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 the end
of Section XVIII. 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.
XXI.
IN WHAT RESPECTS ARE THE FOUNDATIONS OF CLASSICAL MECHANICS AND OF THE
SPECIAL THEORY OF RELATIVITY UNSATISFACTORY?
We have already stated several times that classical mechanics starts
out from the following law: Material particles sufficiently far removed
from other material particles continue to move uniformly in a straight
line or continue in a state of rest. We have also repeatedly emphasised
that this fundamental law can only be valid for bodies of reference _K_
which possess certain unique states of motion, and which are in uniform
50