[15] The objection is of importance more especially when the state of
motion of the reference-body is of such a nature that it does not
require any external agency for its maintenance, _e.g._ in the case
when the reference-body is rotating uniformly.
XXII.
A FEW INFERENCES FROM THE GENERAL PRINCIPLE OF RELATIVITY
The considerations of Section XX show that the general principle of
relativity puts us in a position to derive properties of the
gravitational field in a purely theoretical manner. Let us suppose, for
instance, that we know the space-time course for any natural process
whatsoever, as regards the manner in which it takes place in the
Galileian domain relative to a Galileian body of reference _K_. By
means of purely theoretical operations (_i.e._ simply by calculation)
we are then able to find how this known natural process appears, as
seen from a reference-body _K _ which is accelerated relatively to _K_.
But since a gravitational field exists with respect to this new body of
reference _K _, our consideration also teaches us how the gravitational
field influences the process studied.
For example, we learn that a body which is in a state of uniform
rectilinear motion with respect to _K_ (in accordance with the law of
Galilei) is executing an accelerated and in general curvilinear motion
with respect to the accelerated reference-body _K _ (chest). This
acceleration or curvature corresponds to the influence on the moving
body of the gravitational field prevailing relatively to _K_. It is
known that a gravitational field influences the movement of bodies in
this way, so that our consideration supplies us with nothing
essentially new.
However, we obtain a new result of fundamental importance when we carry
out the analogous consideration for a ray of light. With respect to the
Galileian reference-body _K_, such a ray of light is transmitted
rectilinearly with the velocity _c_. It can easily be shown that the
path of the same ray of light is no longer a straight line when we
consider it with reference to the accelerated chest (reference-body
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