An old and seemingly discredited notion of ether has found its new incarnation in a "metric theory of gravity" by I. Schmelzer, who managed to find for his new ether a consistent and instructive interpretation in terms of condensed matter physics. Prof.V.A.Petrov
is a metric theory of gravity on Newtonian background with condensed matter interpretation and Lagrangian
L = -(8πG)-1(Υg00-Ξgii) (-g)1/2 + LGR(gμν) + Lmatter(gμν,φm)
Papers for professionals:
A generalization of the Lorentz ether to gravity with general-relativistic limit (accepted for publication by the journal "Advances in Applied Clifford Algebras").
Appendix A of A Condensed Matter Interpretation of SM Fermions and Gauge Fields, arXiv:0908.0591, published in Foundations of Physics, vol. 39, nr. 1, p. 73 (2009) contains also a short introduction into GLET.
See also gr-qc/0205035, gr-qc/0001101, a quantum version of Einstein's hole argument and some solutions of GLET forbidden in RTG because of its causality condition.
The FAQ is, instead, written for laymen.
In the preferred coordinates Xi, T, we define a variant of the ADM decomposition. The metric gμν(Xi, T) decomposes into a scalar "ether density" ρ, an "ether velocity" vi and "ether stress tensor" σij:
|gij(-g)1⁄2||=||ρvivj - σij|
The harmonic equation
∂⁄∂Xμ gμλ(-g)1⁄2 ∂⁄∂Xλ Xν = ∂⁄∂Xμ (gμν(-g)1⁄2) = 0
gives classical continuity and Euler equations for the ether variables:
|∂⁄∂T ρ||+||∂⁄∂Xi (ρvi)||=||0|
|∂⁄∂T (ρvj)||+||∂⁄∂Xi (ρvivj-σij)||=||0|
The GLET Lagrangian can be derived from first principles of such an ether interpretation. The basic principle is that continuity and Euler equations of the ether appear as Noether conservation laws in some special variant of the Noether theorem.
The limit Ξ, Υ → 0, gives the GR Einstein equations in harmonic coordinates. This allows to recover the predictions of GR which have been successfully tested (Solar system predictions, gravitational lenses, pulsar orbits). Nonetheless, even in this limit some qualitative differences remain: