 |
 |
 |
 |
|
 |
 |
61
Relativity: The Special and General Theory
Albert Einstein: Relativity
Part II: The General Theory of Relativity
The Solution
of the Problem
of Gravitation
on the Basis of the General
Principle of Relativity
If the reader has followed all our previous considerations, he will have no further difficulty in
understanding the methods leading to the solution of the problem of gravitation.
We start off on a consideration of a Galileian domain, i.e. a domain in which there is no
gravitational field relative to the Galileian reference?body K. The behaviour of measuring?rods and
clocks with reference to K is known from the special theory of relativity, likewise the behaviour of
"isolated" material points; the latter move uniformly and in straight lines.
Now let us refer this domain to a random Gauss coordinate system or to a "mollusc" as
reference?body K¹. Then with respect to K¹ there is a gravitational field G (of a particular kind). We
learn the behaviour of measuring?rods and clocks and also of freely?moving material points with
reference to K¹ simply by mathematical transformation. We interpret this behaviour as the
behaviour of measuring?rods, docks and material points tinder the influence of the gravitational
field G. Hereupon we introduce a hypothesis: that the influence of the gravitational field on
measuringrods, clocks and freely?moving material points continues to take place according to the
same laws, even in the case where the prevailing gravitational field is not derivable from the
Galfleian special care, simply by means of a transformation of co?ordinates.
The next step is to investigate the space?time behaviour of the gravitational field G, which was
derived from the Galileian special case simply by transformation of the coordinates. This behaviour
is formulated in a law, which is always valid, no matter how the reference?body (mollusc) used in
the description may be chosen.
This law is not yet the general law of the gravitational field, since the gravitational field under
consideration is of a special kind. In order to find out the general law?of?field of gravitation we still
require to obtain a generalisation of the law as found above. This can be obtained without caprice,
however, by taking into consideration the following demands:
(a) The required generalisation must likewise satisfy the general postulate of relativity.
(b) If there is any matter in the domain under consideration, only its inertial mass, and thus
according to
Section 15 only its energy is of importance for its etfect in exciting a field.
(c) Gravitational field and matter together must satisfy the law of the conservation of energy (and of
impulse).
Finally, the general principle of relativity permits us to determine the influence of the gravitational
field on the course of all those processes which take place according to known laws when a
gravitational field is absent i.e. which have already been fitted into the frame of the special theory of
relativity. In this connection we proceed in principle according to the method which has already
been explained for measuring?rods, clocks and freely moving material points.
The theory of gravitation derived in this way from the general postulate of relativity excels not only
in its beauty ; nor in removing the defect attaching to classical mechanics which was brought to