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These generally covariant theories describes a spacetime endowed with both a metric and a unit timelike vector field named the aether. The aether in this theory is "a Lorentz-violating vector field" [1] unrelated to older luminiferous aether theories; the "Einstein" in the theory's name comes from its use of Einstein's general relativity ...
As historians such as John Stachel argue, Einstein's views on the "new aether" are not in conflict with his abandonment of the aether in 1905. As Einstein himself pointed out, no "substance" and no state of motion can be attributed to that new aether. [10] Einstein's use of the word "aether" found little support in the scientific community, and ...
But if one requires an exact solution or a solution describing strong fields, the evolution of both the metric and the stress–energy tensor must be solved for at once. To obtain solutions, the relevant equations are the above quoted EFE (in either form) plus the continuity equation (to determine the evolution of the stress–energy tensor):
p. 40: "The cradle of special theory of relativity was the combination of Maxwellian electromagnetism and the electron theory of Lorentz (and to a lesser extent of Larmor) based on Fresnel's notion of the stationary aether…. It is well known that Einstein's special relativity was partially motivated by this failure [to find the aether wind ...
In general relativity, an exact solution is a (typically closed form) solution of the Einstein field equations whose derivation does not invoke simplifying approximations of the equations, though the starting point for that derivation may be an idealized case like a perfectly spherical shape of matter.
And referring to the Fizeau experiment, he even wrote: "The aether is all but in our grasp." He also said the aether is necessary to harmonize Lorentz's theory with Newton's third law. Even in 1912 in a paper called "The Quantum Theory", Poincaré ten times used the word "aether", and described light as "luminous vibrations of the aether". [A 19]
[1] [5] [6] [7] The term "single-postulate" is misleading because these formulations may rely on unsaid assumptions such as the cosmological principle, that is, the isotropy and homogeneity of space. [ 8 ] [ 9 ] As such, the term does not refer to the exact number of postulates, but is rather used to distinguish such approaches from the "two ...
[5] 1845 – George Gabriel Stokes creates his own model of complete aether dragging. [6] 1851 – The Fizeau experiment with light in flowing water confirms Fresnel’s model. [7] 1861 – James Clerk Maxwell publishes his equations of the electromagnetic field, which had a great impact on the later works on aether and special relativity.