rope is just large enough to effect the acceleration of the body. That which
determines the magnitude of the tension of the rope is the inertial mass of the
body." Guided by this example, we see that our extension of the principle of
relativity implies the necessity of the law of the equality of inertial and
gravitational mass. Thus we have obtained a physical interpretation of this law.
From our consideration of the accelerated chest we see that a general theory of
relativity must yield important results on the laws of gravitation. In point of fact,
the systematic pursuit of the general idea of relativity has supplied the laws
satisfied by the gravitational field. Before proceeding farther, however, I must
warn the reader against a misconception suggested by these considerations. A
gravitational field exists for the man in the chest, despite the fact that there was
no such field for the co-ordinate system first chosen. Now we might easily
suppose that the existence of a gravitational field is always only an apparent one.
We might also think that, regardless of the kind of gravitational field which may
be present, we could always choose another reference-body such that no
gravitational field exists with reference to it. This is by no means true for all
gravitational fields, but only for those of quite special form. It is, for instance,
impossible to choose a body of reference such that, as judged from it, the
gravitational field of the earth (in its entirety) vanishes.
We can now appreciate why that argument is not convincing, which we brought
forward against the general principle of relativity at theend of Section 18. It is
certainly true that the observer in the railway carriage experiences a jerk
forwards as a result of the application of the brake, and that he recognises, in this
the non-uniformity of motion (retardation) of the carriage. But he is compelled
by nobody to refer this jerk to a " real " acceleration (retardation) of the carriage.
He might also interpret his experience thus: " My body of reference (the
carriage) remains permanently at rest. With reference to it, however, there exists
(during the period of application of the brakes) a gravitational field which is
directed forwards and which is variable with respect to time. Under the influence
of this field, the embankment together with the earth moves non-uniformly in
such a manner that their original velocity in the backwards direction is
continuously reduced."