D O C . 3 1 I D E A S A N D M E T H O D S 1 4 9
connections to physical reality (except for the number 4 that is required by the
nature of the space-time continuum).
22. General Theory of Relativity and Ether
There is no difficulty to include the laws of nature already known from the special
theory of relativity into the wider framework of the general theory of relativity. The
mathematical methods were completely at hand in the “absolute differential calcu-
lus” based on the research of Gauss and Riemann and further refined by Ricci and
Levi-Civita.[51]
It deals with the simple process of generalizing the equations from
the special case of constant to the case of that are variable in space-time.
In all of these generalized laws, the gravitational potentials play the role
which—in short—expresses the physical properties of empty space.
Again, “empty” space seems to be endowed with physical properties, that is, not
physically empty as it appeared in the special theory of relativity. Therefore, one
can say the ether has been resurrected in the theory of general relativity, even
though in a 〈newer〉 more sublime form. The ether of the general theory of relativity
differs from the one in old optics by not being a substance in the sense of mechan-
ics. Not even the concept of motion can be applied to it. Furthermore, it is by no
means homogeneous, and its 〈structure〉 state has no independent existence but
rather depends upon the field-generating matter. Since the metric facts can no long-
er be separated in the new theory from the physical facts “proper,” the concepts of
“space” and “ether” flow into each
other.[52]
Since the properties of space appear
to be conditioned by matter, space is no longer a precondition for matter in the new
theory. The theory of space (geometry) and time can no longer be treated before
physics proper or developed independently of mechanics and gravitation.
23. The Field Law of Gravitation
The most important problem of the general theory of relativity concerns the law of
gravitation. This law found no place in the special theory of relativity because the
potentials of gravitation are replaced there by certain constants. Nevertheless,
the idea of relativity leads to the solution of the problem of gravitation. For short
〈and simplicity〉 we shall call a domain 〈or space〉 where the special theory of rela-
tivity is valid a “Galilean space.”
gμν gμν
gμν
[p. 35]
gμν