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%%% Primary Title: Experience and the Special Theory of Relativity
%%% Primary Category Code: 03.30.+p
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\begin{document}
\subsection{Experience and the Special Theory of Relativity}
From \htmladdnormallink{Relativity: The Special and General Theory}{http://planetphysics.us/encyclopedia/SpecialTheoryOfRelativity.html} by \htmladdnormallink{Albert Einstein}{http://planetphysics.us/encyclopedia/AlbertEinstein.html}
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 \htmladdnormallink{relative motion}{http://planetphysics.us/encyclopedia/CoriolisEffect.html} 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 \htmladdnormallink{position}{http://planetphysics.us/encyclopedia/Position.html} of the fixed stars resulting from the \htmladdnormallink{motion}{http://planetphysics.us/encyclopedia/CosmologicalConstant.html} 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.
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---{\it i.e.}
without making use of the theory of relativity---appears extraneous.
It is known that cathode rays and the so-called $\beta$-rays emitted by
radioactive substances consist of negatively electrified \htmladdnormallink{particles}{http://planetphysics.us/encyclopedia/Particle.html} (electrons) of very small inertia and large \htmladdnormallink{velocity}{http://planetphysics.us/encyclopedia/Velocity.html}. By examining the
deflection of these rays under the influence of electric and \htmladdnormallink{magnetic fields}{http://planetphysics.us/encyclopedia/NeutrinoRestMass.html}, we can study the law of motion of these particles very
exactly.
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 \htmladdnormallink{masses}{http://planetphysics.us/encyclopedia/CosmologicalConstant.html} 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 \htmladdnormallink{forces}{http://planetphysics.us/encyclopedia/Thrust.html} of another kind operating between
them, the nature of which has hitherto remained obscure to us.\footnotemark\ 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 \htmladdnormallink{classical mechanics}{http://planetphysics.us/encyclopedia/NewtonianMechanics.html}),
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 form of the electron
experiences a contraction in the direction of motion in consequence of
that motion. the contracted length being proportional to the
expression
$$\overline{\sqrt{I-\frac{v^2}{c^2}}}.$$
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.
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
\htmladdnormallink{section}{http://planetphysics.us/encyclopedia/IsomorphicObjectsUnderAnIsomorphism.html} 13 in connection with the experiment of Fizeau, the result
of which is foretold by the theory of relativity without the necessity
of drawing on hypotheses as to the physical nature of the liquid.
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 5 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
Galileian 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 \htmladdnormallink{relations}{http://planetphysics.us/encyclopedia/Bijective.html} of the Galileian transformstion exist between the
co-ordinates of $K$ and $K'$. It thus appears that, of all Galileian
co-ordinate \htmladdnormallink{systems}{http://planetphysics.us/encyclopedia/GenericityInOpenSystems.html}, 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 \ae{}ther of space.
On the other hand, all coordinate systems $K'$ moving relatively to $K$
were to be regarded as in motion with respect to the \ae{}ther. To this
motion of $K'$ against the {\ae}ther (``{\ae}ther-drift'' relative to $K'$) were
attributed the more complicated laws which were supposed to hold
relative to $K'$. Strictly speaking, such an {\ae}ther-drift ought also to
be assumed relative to the earth, and for a long time the efforts of
physicists were devoted to attempts to \htmladdnormallink{detect}{http://planetphysics.us/encyclopedia/CoIntersections.html} the existence of an
{\ae}ther-drift at the earth's surface.
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 \htmladdnormallink{rigid body}{http://planetphysics.us/encyclopedia/CenterOfGravity.html} 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 \ae{}ther. 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 {\ae}ther. And yet another point: it is shown by calculation that
for a given velocity v with reference to the {\ae}ther, 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 \ae{}ther produces a contraction of the body in the
direction of motion, the amount of contraction being just sufficient
to compensate for the differeace in time mentioned above. Comparison
with the discussion in Section 11 shows that also from the
standpoint 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
\ae{}ther-idea, and hence there can be no \ae{}ther-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.
\footnotetext{The general theory of relativity renders it likely that the
electrical masses of an electron are held together by gravitational
forces.}
\subsection{References}
This article is derived from the Einstein Reference Archive (marxists.org) 1999, 2002. \htmladdnormallink{Einstein Reference Archive}{http://www.marxists.org/reference/archive/einstein/index.htm} which is under the FDL copyright.
\end{document}
