Is There An Ether?
The ether theory assumes that the space is filled with some material so that the "speed of sound" of this material is the speed of light. The main philosophical problem related with the ether was that there was no detectable influence of the material on the ether.
In principle, the world view connected with PG is similar to that picture. The space is filled with the gravitational field, and all other material fields interact with this gravitational field. Interpreting the gravitational field as the mathematical description of the ether, we see that the Einstein equations solve the problem of the influence of the material fields on the ether.
This comparison is on some very abstract level. We have not interpreted the components of the metrical tensor as related with some mechanical properties of the ether. It is not necessary to so this.
But, this does not mean that this is not possible. Moreover, there is a simple analogy between obvious mechanical properties and the components of the gravitational field:
The deformation of an elastic body is usually described by the deformation tensor. This tensor is simply the difference between two metrical tensor fields - the metric of the "deformed" state and the metric of the "stress-free reference" state. Instead of using the deformation tensor, we may also use the metrical tensor of the stress-free reference state alone. We have 6 steps of freedom with the same tensor properties as the 6 spatial components of the gravitational field.
We have a scalar "velocity of sound" - a material property. This gives an additional step of freedom.
The related "sound cone" may be shifted by the velocity of the elastic body. This gives 3 additional steps of freedom.
Thus, the number of steps of freedom of the gravitational field and of a deformed, moving elastic body with variable speed of sound coinside.
The Velocity of the Ether
Naming the gravitational field "ether", we can in PG uniquely define the velocity of the ether. At first, we define that the ether is "at rest" if the components g^{0i} are zero. It doesn't change anything if we use the lower indices g_{0i} instead of the upper.
Then we can consider Galilei transformations of the form
x' = x + v t
and ask about the vector v which transforms the ether into the state "at rest". This velocity exists and is uniquely defined by
v^i = g^{0i} / g^{00}
Einstein About the Ether
In "Ether and Relativity", 1920, Sidelights on Relativity, page 23, Einstein writes:
Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether. According to the general theory of relativity space without an ether is unthinkable; for in such a space there not only would be no propogation of light, but also no possibility of existance for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this ether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it.
False. The ether may be thought of as consisting of parts which may be tracked through time. The idea of motion may be applied to it.
To show this, let's consider PG. Because, if this variant is true, GR is also true, things which are correct in PG may be at least thought in GR too.
In PG it is possible to associate a velocity to the ether.
A corrected statement would be: GR does not tell anything about the velocity of this ether. The velocity of this ether is not an observable in GR.
