Essays in Science (12 page)

The evolution of electrical theory along the lines laid down by Clerk Maxwell and Lorentz gave a most peculiar and unexpected turn to the development of our ideas about the ether. For Clerk Maxwell himself the ether was still an entity with purely mechanical properties, though of a far more complicated kind than those of tangible solid bodies. But neither Maxwell nor his successors succeeded in thinking out a mechanical model for the ether capable of providing a satisfactory mechanical interpretation of Maxwell’s laws of the electro-dynamic field. The laws were clear and simple, the mechanical interpretations clumsy and contradictory. Almost imperceptibly theoretical physicists adapted themselves to this state of affairs, which was a most depressing one from the point of view of their mechanistic program, especially under the influence of the electro-dynamic researches of Heinrich Hertz. Whereas they had formerly demanded of an ultimate theory that it should be based upon fundamental concepts of a purely mechanical kind (e.g., mass-densities, velocities, deformations, forces of gravitation), they gradually became accustomed to admitting strengths of electrical and magnetic fields as fundamental concepts alongside of the mechanical ones, without insisting on a mechanical interpretation of them. The purely mechanistic view of nature was thus abandoned. This change led to a dualism in the sphere of fundamental concepts which was in the long run intolerable. To escape from it people took the reverse line of trying to reduce mechanical concepts to electrical ones. The experiments with β-rays and high-velocity cathode rays did much to shake confidence in the strict validity of Newton’s mechanical equations.

Heinrich Hertz took no steps towards mitigating this dualism. Matter appears as the substratum not only of velocities, kinetic energy, and mechanical forces of gravity, but also of electro-magnetic fields. Since such fields are also found in a vacuum—i.e., in the unoccupied ether—the ether also appears as the substratum of electro-magnetic fields, entirely similar in nature to ponderable matter and ranking alongside it. In the presence of matter it shares in the motions of the latter and has a velocity everywhere in empty space; the etheric velocity nowhere changes discontinuously. There is no fundamental distinction between the Hertzian ether and ponderable matter (which partly consists of the ether).

Hertz’s theory not only suffered from the defect that it attributed to matter and the ether mechanical and electrical properties, with no rational connection between them; it was also inconsistent with the result of Fizeau’s famous experiment on the velocity of the propagation of light in a liquid in motion and other well authenticated empirical facts.

Such was the position when H. A. Lorentz entered the field. Lorentz brought theory into harmony with experiment, and did it by a marvelous simplification of basic concepts. He achieved this advance in the science of electricity, the most important since Clerk Maxwell, by divesting the ether of its mechanical, and matter of its electro-magnetic properties. Inside material bodies no less than in empty space the ether alone, not atomically conceived matter, was the seat of electro-magnetic fields. According to Lorentz the elementary particles of matter are capable
only
of executing movements; their electromagnetic activity is entirely due to the fact that they carry electric charges. Lorentz thus succeeded in reducing all electro-magnetic phenomena to Maxwell’s equations for a field in vacuo.

As regards the mechanical nature of Lorentz’s ether, one might say of it, with a touch of humor, that immobility was the only mechanical property which Lorentz left it. It may be added that the whole difference which the special theory of relativity made in our conception of the ether lay in this, that it divested the ether of its last mechanical quality, namely immobility. How this is to be understood I will explain immediately.

The Maxwell-Lorentz theory of the electro-magnetic field served as the model for the space-time theory and the kinematics of the special theory of relativity. Hence it satisfies the conditions of the special theory of relativity; but looked at from the standpoint of the latter, it takes on a new aspect. If C is a co-ordinate system in respect to which the Lorentzian ether is at rest, the Maxwell-Lorentz equations hold good first of all in regard to C. According to the special theory of relativity these same equations hold good in exactly the same sense in regard to any new co-ordinate system C, which is in uniform translatory motion with respect to C. Now comes the anxious question, Why should I distinguish the system C, which is physically perfectly equivalent to the systems C’, from the latter by assuming that the ether is at rest in respect to it? Such an asymmetry of the theoretical structure, to which there is no corresponding asymmetry in the system of empirical facts, is intolerable to the theorist. In my view the physical equivalence of C and C’ with the assumption that the ether is at rest in respect to C but in motion with respect to C’, though not absolutely wrong from a logical point of view, is nevertheless unsatisfactory.

The most obvious line to adopt in the face of this situation seemed to be the following:—There is no such thing as the ether. The electro-magnetic fields are not states of a medium but independent realities, which cannot be reduced to terms of anything else and are bound to no substratum, any more than are the atoms of ponderable matter. This view is rendered the more natural by the fact that, according to Lorentz’s theory, electro-magnetic radiation carries impulse and energy like ponderable matter, and that matter and radiation, according to the special theory of relativity, are both of them only particular forms of distributed energy, inasmuch as ponderable matter loses its exceptional position and merely appears as a particular form of energy.

In the meantime more exact reflection shows that this denial of the existence of the ether is not demanded by the restricted principle of relativity. We can assume the existence of an ether; but we must abstain from ascribing a definite state of motion to it, i.e., we must divest it by abstraction of the last mechanical characteristic which Lorentz left it. We shall see later on that this way of looking at it, the intellectual possibility of which I shall try to make clearer by a comparison that does not quite fit at all points, is justified by the results of the general theory of relativity.

Consider waves on the surface of water. There are two quite different things about this phenomenon which may be described. One can trace the progressive changes which take place in the undulating surface where the water and the air meet. One can also—with the aid of small floating bodies, say—trace the progressive changes in the position of the individual particles. If there were in the nature of the case no such floating bodies to aid us in tracing the movement of the particles of liquid, if nothing at all could be observed in the whole procedure except the fleeting changes in the position of the space occupied by the water, we should have no ground for supposing that the water consists of particles. But we could none the less call it a medium.

Something of the same sort confronts us in the electro-magnetic field. We may conceive the field as consisting of lines of force. If we try to think of these lines of force as something material in the ordinary sense of the word, there is a temptation to ascribe the dynamic phenomena involved to their motion, each single line being followed out through time. It is, however, well known that this way of looking at the matter leads to contradictions.

Generalizing, we must say that we can conceive of extended physical objects to which the concept of motion cannot be applied. They must not be thought of as consisting of particles, whose course can be followed out separately through time. In the language of Minkowski this is expressed as follows:—Not every extended entity in the four-dimensional world can be regarded as composed of world-lines. The special principle of relativity forbids us to regard the ether as composed of particles the movements of which can be followed out through time, but the theory is not incompatible with the ether hypothesis as such. Only we must take care not to ascribe a state of motion to the ether.

From the point of view of the special theory of relativity the ether hypothesis does certainly seem an empty one at first sight. In the equations of an electro-magnetic field, apart from the density of the electrical charge nothing appears except the strength of the field. The course of electro-magnetic events in a vacuum seems to be completely determined by that inner law, independently of other physical quantities. The electro-magnetic field seems to be the final irreducible reality, and it seems superfluous at first sight to postulate a homogeneous, isotropic etheric medium, of which these fields are to be considered as states.

On the other hand, there is an important argument in favor of the hypothesis of the ether. To deny the existence of the ether means, in the last analysis, denying all physical properties to empty space. But such a view is inconsistent with the fundamental facts of mechanics. The mechanical behavior of a corporeal system floating freely in empty space depends not only on the relative positions (intervals) and velocities of its masses, but also on its state of rotation, which cannot be regarded physically speaking as a property belonging to the system as such. In order to be able to regard the rotation of a system at least formally as something real, Newton regarded space as objective. Since he regards his absolute space as a real thing, rotation with respect to an absolute space is also something real to him. Newton could equally well have called his absolute space “the ether”; the only thing that matters is that in addition to observable objects another imperceptible entity has to be regarded as real, in order for it to be possible to regard acceleration, or rotation, as something real.

Mach did indeed try to avoid the necessity of postulating an imperceptible real entity, by substituting in mechanics a mean velocity with respect to the totality of masses in the world for acceleration with respect to absolute space. But inertial resistance with respect to the relative acceleration of distant masses presupposes direct action at a distance. Since the modern physicist does not consider himself entitled to assume that, this view brings him back to the ether, which has to act as the medium of inertial action. This conception of the ether to which Mach’s approach leads, differs in important respects from that of Newton, Fresnel and Lorentz. Mach’s ether not only
conditions
the behavior of inert masses but is also conditioned, as regards its state, by them.

Mach’s notion finds its full development in the ether of the general theory of relativity. According to this theory the metrical properties of the space-time continuum in the neighborhood of separate space-time points are different and conjointly conditioned by matter existing outside the region in question. This spatio-temporal variability of the relations of scales and clocks to each other, or the knowledge that “empty space” is, physically speaking, neither homogeneous nor isotropic, which compels us to describe its state by means of ten functions, the gravitational potentials gμν, has no doubt finally disposed of the notion that space is physically empty. But this has also once more given the ether notion a definite content—though one very different from that of the ether of the mechanical wave-theory of light. The ether of the general theory of relativity is a medium which is itself free of
all
mechanical and kinematic properties, but helps to determine mechanical (and electro-magnetic) happenings.

The radical novelty in the ether of the general theory of relativity as against the ether of Lorentz lies in this, that the state of the former at every point is determined by the laws of its relationship with matter and with the state of the ether at neighboring points expressed in the form of differential equations, whereas the state of Lorentz’s ether in the absence of electromagnetic fields is determined by nothing outside it and is the same everywhere. The ether of the general theory of relativity can be transformed intellectually into Lorentz’s through the substitution of constants for the spatial functions which describe its state, thus neglecting the causes conditioning the latter. One may therefore say that the ether of the general theory of relativity is derived through relativization from the ether of Lorentz.

The part which the new ether is destined to play in the physical scheme of the future is still a matter of uncertainty. We know that it determines both material relations in the space-time continuum, e.g., the possible configurations of solid bodies, and also gravitational fields; but we do not know whether it plays a material part in the structure of the electric particles of which matter is made up. Nor do we know whether its structure only differs materially from that of Lorentz’s in the proximity of ponderable masses, whether, in fact, the geometry of spaces of cosmic extent is, taken as a whole, almost Euclidean. We can, however, maintain on the strength of the relativistic equations of gravitation that spaces of cosmic proportions must depart from Euclidean behavior if there is a positive mean density of matter, however small, in the Universe. In this case the Universe must necessarily form a closed space of finite size, this size being determined by the value of the mean density of matter.

If we consider the gravitational field and the electro-magnetic field from the standpoint of the ether hypothesis, we find a notable fundamental difference between the two. No space and no portion of space without gravitational potentials; for these give it its metrical properties without which it is not thinkable at all. The existence of the gravitational field is directly bound up with the existence of space.

On the other hand a portion of space without an electro-magnetic field is perfectly conceivable, hence the electro-magnetic field, in contrast to the gravitational field, seems in a sense to be connected with the ether only in a secondary way, inasmuch as the formal nature of the electro-magnetic field is by no means determined by the gravitational ether. In the present state of theory it looks as if the electromagnetic field, as compared with the gravitational field, were based on a completely new formal motive; as if nature, instead of endowing the gravitational ether with fields of the electro-magnetic type, might equally well have endowed it with fields of a quite different type, for example, fields with a scalar potential.