Electromagnetic Forces

In 1921 Eddington extended Weyl's geometry into a still more general system of geometry, in which even lengths at the same point were not assumed to be capable of direct comparison. This geometry had a certain advantage over Weyl's original geometry in that the terms which were ultimately called on to explain electro-magnetic phenomena occurred naturally as a necessary development of the geometry. In Weyl's geometry the necessary terms are shaped to fill a gap, and it is then found that they fit exactly. In Eddington's geometry no shaping is necessary, or, rather, the shaping process is performed off the stage or before the curtain rises. The gravitational and electro-magnetic forces are accounted for by the symmetrical and antisymmetrical parts of a single tensor, so that an electro-magnetic field appears almost to be a necessary accompaniment to a gravitational field. But Eddington's geometry, like that of Weyl, predicts precisely the same phenomena as Maxwell's classical electro-magnetic theory, so that again experimental test is impossible.

Both these geometries are successful in interpreting the electro magnetic field in free space in terms of geometry, but show less success in interpreting the ponderomotive forces on charged bod ies, electrons, protons, etc. The difficulty is not that they cannot explain the observed forces, but that they do not explain them in a simple, natural way, and that they explain too much. Although nothing less than the proposed geometries would have sufficed to explain the electro-magnetic field in free space, it looks as if something less would be adequate to explain the ponderomotive forces exerted by the field on its own electric charges. The pro posed geometries are too rich and predict not only observed phenomena but also others which have then to be explained away as being incapable of observation.

After making great advances in the direction of clearing away these difficulties, Einstein washed his hands of the whole attempt in 1926.

Later Einstein proposed a scheme based on a geometry funda mentally different from either of the foregoing, which he describes as the "Unitary Field Theory." His main object is to avoid the dualism by which the gravitational field and the electro-magnetic field were exhibited in former theories as independent construc tions in the space-time continuum, and instead to display "both types of field as manifestations of one comprehensive type of spatial structure in the space-time continuum." The new theory resulted from the discovery that types of geometry exist in which distant lines may be parallel, but in which lengths in the neigh bourhood of a point obey laws of measurement of the same type (Riemannian) as in the simple purely gravitational theory, so that the geometry is not Euclidean. The new geometry has been de scribed as a geometry in which there can be parallels but not parallelograms; if we attempt to draw a figure which is to have pairs of equal and parallel lines as its opposite sides, we find that the parallelogram we are attempting to build refuses to close up at its fourth corner. So far Einstein has developed the conse quences of his "Unitary Field Theory" to a first approximation only. The new theory obviously escapes some of the reproaches which have been brought against its predecessors ; whether it has any claims to finality remains to be seen.

The Position of the Ether.

It is clear that the doctrine of relativity must profoundly affect our views of the ether and its function in the scheme of the universe. At one stage in the his tory of science, there was a tendency to imagine space filled with innumerable ethers, to the extent almost of one ether for every set of phenomena requiring explanation. That stage passed, and by the end of the 19th century only one ether received serious consideration, the so-called electro-magnetic ether of Faraday and Maxwell. This ether gave a plausible mechanical explanation of electrostatic phenomena, although it was more than doubtful whether it could account for the electro-magnetic phenomena from which it took its name, and it was comparatively certain that it could not account for gravitation. It gave, however, a satis factory explanation of the propagation of waves of light—they were simply waves in the ether which travelled with an absolute velocity c determined once and for all by the structure of the ether. On this view it was quite certain that an observer moving through the ether with a velocity u would measure the velocity of light travelling in the same direction as himself as c—u. Rela tivity, teaching that this velocity is always precisely c, dis misses the particular type of ether imagined by Faraday and Maxwell. Whether any new ether will be devised to replace it remains to be seen, but none appears to be necessary. Any ether which can be imagined would appear to depend upon an ob jective separation of time and space. Relativity does not deny that such an objective separation may, in the last resort, really exist, but it shows that no material phenomena are concerned with such a separation. By a very slight turn of thought, the primary postulate of relativity may be expressed in the form that the material world goes on as though no ether existed.

To the relativist the essential background to the picture of the universe is not the varying agitation of a sea of ether in a three-dimensional space but a tangle of world lines in a four dimensional space. Only the intersections of the world lines are important. An intersection at a point in the continuum rep resents an event, while the part of a world line which is free from intersections represents the mere uneventful existence of a par ticle or a pulse of light. And so, since our whole knowledge of the universe is made up of events, it comes about that the tangle of world lines may be distorted and bent to any degree we please; so long as the order of the intersections is not altered, it will still represent the same universe. Thus the last function of the ether, that of providing a scale of absolute measurements in space, becomes a superfluity. To the physicist who urges that space measurements without an underlying ether become meaningless, the relativist can reply that time-measurements without an un derlying "time-ether" are equally meaningless. A "time-ether" has never been regarded as a necessity, and the relativist may fairly argue that the "space-ether" has no greater claim to retention.

Probably, however, final judgment on this, as on other similar questions, must be suspended until the position of electro-magnetic forces in the general scheme of relativity is better understood than it is now.