XXIX

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 from 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 co-ordinate system or to a "mollusk" as reference-body $K^{'}$ . Then with respect to $K^{'}$ 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 $K^{'}$ simply by mathematical transformation. We interpret this behaviour as the behaviour of measuring-rods, clocks and material

points under the influence of the gravitational field $G$ .

Hereupon we introduce a hypothesis: that the influence of the gravitational field on measuring-rods,

clocks and freely-moving material points continues to take place according to the same laws, even in the case when the prevailing gravitational field is not derivable

from the Galileian special case, 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 co-ordinates. This behaviour is formulated in a law, which is always valid, no matter how the

reference-body (mollusk) 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 [chapter:XV]Section XV only its energy is of importance for its effect in exciting a field.