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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 ...
The solutions that are not exact are called non-exact solutions. Such solutions mainly arise due to the difficulty of solving the EFE in closed form and often take the form of approximations to ideal systems. Many non-exact solutions may be devoid of physical content, but serve as useful counterexamples to theoretical conjectures.
To obtain 4 liters using 3-liter and 5-liter jugs, we want to reach the point (4, 0). From the point (4, 0), there are only two reversible actions: filling the empty 3-liter jug to full from the tap (4,3), or transferring 1 liter of water from the 5-liter jug to the 3-liter jug (1,3). Therefore, there are only two solutions to the problem:
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 ...
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.
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 ...
Einstein's paper includes a fundamental description of the kinematics of the rigid body, and it did not require an absolutely stationary space, such as the aether. Einstein identified two fundamental principles, the principle of relativity and the principle of the constancy of light (light principle), which served as the axiomatic basis of his ...
1. First postulate (principle of relativity) The laws of physics take the same form in all inertial frames of reference.. 2. Second postulate (invariance of c) . As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body.