeless; but the argument rests on an implied postulate of stability and continuity of constitution of material substances, so that after a cycle of transformations we expect to recover them again as they were originally—on the postulate, in fact, that we do not expect them to melt out of organized existence in our hands. The laws of thermodynamics, including the fundamental principle that a physical property, called temperature, can be defined, which tends towards uniformity, are thus relations between the properties of types of material bodies that can exist permanently in presence of each other; why they so maintain themselves remains unknown, but the fact gives the point d'appui. The fundamental character of energy in material systems here comes into view; if there were any other independent scalar entity, besides mass and energy, that pervaded them with relations of equivalence, we should expect the existence of yet another set of pualities analogous to those connected with temperature. (See Energetics.)
Returning now to the aether, on our present point of view no such complications there arise; it must be regarded as a continuous uniform medium free from any complexities of atomic aggregation, whose function is confined to the transmission of the various types of physical effect between the portions of matter. The problem of its constitution is thus one which can be attacked and continually approximated to, and which may possibly be definitely resolved. It has to be competent to transmit the transverse waves of light and electricity, and the other known radiant and electric actions; the way in which this is done is now in the main known, though there are still questions as to the mode of expression and formulation of our knowledge, and also as regards points of detail. This great advance, which is the result of the gradual focussing of a century's work in the minute exploration of the exact laws of optical and electric phenomena, clearly carries with it deeper insight into the physical nature of matter itself and its modes of inanimate interaction.
If we rest on the synthesis here described, the energy of the matter, even the thermal part, appears largely as potential energy of strain in the aether which interacts with the kinetic energy associated with disturbances involving finite velocity of matter. It may, however, be maintained that an ultimate analysis would go deeper, and resolve all phenomena of elastic resilience into consequences of the kinetic stability of steady motional states, so that only motions, but not strains, would remain. On such a view the aether might conceivably be a perfect fluid, its fundamental property of elastic reaction arising (as at one time suggested by Kelvin and G. F. FitzGerald) from a structure of tangled or interlaced vortex filaments pervading its substance, which might conceivably arrange themselves into a stable configuration and so resist deformation. This raises the further question as to whether the transmission of gravitation can be definitely recognized among the properties of an ultimate medium; if so, we know that it must be associated with some feature, perhaps very deep-seated, or on the other hand perhaps depending simply on incompressibility, which is not sensibly implicated in the electric and optical activities. With reference to all such further refinements of theory, it is to be borne in mind that the perfect fluid of hydrodynamic analysis is not a merely passive inert plenum; it is also a continuum with the property that no finite internal slip or discontinuity of motion can ever arise in it through any kind of disturbance; and this property must be postulated, as it cannot be explained.
Motion of Material Atoms through the Aether.—An important question arises whether, when a material body is moved through the aether, the nucleus of each atom carries some of the surrounding aether along with it; or whether it practically only carries on its strain-form or physical atmosphere, which is transferred from one portion of aether to another after the manner of a shadow, or rather like a loose knot which can slip along a rope without the rope being required to go with it. We can obtain a pertinent illustration from the motion of a vortex ring in a fluid; if the circular core of the ring is thin compared with its diameter, and the vorticity is not very great, it is the vortical state of motion that travels across the fluid without transporting the latter bodily with it except to a slight extent very close to the core. We might thus examine a structure formed of an aggregation of very thin vortex rings, which would move across the fluid without sensibly disturbing it; on the other hand, if formed of stronger vortices, it may transport the portion of the fluid that is within, or adjacent to, its own structure along with it as if it were a solid mass, and therefore also push aside the surrounding fluid as it passes. The motion of the well-known steady spherical vortex is an example of the latter case.
Convection of Optical Waves.—The nature of the motion, if any, that is produced in the surrounding regions of the aether by the translation of matter through it can be investigated by optical experiment. The obvious body to take in the first instance is the earth itself, which on account of its annual orbital motion is travelling through space at the rate of about 18 miles per second. If the surrounding aether is thereby disturbed, the waves of light arriving from the stars will partake of its movement; the ascertained phenomena of the astronomical aberration of light show that the rays travel to the observer, across this disturbed aether near the earth, in straight lines. Again, we may split a narrow beam of light by partial reflexion from a transparent plate, and recombine the constituent beams after they have traversed different circuits of nearly equivalent lengths, so as to obtain interference fringes. The position of these fringes will depend on the total retardation in time of the one beam with respect to the other; and thus it might be expected to vary with the direction of the earth's motion relative to the apparatus. But it is found not to vary at all, even up to the second order of the ratio of the earth's velocity to that of light. It has in fact been found, with the very great precision of which optical experiment is capable, that all terrestrial optical phenomena—reflexion, refraction, polarization linear and circular, diffraction —are entirely unaffected by the direction of the earth's motion, while the same result has recently been extended to electrostatic forces; and this is our main experimental clue.
We pass on now to the theory. We shall make the natural supposition that motion of the aether, say with velocity (u,v,w) at the point (x,y,z), is simply superposed on the velocity V of the optical undulations through that medium, the latter not being intrinsically altered. Now the direction and phase of the light are those of the ray which reaches the eye; and by Fermat's principle, established by Huygens for undulatory motion, the path of a ray is that track along which the disturbance travels in least time, in the restricted sense that any alteration of any short reach of the path will increase the time. Thus the path of the ray when the aether is at rest is the curve which makes ∫ds/V least; but when it is in motion it is the curve which makes ∫ds/(V+lu+my+nw) least, where (l,m,n) is the direction vector of δs. The latter integral becomes, on expanding in a series,
∫ds/V - ∫(udx + vdy + wdz)/V2 + ∫(udx + vdy + wdz)2/V3 + ...,
since lds=dx. If the path is to be unaltered by the motion of the aether, as the law of astronomical aberration suggests, this must differ from ∫ds/V by terms not depending on the path—that is, by terms involving only the beginning and end of it. In the case of the free aether V is constant; thus, if we neglect squares like (u/V)2, the condition is that udx + vdy + wdz be the exact differential of some function f. If this relation is true along all paths, the velocity of the aether must be of irrotational type, like that of frictionless fluid. Moreover, this is precisely the condition for the absence of interference between the component of a split beam; because, the time of passage being to the first order
∫ds/V - ∫(udx + vdy + wdz)/V2
the second term will then be independent of the path (f being a single valued function) and therefore the same for the paths of both the interfering beams. If therefore the aether can be put into motion, we conclude (with Stokes) that such motion, in free space, must be of strictly irrotational type.
But our experimental data are not confined to free space. if c is the velocity of radiation in free space and µ the refractive index of a transparent body, V=C/µ; thus it is the expression c-2 ∫µ2(u'dx + v'dy + w'dz) that is to be integrable explicitly, where now (u',v',w') is what is added to V owing to the velocity (u,v,w) of the medium. As, however, our terrestrial optical apparatus is now all in motion along with the matter, we must deal with the rays relative to the moving system, and to these also Fermat's principle clearly applies; thus V + (lu' + mv' + nw') is here the velocity of radiation in the direction of the ray, but relative to the moving material system. Now the expression above given cannot be integrable exactly, under all circumstances and whatever be the axes of co-ordinates, unless (µ2u',µ2v',µ2w') is the gradient of a continuous function. In the simplest case, that of uniform translation, these components of the gradient will each be constant throughout the region; at a distant place in free aether where there is no motion, they must thus be equal to -u,-v, -w, as they refer to axes moving with the matter. Hence the paths and times of passage of all rays relative to the material system will not be altered by a uniform motion of the system, provided the velocity of radiation relative to the system, in material of index m, is diminished by µ-2 times the velocity of the system in the direction of the radiation, that is, provided the absolute velocity of radiation is increased by 1 - µ-2 times the velocity of the material system; this involves that the free aether for which µ is unity shall remain at rest. This statement constitutes the famous hypothesis of Fresnel, which thus ensures that all phenomena of ray-path and refraction, and all those depending on phase, shall be unaffected by uniform convection of the material medium, in accordance with the results of experiment.
Is the Aether Stationary or Mobile?—This theory secures that the times of passage of the rays shall be independent of the motion of the system, only up to the first order of the ratio of its velocity to that of radiation. But a classical experiment of A. A. Michelson, in which the ray-path was wholly in air, showed that the independence extends to higher orders. This result is inconsistent with the aether remaining at rest, unless we assume that the dimensions of the moving system depend, though to an extent so small as to be not otherwise detectable, on its orientation with regard to the aether that is streaming through it. It is, however, in complete accordance with a view that would make the aether near the earth fully partake in its orbital motion—a view which the null effect of convection on all terrestrial optical and electrical phenomena also strongly suggests. But the aether at a great distance must in any case be at rest; while the facts of astronomical aberration require that the motion of that medium must be irrotational. These conditions cannot be consistent with sensible convection of the aether near the earth without involving discontinuity in its motion at some intermediate distance, so that we are thrown back on the previous theory.
Another powerful reason for taking the aether to be stationary is afforded by the character of the equations of electrodynamics; they are all of linear type, and superposition of effects is possible. Now the kinetics of a medium in which the parts can have finite relative motions will lead to equations which are not linear—as, for example, those of hydrodynamics—and the phenomena will be far more complexly involved. It is true that the theory of vortex rings in hydrodynamics is of a simpler type; but electric currents cannot be likened to permanent vortex rings, because their circuits can be broken and the element of cyclic steadiness on which the simplicity depends is thereby destroyed.
Dynamical Theories of the Aether.—The analytical equations which represent the propagation of light in free aether, and also in aether modified by the presence of matter, were originally developed on the analogy of the equations of propagation of elastic effects in solid media. Various types of elastic solid medium have thus been invented to represent the aether, without complete success in any case. In T. MacCullagh's hands the correct equations were derived from a single energy formula by the principle of least action; and while the validity of this dynamical method was maintained, it was frankly admitted that no mechanical analogy was forthcoming. When Clerk Maxwell pointed out the way to the common origin of optical and electrical phenomena, these equations naturally came to repose on an electric basis, the connexion having been first definitely exhibited by FitzGerald in 1878; and according as the independent variable was one or other of the vectors which represent electric force, magnetic force or electric polarity, they took the form appropriate to one or other of the elastic theories above mentioned.
In this place it must suffice to indicate the gist of the more recent developments of the electro-optical theory, which involve the dynamical verification of Fresnel's hypothesis regarding optical convection and the other relations above described. The aether is taken to be at rest; and the strain-forms belonging to the atoms are the electric fields of the intrinsic charges, or electrones, involved in their constitution. When the atoms are in motion these strain-forms produce straining and unstraining in the aether as they pass across it, which in its motional or kinetic aspect constitutes the resulting magnetic field; as the strains are slight the coefficient of ultimate inertia here involved must be great. True electric current arises solely from convection of the atomic charges or electrons; this current is therefore not restricted as to form in any way. But when the rate of change of aethereal strain—-that is, of (f,g,h) specified as Maxwell's electric displacement in free aether—is added to it, an analytically convenient vector (u,v,w) is obtained which possesses the characteristic property of being circuital like the flow of an incompressible fluid, and has therefore been made fundamental in the theory by Maxwell under the name of the total electric current.
As already mentioned, all efforts to assimilate optical propagation to transmission of waves in an ordinary solid medium have failed; and though the idea of regions of intrinsic strain, as for example in unannealed glass, is familiar in physics, yet on account of the absence of mobility of the strain no attempt had been made to employ them to illustrate the electric fields of atomic charges. The idea of MacCullagh's aether, and its property of purely rotational elasticity which had been expounded objectively by W. J. M. Rankine, was therefore much vivified by Lord Kelvin's specification (Comptes Rendus, 1889) of a material gyrostatically constituted medium which would possess this character. More recently a way has been pointed out in which a mobile permanent field of electric force could exist in such a medium so as to travel freely in company with its nucleus or intrinsic charge—the nature of the mobility of the latter, as well as its intimate constitution, remaining unknown.
A dielectric substance is electrically polarized by a field of electric force, the atomic poles being made up of the displaced positive and negative intrinsic charges in the atom: the polarization per unit volume (f',g',h') may be defined on the analogy of magnetism, and d/dt(f', g', h') thus constitutes true electric current of polarization, i.e. of electric separation in the molecules, specified per unit volume. The convection of a medium thus polarized involves electric disturbance, and therefore must contribute to the true electric current; the determination of this constituent of the current is the most delicate point in the investigation. The usual definition of the component current in any direction, as the net amount of electrons which crosses, towards the positive side, an element of surface fixed in space at right angles to that direction, per unit area per unit time, here gives no definite result. The establishment and convection of a single polar atom constitutes in fact a quasi-magnetization, in addition to the polarization current as above defined, the negative poles completing the current circuits of the positive ones. But in the transition from molecular theory to the electrodynamics of extended media, all magnetism has to be replaced by a distribution of current; the latter being now specified by volume as well as by flow so that (u,v,w) δτ is the current in the element of volume δτ. In the present case the total dielectric contribution to this current works out to be the change per unit time in the electric separation in the molecules of the element of volume, as it moves uniformly with the matter, all other effects being compensated molecularly without affecting the propagation. On subtracting from this total the current of establishment of polarization d/dt/(f,g',h') as formulated above, there remains vd/dx(f',g',h') as the current of convection of polarization when the convection is taken for simplicity to be in the direction of the axis of x with velocity v. The polarization itself is determined from the electric force (P,Q,R) by the usual statical formula of linear type which becomes tor an isotropic medium
because any change of the dielectric constant K arising from the convection of the material through the aether must be independent of the sign of v and therefore be of the second order. Now the electric force (P,Q,R) is the force acting on the electrons of the medium moving with velocity v; consequently by Faraday's electrodynamic law
where (P', Q', R') is the force that would act on electrons at rest, and (a,b,c) is the magnetic induction. The latter force is, by Maxwell's hypothesis or by the dynamical theory of an aether pervaded by electrons, the same as that which strains the aether, and may be called the aethereal force; it thereby produces an aethereal electric displacement, say (f,g,h), according to the relation
in which c is a constant belonging to the aether, which turns out to be the velocity of light. The current of aethereal displacement d/dt(f,g,h) is what adds on to the true electric current to produce the total circuital current of Maxwell.
We have now to substitute these data in the universally valid circuital relations—namely, (i) line integral of magnetic force round a circuit is equal to 4π times the current through its aperture, which may be regarded as a definition of the constitution of the aether and its relation to the electrons involved in it; and (ii) line integral of the electric force belonging to any material circuit (i.e. acting on the electrons situated on it which move with the velocity of the matter) is equal to minus the time-rate of change of the magnetic induction through that circuit as it moves with the matter, this being a dynamical consequence of the aethereal constitution assigned in (i).
We may now, as is somewhat the more natural course in the terrestrial application, take axes (x,y,z) which move with the matter; but the current must be invariably defined by the flux across surfaces fixed in space, so that we may say that relation (i) refers to a circuit fixed in space, while (ii) refers to one moving with the matter. These circuital relations, when expressed analytically, are then for a dielectric medium of types
These equations determine all the phenomena. They take this simple form, however, only when the movement of the matter is one of translation. If v varies with respect to locality, or if there is a velocity of convection (p,q,r) variable with respect to direction and position, and analytical expression of the relation (ii) assumes a more complex form; we thus derive the most general equations of electrodynamic propagation for matter treated as continuous, anyhow distributed and moving in any manner.
For the simplest case of polarized waves travelling parallel to the axis of x, with the magnetic oscillation γ along z and the electric oscillation Q along y, all the quantities are functions of x and t alone; the total current is along y and given with respect to our moving axes by
also the circuital relations here reduce to
giving, on substitution for v,
For a simple wave-train, Q varies as sin m(x-Vt), leading on substitution to the velocity of propagation V relative to the moving material, by means of the equation KV2 + 2 vV = c2-v2; this gives, to the first order of v/c, V = c/√K - v/K, which is in accordance with Fresnel's law. Trains of waves nearly but not quite homogeneous as regards wave-length will as usual be propagated as wave-groups travelling with the slightly different velocity d(Vλ-1)/ dλ-1, the value of K occurring in V being a function of λ determined by the law of optical dispersion of the medium.
For purposes of theoretical discussions relating to moving radiators and reflectors, it is important to remember that the dynamics of all this theory of electrons involves the neglect of terms of the order (v/c)2, not merely in the value of K but throughout.
Recent Experimental Developments.—The modification of the spectrum of a radiating gas by a magnetic field, such as would result from the hypothesis that the radiators are the system of revolving or oscillating electrons in the molecule, was detected by P. Zeeman in 1896, and worked up, in conjunction with H. A. Lorentz, on the general lines suggested by the electron-theory of molecular constitution. While it cannot be said that the full significance of this very definite phenomenon, consisting of the splitting of the spectral line into a number of polarized components, has yet been made out, a wide field of correlation with optical theory, especially in the neighbourhood of absorption bands, has been developed by Zeeman himself, by A. H. Becquerel, by D. Macaluso and O. M. Corbino, and by other workers.
The most fundamental experimental confirmation that the theory of the aether has received on the optical side in recent years has been the verification of Maxwell's proposition that radiation exerts mechanical force on a material system, on which it falls, which may be represented in all cases as the resultant of pressures operating along the rays, and of intensity equal at each point of free space to the density of radiant energy. A high vacuum is needed for the detection of the minute forces here concerned; but just in that case the indirect radiometer-effect of the heating of the residual gas masks the effect. P. N. Lebedew in 1900 succeeded, by operating on metallic vanes so thin that the exposed and averted faces were practically at the same temperature, in satisfactorily verifying the relation for metals; and very soon after, E. F. Nichols and G. F. Hull published accounts of an exact and extensive research, in which the principle had been fully and precisely confirmed as regards both transparent and opaque bodies. The experiment of J. H. Poynting may also be mentioned, in which the tangential component of the thrust of obliquely incident radiation is separately put in evidence, by the torsion produced in an arrangement which is not sensitive to the normal component or to the radiometer-pressure of the residual gas. (See Radiometer.)
Next to these researches on the pressure of radiation, which, by forming the mechanical link between radiation and matter, are fundamental for the thermodynamics of radiant energy, the most striking recent result has been the discovery of H. Rubens and E. Hagen that for dark heat rays of only about ten times the wave-length of luminous radiation, the properties of metals are determined by their electric resistance alone, which then masks all resonance due to periods of free vibration of the molecules; and, moreover, that the resistance for such alternations is practically the same as the ohmic resistance for ordinary steady currents. They found that the absorbing powers of the metals, and therefore, by the principle of exchanges, their radiating powers also, are proportional to the square roots of their electric conductivities. Maxwell had himself, at an early stage of his theory, tested the absorbing power of gold-leaf for light, and found that the effective conductivity for luminous vibrations must be very much greater than its steady ohmic value; it is, in fact, there a case of incipient conductivity, which is continually being undone on account of the rapid alternation of force before it is fully established. That, however, complete conduction should arrive with alternations only ten times slower than light was an unexpected and remarkable fact, which verifies the presumption that the process of conduction is one in which the dynamic activities of the molecules do not come into play. The corollary, that the electric resistance of a metal can be determined in absolute units by experiments on the reflexion of heat-rays from its surface, is a striking illustration of the unification of the various branches of physical science, which has come in the train of the development of the theory of the aether. (See Radiation.)
Finally, reference should be made to the phenomena of radioactivity, whether excited by the electric discharge in vacuum tubes, foreshadowed in part by Sir Wm. Crookes and G. G. Stokes, and later by A. Schuster and others, but first fully developed with astonishing results including the experimental discovery of the free electron by J. J. Thomson, or the correlated phenomena occurring spontaneously in radio-active bodies as discovered by H. Becquerel and by M. and Mme Curie, and investigated by them and by E. Rutherford and others. These results constitute a far-reaching development of the modern or electrodynamic theory of the aether, of which the issue can hardly yet be foreseen.
- See H. A. Lorentz, loc. cit. infra.; J. Larmor, Aether and Matter, p. 262 and passim.