These two sentences may be considered as authoritative, being quoted in Einstein’s own words.[1] The first of these principles need not greatly surprise us. The second is not well expressed, because it is ambiguous. He does not say how the first “velocity” is measured, whether relatively to the ether or relatively to the observer. In fact this is the very gist of the whole matter, as we shall presently see. In the case of sound the velocity is constant with regard to the medium, the air, in the case of light it is supposed to be constant with regard to the observer. It reaches him with a constant velocity, no matter how he moves.

In order to understand this statement clearly let us consider the appended tabular diagram. On a calm day imagine a source of sound at S in line a. This may be either a gun or a bell. Imagine an observer 1,100 feet distant, located at O. The velocity of sound in air is 1,100 feet per second. This velocity we will take as unity, as indicated in the third column, and the velocity with which the sound reaches the observer is also 1, as shown in the fourth. It will reach him in a unit interval of 1 second, as shown in the fifth. If the bell is struck, it will give its normal pitch or frequency, which we will also call unity, in the sixth column.

Now imagine case b where the observer is on a train advancing toward S. When he is 1,100 feet distant, the gun is fired, but as he is advancing toward it, he hears it at O in rather less than a second, as shown in the fifth column. The velocity of the sound with regard to him is rather more than unity, as shown in the fourth column. If the bell is sounded, the pitch, that is the frequency, is raised, because he receives more sound waves per second than before.

In case c the observer is stationary, but the source of sound is receding. At a distance of 1,100 feet the gun is fired, and the observer hears it after an interval of just one second, as in case a. The velocities with regard to the observer and through the medium are also unity. If the bell is struck the pitch is lowered, since he receives fewer sound waves per second, the reverse of case b.

Velocity
Source in Medium to Observer Interval Frequency Observer
Air
a S 1 1 1 1 O
b S 1 1 + 1 - 1 + O
c S 1 1 1 1 - O
d S 1 1 + 1 - 1 O
Ether
A S 1 1 1 1 O
B S 1 - 1 1 1 + O
C S 1 1 1 1 - O
D S 1 - 1 1 1 O

In case d imagine the source and the observer 1,100 feet apart, and advancing on the same train. When the gun is fired, the velocity of the sound waves will be greater with regard to the observer, and he will hear the sound in less than a second, as in case b. When the bell is struck it will have the normal pitch, the same as in case a.

We find therefore that for sound the velocity with regard to the medium is always unity, while the velocity with regard to the observer, and the interval elapsed, depend only on the motion of the observer himself, and are independent of the motion of the source. The frequency of the vibrations, on the other hand, depends only on the relative motion of the observer and the source, but is independent of their common motion in any direction. Further, it makes no difference whether the source and the observer are moving on a train, or whether they are stationary, and a uniform wind is blowing past them.

In the case of light waves we shall find a very different state of affairs, although the rules for frequency are the same as they are for sound. In case A we have the normal conditions, where both the source and observers are stationary. In case B we have a representation of the Michelson-Morley experiment as supplemented by that of Majorana,[2] where the source is stationary and the observer advances. Unlike the case of sound, the interval elapsed, as shown by the experiment, is now the same as in case A, and since the distance to the observer is less, the velocity of light with respect to the ether must also be less than unity. Since the observer is advancing against the light, this will permit the velocity of light with regard to the observer to remain unity, in conformity with the second principle of relativity. Compare with case b for sound. As Jeans expresses it, “The velocity of light in all directions is the same, whatever the motion of the observer.”[3] That is to say it appears to be the same to him, however he moves.

Case C represents Einstein’s statement, as confirmed by Majorana’s experiment. It does not differ from case c for sound. Case D is more complex, but accepting the statement above that the velocity is constant with regard to the observer, we see that the velocity through the medium must be less, and that the interval elapsed will be constant, as in case B. Could we use the brighter stars and planets as sources of light, several of these cases could be further tested.

This brings us at once to statements that contradict our common sense. For instance, Jeans says “no matter what the velocity of the observer is, the light surface, as observed by that observer, is invariably a sphere having that observer as center.”[3] That is to say the light surface, or wave front, is a contracting, not an expanding, sphere. This, if confirmed, would go a long way toward making our universe a subjective rather than an objective phenomenon. Again imagine a flash of light, such as an explosion, to occur when an observer is in a given position. It makes no difference how the observer may move while the light is approaching him, whether several miles forward or backward, the light will reach him in exactly the same time, as is shown by Michelson’s experiment. Or if two observers are at the same spot when the explosion occurs, and one moves forward, and the other backward, they will both see the explosion at exactly the same instant.