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