Why is the Luminiferous aether theory wrong? I saw on this page about the constant speed of light that there are two ways of interpreting this constant speed:


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*General relativity

*The Luminiferous aether theory


I understand why the theory of general relativity is right, I just wanted to know way the luminiferous aether theory is wrong.
 A: Firstly, I need to clarify that the constancy of the speed of light is explained by Special Relativity and not General Relativity which is the theory of gravity.
The luminiferous aether theory was a proposed theory to explain the medium that light uses to propagate. Just like sound needs a medium to propagate (sound is just vibrations in air) It was proven wrong by the famous Michelson-Morley experiment which tested the speed of light and found no difference.
So why was the theory of the aether wrong? Well people thought that the aether formed an absolute reference frame in the universe and hence everything else is moving with respect to it. This means that as the earth orbits around the sun, and hence with respect to the aether, we should be able to detect small differences in the speed of light (light would sometimes travel with the aether and sometimes against it) but the experiment showed no difference in the speed of light in any direction that it was measured. 
To avoid confusion, a little comment on @ACuriousMind's answer. The Lorentz aether theory is a special type of aether theory developed after the MM experiments in order to explain the results. The rest follows from his answer.
A: One particular luminiferous (just meaning "light-bearing") aether interpretation of the constant speed of light, the Lorentz aether (or ether) theory (LET), is not wrong. Other theories about a luminiferous aether are wrong, since they always lead to the conclusion that the speed of light is not constant in every frame.
The LET is experimentally indistinguishable from special relativity1, and hence as "right" as special relativity. But there are two main reasons to prefer SR as the theory we work with:


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*The assumption of an undectable "preferred reference frame" by LET is unnecessary - we can just start with assuming the principle of relativity, all this assumption does is add another unphysical, unmeasurable axiom to the theory. By Occam's razor, we thus prefer SR over LET

*SR, when formulated in terms of the Minkowski metric, generalizes nicely to GR, almost naturally. There is no obvious path from LET to GR.
It is important to stress that, if two theories have the same experimental predictions, then neither is wrong. Yet, "undetectable aether" is experimentally indistinguishable from SR's perspective of "no aether at all" and to assume the "existence" of undetectable objects when you've got a theory that doesn't need their existence is just ill-advised.

1Note that it is special relativity that predicts a "constant speed of light" or rather, "upper bound of speed of frames into which one may Lorentz transform". Whenever you read "Lorentz invariance", it is about special, not general relativity. In general relativity, all coordinate transformations are allowed, and the "constant speed of light" is recovered by noting that GR locally is SR.
