## Einstein 1938: The Wave Theory of Light

##### Reference: Evolution of Physics

This paper presents Chapter II, section 8 from the book THE EVOLUTION OF PHYSICS by A. EINSTEIN and L. INFELD. The contents are from the original publication of this book by Simon and Schuster, New York (1942).

The paragraphs of the original material (in black) are accompanied by brief comments (in color) based on the present understanding.  Feedback on these comments is appreciated.

.

## The Wave Theory of Light

Let us recall why we broke off the description of optical phenomena. Our aim was to introduce another theory of light, different from the corpuscular one, but also attempting to explain the same domain of facts. To do this we had to interrupt our story and introduce the concept of waves. Now we can return to our subject.

It was Huygens, a contemporary of Newton, who put forward quite a new theory. In his treatise on light he wrote:

If, in addition, light takes time for its passage which we are now going to examine it will follow that this movement, impressed on the intervening matter, is successive; and consequently it spreads, as sound does, by spherical surfaces and waves, for I call them waves from their resemblance to those which are seen to be formed in water when a stone is thrown into it, and which present a successive spreading as circles, though these arise from another cause, and are only in a flat surface.

According to Huygens, light is a wave, a transference of energy and not of substance. We have seen that the corpuscular theory explains many of the observed facts. Is the wave theory also able to do this? We must again ask the questions which have already been answered by the corpuscular theory, to see whether the wave theory can do the answering just as well. We shall do this here in the form of a dialogue between N and H, where N is a believer in Newton’s corpuscular theory, and H in Huygen’s theory. Neither is allowed to use arguments developed after the work of the two great masters was finished.

According to Huygens, light is a wave, transference of energy and not of substance.

N. In the corpuscular theory the velocity of light has a very definite meaning. It is the velocity at which the corpuscles travel through empty space. What does it mean in the wave theory?

H. It means the velocity of the light wave, of course. Every known wave spreads with some definite velocity, and so should a wave of light.

In N-theory it is the particle that is moving. In H-theory, it is not the particle, but a disturbance that is moving.

N. That is not as simple as it seems. Sound waves spread in air, ocean waves in water. Every wave must have a material medium in which it travels. But light passes through a vacuum, whereas sound does not. To assume a wave in empty space really means not to assume any wave at all.

H. Yes, that is a difficulty, although not a new one to me. My master thought about it very carefully, and decided that the only way out is to assume the existence of a hypothetical substance, the ether, a transparent medium permeating the entire universe. The universe is, so to speak, immersed in ether. Once we have the courage to introduce this concept, everything else becomes clear and convincing.

The N-theory does not require a medium for light, but the H-theory assumes aether as a transparent medium permeating the entire universe, which acts as a medium for light.

N. But I object to such an assumption. In the first place it introduces a new hypothetical substance, and we already have too many substances in physics. There is also another reason against it. You no doubt believe that we must explain everything in terms of mechanics. But what about the ether? Are you able to answer the simple question as to how the ether is constructed from its elementary particles and how it reveals itself in other phenomena?

H. Your first objection is certainly justified. But by introducing the somewhat artificial weightless ether we at once get rid of the much more artificial light corpuscles. We have only one “mysterious” substance instead of an infinite number of them corresponding to the great number of colours in the spectrum. Do you not think that this is real progress? At least all the difficulties are concentrated on one point. We no longer need the factitious assumption that particles belonging to different colours travel with the same speed through empty space. Your second argument is also true. We cannot give a mechanical explanation of ether. But there is no doubt that the future study of optical and perhaps other phenomena will reveal its structure. At present we must wait for new experiments and conclusions, but finally, I hope, we shall be able to clear up the problem of the mechanical structure of the ether.

The N-theory is assuming many different substance for light (one for each color), whereas, H-theory is only assuming the substance of aether to explain all colors.

N. Let us leave the question for the moment, since it cannot be settled now. I should like to see how your theory, even if we waive the difficulties, explains those phenomena which are so clear and understandable in the light of the corpuscular theory. Take, for example, the fact that light rays travel in vacuo or in air along straight lines. A piece of paper placed in front of a candle produces a distinct and sharply outlined shadow on the wall. Sharp shadows would not be possible if the wave theory of light were correct, for waves would bend around the edges of the paper and thus blur the shadow. A small ship is not an obstacle for waves on the sea, you know; they simply bend around it without casting a shadow.

H. That is not a convincing argument. Take short waves on a river impinging on the side of a large ship. Waves originating on one side of the ship will not be seen on the other. If the waves are small enough and the ship large enough, a very distinct shadow appears. It is very probable that light seems to travel in straight lines only because its wave-length is very small in comparison with the size of ordinary obstacles and of apertures used in experiments. Possibly, if we could create a sufficiently small obstruction, no shadow would occur. We might meet with great experimental difficulties in constructing apparatus which would show whether light is capable of bending. Nevertheless, if such an experiment could be devised it would be crucial in deciding between the wave theory and the corpuscular theory of light.

Both N-theory and H-theory can explain light traveling in straight line and casting shadows. Experiments may be designed, however, to test light for wave properties.

N. The wave theory may lead to new facts in the future, but I do not know of any experimental data confirming it convincingly. Until it is definitely proved by experiment that light may be bent, I do not see any reason for not believing in the corpuscular theory, which seems to me to be simpler, and therefore better, than the wave theory.

At this point we may interrupt the dialogue, though the subject is by no means exhausted.

It still remains to be shown how the wave theory explains the refraction of light and the variety of colours. The corpuscular theory is capable of this, as we know. We shall begin with refraction, but it will be useful to consider first an example having nothing to do with optics.

The corpuscular theory is able to explain refraction of light and the colors.

There is a large open space in which there are walking two men holding between them a rigid pole. At the beginning they are walking straight ahead, both with the same velocity. As long as their velocities remain the same, whether great or small, the stick will be undergoing parallel displacement; that is, it does not turn or change its direction. All consecutive positions of the pole are parallel to each other. But now imagine that for a time which may be as short as a fraction of a second the motions of the two men are not the same. What will happen? It is clear that during this moment the stick will turn, so that it will no longer be displaced parallel to its original position. When the equal velocities are resumed, it is in a direction different from the previous one. This is shown clearly in the drawing. The change in direction took place during the time interval in which the velocities of the two walkers were different.

This example will enable us to understand the refraction of a wave. A plane wave travelling through the ether strikes a plate of glass. In the next drawing we see a wave which presents a comparatively wide front as it marches along. The wave front is a plane on which at any given moment all parts of the ether behave in precisely the same way. Since the velocity depends on the medium through which the light is passing, it will be different in glass from the velocity in empty space. During the very short time in which the wave front enters the glass, different parts of the wave front will have different velocities. It is clear that the part which has reached the glass will travel with the velocity of light in glass, while the other still moves with the velocity of light in ether. Because of this difference in velocity along the wave front during the time of “immersion” in the glass, the direction of the wave itself will be changed.

Thus we see that not only the corpuscular theory, but also the wave theory, leads to an explanation of refraction. Further consideration, together with a little mathematics, shows that the wave theory explanation is simpler and better, and that the consequences are in perfect agreement with observation. Indeed, quantitative methods of reasoning enable us to deduce the velocity of light in a refractive medium if we know how the beam refracts when passing into it. Direct measurements splendidly confirm these predictions, and thus also the wave theory of light.

The wave theory can also explain the refraction of light. Actually, it does so in a simpler and better way.

There still remains the question of colour.

It must be remembered that a wave is characterized by two numbers, its velocity and its wave-length. The essential assumption of the wave theory of light is that different wave-lengths correspond to different colours. The wave-length of homogeneous yellow light differs from that of red or violet. Instead of the artificial segregation of corpuscles belonging to various colours we have the natural difference in wave-length.

The wave theory explains the differences in colors as corresponding to differences in wave lengths.

It follows that Newton’s experiments on the dispersion of light can be described in two different languages, that of the corpuscular theory and that of the wave theory. For example:

It would seem wise to avoid the ambiguity resulting from the existence of two distinct theories of the same phenomena, by deciding in favour of one of them after a careful consideration of the faults and merits of each. The dialogue between N and H shows that this is no easy task. The decision at this point would be more a matter of taste than of scientific conviction. In Newton’s time, and for more than a hundred years after, most physicists favoured the corpuscular theory.

In Newton’s time, and for more than a hundred years after, most physicists favoured the corpuscular theory.

History brought in its verdict, in favour of the wave theory of light and against the corpuscular theory, at a much later date, the middle of the nineteenth century. In his conversation with H, N stated that a decision between the two theories was, in principle, experimentally possible. The corpuscular theory does not allow light to bend, and demands the existence of sharp shadows. According to the wave theory, on the other hand, a sufficiently small obstacle will cast no shadow. In the work of Young and Fresnel this result was experimentally realized and theoretical conclusions were drawn.

A switch to wave theory occurred in the middle of the nineteenth century.

An extremely simple experiment has already been discussed, in which a screen with a hole was placed in front of a point source of light and a shadow appeared on the wall. We shall simplify the experiment further by assuming that the source emits homogeneous light. For the best results the source should be a strong one. Let us imagine that the hole in the screen is made smaller and smaller. If we use a strong source and succeed in making the hole small enough, a new and surprising phenomenon appears, something quite incomprehensible from the point of view of the corpuscular theory. There is no longer a sharp distinction between light and dark. Light gradually fades into the dark background in a series of light and dark rings. The appearance of rings is very characteristic of a wave theory. The explanation for alternating light and dark areas will be clear in the case of a somewhat different experimental arrangement. Suppose we have a sheet of dark paper with two pinholes through which light may pass. If the holes are close together and very small, and if the source of homogeneous light is strong enough, many light and dark bands will appear on the wall, gradually fading off at the sides into the dark background. The explanation is simple. A dark band is where a trough of a wave from one pinhole meets the crest of a wave from the other pinhole, so that the two cancel. A band of light is where two troughs or two crests from waves of the different pinholes meet and reinforce each other. The explanation is more complicated in the case of the dark and light rings of our previous example in which we used a screen with one hole, but the principle is the same. This appearance of dark and light stripes in the case of two holes and of light and dark rings in the case of one hole should be borne in mind, for we shall later return to a discussion of the two different pictures. The experiments described here show the diffraction of light, the deviation from the rectilinear propagation when small holes or obstacles are placed in the way of the light wave.

The experiments described here show the diffraction of light, the deviation from the rectilinear propagation when small holes or obstacles are placed in the way of the light wave.

With the aid of a little mathematics we are able to go much further. It is possible to find out how great or, rather, how small the wave-length must be to produce a particular pattern. Thus the experiments described enable us to measure the wave-length of the homogeneous light used as a source. To give an idea of how small the numbers are we shall cite two wavelengths, those representing the extremes of the solar spectrum, that is, the red and the violet.

The wave-length of red light is 0.00008 cm.
The wave-length of violet light is 0.00004 cm.

The experiments described enable us to measure the wave-length of the homogeneous light used as a source.

We should not be astonished that the numbers are so small. The phenomenon of distinct shadow, that is, the phenomenon of rectilinear propagation of light, is observed in nature only because all apertures and obstacles ordinarily met with are extremely large in comparison with the wave-lengths of light. It is only when very small obstacles and apertures are used that light reveals its wave-like nature.

It is only when very small obstacles and apertures are used that light reveals its wave-like nature.

But the story of the search for a theory of light is by no means finished. The verdict of the nineteenth century was not final and ultimate. For the modern physicist the entire problem of deciding between corpuscles and waves again exists, this time in a much more profound and intricate form. Let us accept the defeat of the corpuscular theory of light until we recognize the problematic nature of the victory of the wave theory.

But the victory for wave-theory comes with its own problems.

.

It is interesting that light can be explained both as corpuscles and as a wave. Newton (1642 – 1727) proposed the corpuscular theory, while his contemporary, Huygens (1629 – 1695), proposed the wave theory.

The wave theory requires a medium, whereas the corpuscular theory requires particles and no medium. In both cases a substance is required either as a medium or as a particle. The medium is assumed to be continuous, whereas, particles are discrete. The underlying philosophical question is: In the final analysis, is the substance continuous or discrete?

It seems that an extremely light particle moving very fast shall appear as a wave. This means that the particle is its own medium and no other medium is required. There is no medium necessary for light because light is its own medium.

.