Suppose that we go out on a summer night and look into the dark depths of the sky. A thousand bright specks are flashing there, blue, red, yellow against the dark velvet of space. And as we look we must all be impressed by the fact that such remote objects as the stars can be known to us at all. How is it that light, that curious thing which falls upon the optic nerve and transmits its pictures to the brain, can ever reach us through the black regions of interstellar space? That is the question which has for its answer the electromagnetic theory of light.

The first theory to be advanced was Newton’s “corpuscular” theory which supposed that the stars are sending off into space little pellets of matter so infinitesimally small that they can move at the rate of 186,000 miles a second without injuring even so delicate a thing as the eye when they strike against it.

But in 1801, when Thomas Young made the very important discovery of interference, this had to give way to the wave theory, first proposed by Huyghens in the 17th century. The first great deduction from this, of course, was the “luminiferous ether,” because a wave without some medium for its propagation was quite unthinkable. Certain peculiar properties of the ether were at once evident, since we deduce that it must fill all space and at the same time be so extremely tenuous that it will not retard to any noticeable degree the motion through it of material bodies like the planets.

But how light was propagated through the ether still remained a perplexing problem and various theories were proposed, most prominent among them being the “elastic solid” theory which tried to ascribe to ether the properties of an elastic body. This theory, however, laid itself open to serious objection on the ground that no longitudinal waves had been detected in the ether, so that it began to appear that further insight into the nature of light had to be sought for in another direction.

This was soon forthcoming for in 1864 a new theory was proposed by James Clerk Maxwell which seemed to solve all of the difficulties. Maxwell had been working with the facts derived from a study of electrical and magnetic phenomena and had shown that electromagnetic disturbances were propagated through the ether at a velocity identical with that of light. This, of course, might have been merely a strange coincidence, but Maxwell went further and demonstrated the interesting fact that an oscillating electric charge should give rise to a wave that would behave in a manner identical with all of the known properties of a light wave. One particularly impressive assertion was that these waves, consisting of an alternating electric field accompanied by an alternating magnetic field at right angles to it, and hence called electromagnetic waves, would advance in a direction perpendicular to the alternating fields. This satisfied the first essential property of light rays, i.e., that they must be transverse waves, and the ease with which it explained all of the fundamental phenomena of optics and predicted a most striking interrelation between the electrical and optical properties of material bodies, gave it at once a prominent place among the various theories.

The electromagnetic theory, however, had to wait until 1888 for verification when Heinrich Hertz, in a series of brilliant experiments, succeeded in producing electromagnetic waves in the laboratory and in showing that they possessed all of the properties predicted by Maxwell. These waves moved with the velocity of light: they could be reflected, refracted, and polarized: they exhibited the phenomenon of interference and, in short, could not be distinguished from light waves except for their difference in wave length.

With the final establishment of the electromagnetic theory of light as a fact of physics, we have at last endowed the ether with an actual substantiality. The “empty void” is no longer empty, but a great ocean of ether through which the planets and the suns turn without ever being aware that it is there.

In 1881 A.A. Michelson undertook an experiment, originally suggested by Maxwell, to determine the relative motion of our earth to the ether ocean and six years later he repeated it with the assistance of E.W. Morley. The experiment is now known as the Michelson-Morley experiment and since it is the great physical fact upon which the theory of relativity rests, it will be well for us to examine it in detail.

Since we can scarcely think that our earth is privileged in the universe and that it is at rest with respect to this great ether ocean that fills space, we propose to discover how fast we are actually moving. But the startling fact is that the experiment devised for this purpose failed to detect any motion whatever of the earth relative to the ether.1

The explanation of this very curious fact was given by both H.A. Lorentz and G.F. Fitzgerald in what is now widely known under the name of the “contraction hypothesis.” It is nothing more nor less than this:

Every solid body undergoes a slight change in dimensions, of the order of (v squared slash c squared), when it moves with a velocity v through the ether.

The reason why the experiment failed, then, was not because the earth was not moving through the ether, but because the instruments with which the experiment was being conducted had shrunk just enough to negative the effect that was being looked for.2

We can not at this point forebear introducing a little mathematics to further emphasize the theory and the very logical nature of this contraction hypothesis.

Let us suppose that we were on a world that was absolutely motionless with respect to the ether and were looking at a ray of light. The magnetic and electric fields which form the ray can be described by means of four mathematical expressions which have come to bear the name of “Maxwell’s field equations.” Now suppose that we ask ourselves the question: How must these equations be changed so that they will apply to a ray of light which is being observed by people on a world that is moving with a velocity v through the ether?

The answer is immediate. From the Michelson-Morley experiment we know that we can not tell how fast or how slowly we are moving with respect to the ether. This means that no matter what world we may be upon, the form of the Maxwell field equations will always be the same, even though the second set of axes (or frame of reference) may be moving with high velocity with respect to the first.

Starting from this hypothesis (called in technical language the covariance of the equations with respect to a transformation of coordinates), Lorentz found that the transformation which leaves the field equations unchanged in form was the following: x prime equals k left-parenthesis x minus v t right-parenthesis comma y prime equals y comma z prime equals z comma t prime equals k left-parenthesis t minus v x slash c right-parenthesis

where k is as on page 92.

And what, now, can be deduced from these very simple looking equations? In the first place we see that the space of x', y', z', t' is not our ordinary concept of space at all, but a space in which time is all tangled up with length. To put it more concretely, we may deduce from them the interesting fact that whenever an aviator moves with respect to our earth, his shape changes, and if he were to compare his watch with one on the earth, he would find that his time had changed also. A sphere would flatten into an ellipse, a meter stick would shorten up, a watch would slow down and all because, as H. Minkowski has shown us from these very equations, we are really living in a physical world quite different from the world of Euclid’s geometry in which we are accustomed to think we live.

A variety of objections has very naturally been made to this rather radical hypothesis in an attempt to discredit the entire theory, but it is easily seen that any result obtained through the field equations must necessarily be in conformity with the theory of contraction, since this theory is only the physical interpretation of that transformation which leaves the field equations unaltered. Indeed, it is even possible to postulate the Lorentz transformation together with the assumption that each element of charge is a center of uniformly diverging tubes of strain and derive the Maxwell field equations from this, which shows from another point of view the truly fundamental nature of the transformation.

The whole question of the ether had arrived at this very interesting point when Professor Einstein in 1905 stated the theory of relativity. He had noticed that the equations of dynamics as formulated by Newton did not admit the Lorentz transformation, but only the simple Galilean transformation: x prime equals x minus v t comma y prime equals y comma z prime equals z semicolon t prime equals t period

Here, indeed, was a curious situation. Two physical principles, that of dynamics and that of electromagnetism, were coexistent and yet each one admitted a different transformation when the system of reference was transferred to axes moving with constant velocity with respect to the ether.

Now the electromagnetic equations and their transformation had been shown to be in accord with experimental fact, whereas it had long been felt that Newton’s equations were only a first approximation to the truth. For example, the elliptic orbit of a planet had been observed by Leverrier to exhibit a disquieting tendency to rotate in the direction of motion. This precession, which in the case of Mercury was as large as 43 per century, could not be accounted for in any way by the ordinary Newtonian laws and was, consequently, a very celebrated case of discordance in gravitational astronomy.

With this example clearly before him, Einstein took the great step and said that the laws of dynamics and all other physical laws had to be remade so that they, also, admit the Lorentz transformation. That is to say,

The laws of physical phenomena, or rather the mathematical expressions for these laws, are covariant (unchanged in form) when we apply the Lorentz transformation to them.

The deductions from the Michelson-Morley experiment now seem to have reached their ultimate conclusion.

One discordant fact in this new theory remained, however. That same precession of the perihelion of Mercury which had first lead Einstein to his theory remained unsettled. When the new approximations were applied to the formula of orbital motion, a precession was, indeed, obtained, but the computed value fell considerably below that of the observed 43 per century.

With the idea of investigating the problem from the very bottom, Einstein now undertook a broader and more daring point of view. In the first place he said that there is no apparent reason in the great scheme of world events why any one special system of coordinates should be fundamental to the description of phenomena, just as in the special theory a ray of light would appear the same whether viewed from a fixed system or a system moving with constant velocity with respect to the ether. This makes the very broad assumption that no matter what system of coordinates we may use, the mathematical expressions for the laws of nature must be the same. In Einstein’s own words, then, the first principle of this more general theory of relativity must be the following:

“The general laws of nature are expressed through equations which hold for all systems of coordinates, that is, they are covariant with respect to arbitrary substitutions.”3

But this was not enough to include gravitation so Einstein next formulated what he was pleased to call his “equivalence hypothesis.” This is best illustrated by an example. Suppose that we are mounting in an elevator and wish to investigate the world of events from our moving platform. We mount more and more rapidly, that is with constant acceleration, and we appear to be in a strong gravitational field due to our own inertia. Suppose, on the other hand, that the elevator descends with an acceleration equal to that of gravity. We would now feel certain that we were in empty space because our own relative acceleration has entirely destroyed that of the earth’s gravitational field and all objects placed upon scales in an elevator would apparently be without weight.

Applying this idea, then, Einstein decided to do away with gravitation entirely by referring all events in a gravitational field to a new set of axes which should move with constant acceleration with respect to the first. In other words we are going to deal with a system moving with uniform acceleration with respect to the ether, just as we considered a system moving with uniform velocity in the special theory.

The next step in the construction of this complicated theory is to reduce these two hypotheses to the language of mathematics and this was accomplished by Einstein with the help of M. Grossmann by means of the theory of tensors.

On account of the very great intricacy of the details, we must content ourselves with the mere statement that this really involved the generalization of the famous expressions known as Laplace’s and Poisson’s equations, on the explicit assumption that these two equations would still describe the gravitational field when we are content to use a first approximation to the truth. The set of ten differential equations which Einstein got as a result of his generalization he called his field equations of gravitation.4