The Einstein Theory of Relativity | Page 6

may describe the motion of the body in
respect to the measure always in the same way--i.e., as one uniformly
accelerated, as we ascribe now and again a fixed value to the
acceleration of the sphere of gravitation, in a particular case the value
of zero.
Of course, in the case here under consideration the use of a measure
fixed immovably upon the earth should merit all recommendation. But
in the spaces of the solar system we have, now that we have abandoned
the ether, no such support. We can no longer establish a system of
co-ordinates, like the one just mentioned, in a universal intermediate

matter, and if we were to arrive in one way or another at a definite
system of lines crossing each other in three directions, then we should
be able to use just as well another similar system that in respect to the
first moves this or that way. We should also be able to remodel the
system of co-ordinates in all kinds of ways, for example by extension
or compression. That in all these cases for fixed bodies that do not
participate in the movement or the remodelling of the system other
co-ordinates will be read off again and again is clear.

NEW SYSTEM OR CO-ORDINATES
What way Einstein had to follow is now apparent. He must--this hardly
needs to be said--in calculating definite, particular cases make use of a
chosen system of co-ordinates, but as he had no means of limiting his
choice beforehand and in general, he had to reserve full liberty of
action in this respect. Therefore he made it his aim so to arrange the
theory that, no matter how the choice was made, the phenomena of
gravitation, so far as its effects and its stimulation by the attracting
bodies are concerned, may always be described in the same way--i.e.,
through comparisons of the same general form, as we again and again
give certain values to the numbers that mark the sphere of gravitation.
(For the sake of simplification I here disregard the fact that Einstein
desires that also the way in which time is measured and represented by
figures shall have no influence upon the central value of the
comparisons.)
Whether this aim could be attained was a question of mathematical
inquiry. It really was attained, remarkably enough, and, we may say, to
the surprise of Einstein himself, although at the cost of considerable
simplicity in the mathematical form; it appeared necessary for the
fixation of the field of gravitation in one or the other point in space to
introduce no fewer than ten quantities in the place of the one that
occurred in the example mentioned above.
In this connection it is of importance to note that when we exclude
certain possibilities that would give rise to still greater intricacy, the
form of comparison used by Einstein to present the theory is the only
possible one; the principle of the freedom of choice in co-ordinates was
the only one by which he needed to allow himself to be guided.
Although thus there was no special effort made to reach a connection

with the theory of Newton, it was evident, fortunately, at the end of the
experiment that the connection existed. If we avail ourselves of the
simplifying circumstance that the velocities of the heavenly bodies are
slight in comparison with that of light, then we can deduce the theory
of Newton from the new theory, the "universal" relativity theory, as it
is called by Einstein. Thus all the conclusions based upon the
Newtonian theory hold good, as must naturally be required. But now
we have got further along. The Newtonian theory can no longer be
regarded as absolutely correct in all cases; there are slight deviations
from it, which, although as a rule unnoticeable, once in a while fall
within the range of observation.
Now, there was a difficulty in the movement of the planet Mercury
which could not be solved. Even after all the disturbances caused by the
attraction of other planets had been taken into account, there remained
an inexplicable phenomenon--i.e., an extremely slow turning of the
ellipsis described by Mercury on its own plane; Leverrier had found
that it amounted to forty-three seconds a century. Einstein found that,
according to his formulas, this movement must really amount to just
that much. Thus with a single blow he solved one of the greatest
puzzles of astronomy.
Still more remarkable, because it has a bearing upon a phenomenon
which formerly could not be imagined, is the confirmation of Einstein's
prediction regarding the influence of gravitation upon the course of the
rays of light. That such an influence must exist is taught by a simple
examination; we have only to turn back for a moment to the following
comparison