| TO what extent is the special theory of relativity supported by experience? This question is not easily answered for the reason already mentioned in connection with the fundamental experiment of Fizeau. The special theory of relativity has crystallised out from the Maxwell-Lorentz theory of electromagnetic phenomena. Thus all facts of experience which support the electromagnetic theory also support the theory of relativity. As being of particular importance, I mention here the fact that the theory of relativity enables us to predict the effects produced on the light reaching us from the fixed stars. These results are obtained in an exceedingly simple manner, and the effects indicated, which are due to the relative motion of the earth with reference to those fixed stars, are found to be in accord with experience. We refer to the yearly movement of the apparent position of the fixed stars resulting from the motion of the earth round the sun (aberration), and to the influence of the radial components of the relative motions of the fixed stars with respect to the earth on the colour of the light reaching us from them. The latter effect manifests itself in a slight displacement of the spectral lines of the light transmitted to us from a fixed star, as compared with the position of the same spectral lines when they are produced by a terrestrial source of light (Doppler principle). The experimental arguments in favour of the Maxwell-Lorentz theory, which are at the same time arguments in favour of the theory of relativity, are too numerous to be set forth here. In reality they limit the theoretical possibilities to such an extent, that no other theory than that of Maxwell and Lorentz has been able to hold its own when tested by experience. | 1 |
| But there are two classes of experimental facts hitherto obtained which can be represented in the Maxwell-Lorentz theory only by the introduction of an auxiliary hypothesis, which in itself—i.e. without making use of the theory of relativity—appears extraneous. | 2 |
It is known that cathode rays and the so-called  -rays emitted by radioactive substances consist of negatively electrified particles (electrons) of very small inertia and large velocity. By examining the deflection of these rays under the influence of electric and magnetic fields, we can study the law of motion of these particles very exactly. | 3 |
In the theoretical treatment of these electrons, we are faced
with the difficulty that electrodynamic theory of itself is unable to give
an account of their nature. For since electrical masses of one sign repel
each other, the negative electrical masses constituting the electron would
necessarily be scattered under the influence of their mutual repulsions,
unless there are forces of another kind operating between them, the nature
of which has hitherto remained obscure to us. 1
If we now assume that the relative distances between the electrical masses
constituting the electron remain unchanged during the motion of the electron
(rigid connection in the sense of classical mechanics), we arrive at a law
of motion of the electron which does not agree with experience. Guided by
purely formal points of view, H. A. Lorentz was the first to introduce the
hypothesis that the particles constituting the electron experience a contraction
in the direction of motion in consequence of that motion, the amount of
this contraction being proportional to the expression
This hypothesis, which is not justifiable by any electrodynamical facts, supplies us then with that particular law of motion which has been confirmed with great precision in recent years. | 4 |
| The theory of relativity leads to the same law of motion,
without requiring any special hypothesis whatsoever as to the structure
and the behaviour of the electron. We arrived at a similar conclusion in
Section XIII in connection with the experiment of Fizeau, the result of
which is fore-told by the theory of relativity without the necessity of
drawing on hypotheses as to the physical nature of the liquid. |
5 |
| The second class of facts to which we have alluded has reference
to the question whether or not the motion of the earth in space can be made
perceptible in terrestrial experiments. We have already remarked in Section
V that all attempts of this nature led to a negative result. Before the
theory of relativity was put forward, it was difficult to become reconciled
to this negative result, for reasons now to be discussed. The inherited
prejudices about time and space did not allow any doubt to arise as to the
prime importance of the Galilei transformation for changing over from one
body of reference to another. Now assuming that the Maxwell-Lorentz equations
hold for a reference-body K, we then find that they do not hold for
a reference-body K' moving uniformly with respect to K, if
we assume that the relations of the Galileian transformation exist between
the co-ordinates of K and K'. It thus appears that of all
Galileian co-ordinate
systems one (K) corresponding to a particular state of motion is
physically unique. This result was interpreted physically by regarding K
as at rest with respect to a hypothetical æther of space. On the other
hand, all co-ordinate systems K' moving relatively to K were
to be regarded as in motion with respect to the æther. To this motion
of K' against the æther (“æther-drift” relative
to K') were assigned the more complicated laws which were supposed
to hold relative to K'. Strictly speaking, such an æther-drift
ought also to be assumed relative to the earth, and for a long time the
efforts of physicists were devoted to attempts to detect the existence of
an æther-drift at the earth’s surface. |
6 |
| In one of the most notable of these attempts Michelson devised
a method which appears as though it must be decisive. Imagine two mirrors
so arranged on a rigid body that the reflecting surfaces face each other.
A ray of light requires a perfectly definite time T to pass from
one mirror to the other and back again, if the whole system be at rest with
respect to the æther. It is found by calculation, however, that a slightly
different time T' is required for this process, if the body, together
with the mirrors, be moving relatively to the æther. And yet another
point: it is shown by calculation that for a given velocity v with
reference to the æther, this time T' is different
when the body is moving perpendicularly to the planes of the mirrors from
that resulting when the motion is parallel to these planes. Although the
estimated difference between these two times is exceedingly small, Michelson
and Morley performed an experiment involving interference in which this
difference should have been clearly detectable. But the experiment gave
a negative result—a fact very perplexing to physicists. Lorentz and
FitzGerald rescued the theory from this difficulty by assuming that the
motion of the body relative to the æther produces a contraction of
the body in the direction of motion, the amount of contraction being just
sufficient to compensate for the difference in time mentioned above. Comparison
with the discussion in Section XII shows that from the standpoint also of
the theory of relativity this solution of the difficulty was the right one.
But on the basis of the theory of relativity the method of interpretation
is incomparably more satisfactory. According to this theory there is no
such thing as a “specially favoured” (unique) co-ordinate system
to occasion the introduction of the æther-idea, and hence there can
be no æther-drift, nor any experiment with which to demonstrate it.
Here the contraction of moving bodies follows from the two fundamental principles
of the theory without the introduction of particular hypotheses; and as
the
prime factor involved in this contraction we find, not the motion in itself,
to which we cannot attach any meaning, but the motion with respect to the
body of reference chosen in the particular case in point. Thus for a co-ordinate
system moving with the earth the mirror system of Michelson and Morley is
not shortened, but it is shortened for a co-ordinate system which
is at rest relatively to the sun. |
7 |
