Certainly any effect of refraction seems to be excluded.
It is thus seen that the formulæ deduced by Einstein have been
confirmed in a variety of ways and in a most brilliant manner. In
connection with these formulæ one question must arise in the minds of
everyone; by what process, where in the course of the mathematical
development, does the idea of mass reveal itself? It was not in
the equations at the beginning and yet here it is at the end. How
does it appear? As a matter of fact it is first seen as a constant
of integration in the discussion of the problem of the gravitational
field due to a single particle; and the identity of this constant with
mass is proved when one compares Einstein's formulæ with Newton's
law which is simply its degenerated form. This mass, though, is the
mass of which we become aware through our experiences with weight;
and Einstein proceeded to prove that this quantity which entered as
a constant of integration in his ideally simple problem also obeyed
the laws of conservation of mass and conservation of momentum when
he investigated the problems of two and more particles. Therefore
Einstein deduced from his study of gravitational fields the well-known
properties of matter which form the basis of theoretical mechanics. A
further logical consequence of Einstein's development is to show that
energy has mass, a concept with which every one nowadays is familiar.
The description of Einstein's method which I have given so far is
simply the story of one success after another; and it is certainly
fair to ask if we have at last reached finality in our investigation
of nature, if we have attained to truth. Are there no outstanding
difficulties? Is there no possibility of error? Certainly, not
until all the predictions made from Einstein's formulæ have been
investigated can much be said; and further, it must be seen whether
any other lines of argument will lead to the same conclusions. But
without waiting for all this there is at least one difficulty which
is apparent at this time. We have discussed the laws of nature as
independent in their form of reference axes, a concept which appeals
strongly to our philosophy; yet it is not at all clear, at first sight,
that we can be justified in our belief. We can not imagine any way
by which we can become conscious of the translation of the earth in
space; but by means of gyroscopes we can learn a great deal about its
rotation on its axis. We could locate the positions of its two poles,
and by watching a Foucault pendulum or a gyroscope we can obtain a
number which we interpret as the angular velocity of rotation of axes
fixed in the earth; angular velocity with reference to what? Where
is the fundamental set of axes? This is a real difficulty. It can be
surmounted in several ways. Einstein himself has outlined a method
which in the end amounts to assuming the existence on the confines
of space of vast quantities of matter, a proposition which is not
attractive.
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