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Relativity: The Special and General Theory

Experience and the Special Theory of Relativity
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.
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.
It is known that cathode rays and the so-called β-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.
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 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
 
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