It is just the same in the case of
space-measurements by means of measuring-rods, as a litttle
consideration will show.
The following statements hold generally : Every physical description
resolves itself into a number of statements, each of which refers to
the space-time coincidence of two events A and B. In terms of Gaussian
co-ordinates, every such statement is expressed by the agreement of
their four co-ordinates x[1], x[2], x[3], x[4]. Thus in reality, the
description of the time-space continuum by means of Gauss co-ordinates
completely replaces the description with the aid of a body of
reference, without suffering from the defects of the latter mode of
description; it is not tied down to the Euclidean character of the
continuum which has to be represented.
EXACT FORMULATION OF THE GENERAL PRINCIPLE OF RELATIVITY
We are now in a position to replace the pro. visional formulation of
the general principle of relativity given in Section 18 by an exact
formulation. The form there used, "All bodies of reference K, K1,
etc., are equivalent for the description of natural phenomena
(formulation of the general laws of nature), whatever may be their
state of motion," cannot be maintained, because the use of rigid
reference-bodies, in the sense of the method followed in the special
theory of relativity, is in general not possible in space-time
description.
Pages:
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117