There exists a simple extension of the Lorentz ether to gravity - a Lorentz ether interpretation of the the Einstein equations of General Relativity (GR). I give an introduction on my website.

The basic formulas of this interpretation are:

Let's note that this generalization of the Lorentz ether to gravity removes some important arguments against the ether.

It should be noted that this ether interpretation of the Einstein equations is not completely equivalent, as a physical theory, to general relativity. Here are some differences:

Of course, this holds only until this additional empirical prediction does not actually falsify the ether interpretation. But, up to now, this has not yet happened: We have not observed no nontrivial topologies like wormholes, nor closed causal loops.

Beyond the experiment, there are also other, theoretical arguments in favor of interpretations. Namely the compatibility with other, independent physical principles. Here, the following differences exist:

The basic formulas of this interpretation are:

- There exists a global absolute space \(\mathbb{R}^3\) and absolute time \(\mathbb{R}\), which are defined by preferred coordinates \(X^\mu\) with \(X^0=T\).

- The preferred coordinates are defined by the harmonic coordinate condition \[\square X^\mu = \partial_\nu (g^{\mu\nu}\sqrt{-g}) = 0,\]which, together with the Einstein equations, and the usual general-relativistic equations for matter fields, define the physical equations of the theory.

- The gravitational field defines:
- the density \(\rho(X,T)\) of the ether by \(\rho=g^{00}\sqrt{-g}\);

- the velocity \(v^i(X,T)\) of the ether by \(v^i=g^{0i}/g^{00}\),

- the stress tensor \(\sigma^{ij}(X,T)\) of the ether by \(\rho v^i v^j +\sigma^{ij} = g^{ij}\sqrt{-g}\).

- the density \(\rho(X,T)\) of the ether by \(\rho=g^{00}\sqrt{-g}\);
- This identification transforms the harmonic conditions into continuity and Euler equations for the ether:

\[\partial_0 \rho + \partial_i (\rho v^i) = 0\]\[\partial_0 (\rho v^j) + \partial_i(\rho v^i v^j + \sigma^{ij}) = 0\]

Let's note that this generalization of the Lorentz ether to gravity removes some important arguments against the ether.

- First of all, the argument which, it seems, has killed ether theory: That there was no viable ether theory of gravity. There was a theory which has developed the Minkowski spacetime to a curved spacetime - general relativity - but no ether-theoretical alternative. That the harmonic coordinates, which are used in this ether interpretaion, essentially simplify the equations of GR, was known, and they have always been popular. But that they could have been easily used to define an ether interpretation remained unknown. But if there was no ether theory of gravity, but a successful spacetime theory of gravity, was a very strong, a decisive argument against the ether.

- A known argument against the Lorentz ether was that he was static and incompressible. The ether of this interpretation is no longer static and incompressible. Instead, we have classical equations, known from classical condensed matter theory for compressible media, for this ether.

- Given that the ether fulfills continuity and Euler equations, which are classical conservation laws for mass and momentum, there is no interaction of the ether with other matter - else, an exchange of momentum between ether and other matter would lead to additional terms in the Euler equation. This leads to an interpretation of all matter fields as fields describing other properties of the ether itself. But this removes yet another argument against the ether - that, on the one hand, he should be quite rigid, but, on the other hand, we do not feel any resistance if we move. But waves of the ether should not feel any resistance by the ether.

It should be noted that this ether interpretation of the Einstein equations is not completely equivalent, as a physical theory, to general relativity. Here are some differences:

- GR allows solutions with nontrivial topology. The most well-known example are wormholes. Another important one a spherical closed universe. These solutions do not allow an ether interpretation - the ether interpretation requires a flat background with trivial topology \(\mathbb{R}^3\times \mathbb{R}\).

- GR allows solutions with closed causal loops. The most well-known example is the Gödel solution for a rotating universe. But in some variants of the Kerr solution for rotating black holes there are also parts with closed causal loops. These solutions do not allow an ether interpretation: The preferred time T is time-like everywhere. Such a global time-like function does not exist for solutions with closed causal loops. An ether interpretation would be possible only for parts of such a solution. For other parts, the ether interpretation would be meaningless because the ether density would have to be negative there.

- Another unexpected difference is that the solution of some part of the complete GR solution may already complete as a solution of the ether interpretation. The point is that they have different notions of completeness. A solution of ether theory is complete if it is defined for the whole spacetime \(-\infty < X^i, T < \infty\). A GR solution is complete if it is geodesically complete. These are different notion. And there are also important physical examples: The first is the gravitational collapse, where the part before horizon formation is already complete. The other one the Big Bang. It is incomplete, singular from point of view of GR, but harmonic time goes for usual matter to \(-\infty\). Above cases illustrate the conceptual difference between GR proper time and the absolute time of the ether. In the ether interpretation, "proper time" is interpreted as clock time, shown by clocks which are distorted by the ether. If such a clock stops completely, forever, it does not mean that something will happen to this clock after infinity, which is defined by absolute time.

Of course, this holds only until this additional empirical prediction does not actually falsify the ether interpretation. But, up to now, this has not yet happened: We have not observed no nontrivial topologies like wormholes, nor closed causal loops.

Beyond the experiment, there are also other, theoretical arguments in favor of interpretations. Namely the compatibility with other, independent physical principles. Here, the following differences exist:

- With absolute space as a background and absolute time, the ether interpretation does not have a "problem of time" of quantization.

- Once the ether theory has a preferred frame, causality is connected with this preferred frame. So, the ether allows faster than light hidden causal influences. This makes the ether interpretation compatible with the violation of Bell's inequality.