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The action of the Einstein-aether theory is generally taken to consist of the sum of the Einstein–Hilbert action with a Lagrange multiplier λ that ensures that the time vector is a unit vector and also with all of the covariant terms involving the time vector u but having at most two derivatives.
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):
Einstein showed how the velocity of light in a moving medium is calculated, in the velocity-addition formula of special relativity. Einstein's theory of general relativity provides the solution to the other light-dragging effects, whereby the velocity of light is modified by the motion or the rotation of nearby masses.
Although the failure to detect an aether wind was a disappointment, the results were accepted by the scientific community. [14] In an attempt to salvage the aether paradigm, FitzGerald and Lorentz independently created an ad hoc hypothesis in which the length of material bodies changes according to their motion through the aether. [17]
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.
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 ...
A more modern example of deriving the Lorentz transformation from electrodynamics (without using the historical aether concept at all), was given by Richard Feynman. [ 5 ] George Francis FitzGerald already made an argument similar to Einstein's in 1889, in response to the Michelson–Morley experiment seeming to show both postulates to be true.
Einstein explained that the "aether of general relativity" is not absolute, because matter is influenced by the aether, just as matter influences the structure of the aether. [ A 23 ] The only similarity of this relativistic aether concept with the classical aether models lies in the presence of physical properties in space, which can be ...