If we desire to adhere to our "old-time" three-dimensional view of
things, then we can characterise the development which is being
undergone by the fundamental idea of the general theory of relativity
as follows : The special theory of relativity has reference to
Galileian domains, i.e. to those in which no gravitational field
exists. In this connection a Galileian reference-body serves as body
of reference, i.e. a rigid body the state of motion of which is so
chosen that the Galileian law of the uniform rectilinear motion of
"isolated" material points holds relatively to it.
Certain considerations suggest that we should refer the same Galileian
domains to non-Galileian reference-bodies also. A gravitational field
of a special kind is then present with respect to these bodies (cf.
Sections 20 and 23).
In gravitational fields there are no such things as rigid bodies with
Euclidean properties; thus the fictitious rigid body of reference is
of no avail in the general theory of relativity. The motion of clocks
is also influenced by gravitational fields, and in such a way that a
physical definition of time which is made directly with the aid of
clocks has by no means the same degree of plausibility as in the
special theory of relativity.
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