Does aether not exist or is it simply superfluous? My question is motivated from studying the null result of the Michelson Morley experiment. 


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*Does the experiment prove that the aether does not exist? Wikipedia says that it was more broadly interpreted that the aether was not needed, rather than it definitely not existing. If so, how could it be possible that the aether exists, when one of its properties is that it must be stationary, but we know that according to special relativity, there is no such thing as an absolute frame of reference. 

*Why was the aether not observed in the MM experiment?
 A: I'll try to be brief: the null result of the MM experiments demonstrated that the conceptual picture held by most physicists of the day about how light is propagated had something wrong with it on a very basic level, and the ideas about how exactly to repair that picture to square it with the experimental results (ether drag, fitzgerald contraction and so forth) were ad-hoc and lacked satisfactory theoretical justification. 
The easiest explanation of why the aether was not revealed by MM is that it wasn't there in the first place. 
I hope this helps, and I invite others here to weigh in with a more complete answer than this, should mine be deemed insufficient.             
A: The aether is linked with the history of gravity. 
When Newton conceived of his theory he admitted that it used action at a distance and to him this was problematic. Action ought to be local, but he couldn't see his way around the conceptual problems.
Other physicists later hypothesised the aether to get a local theory. They conceptualised it as mechanical but the theories were like Ptolemys, cumbersome. 
These problems were swept away by Einstein by using the field concept; he showed that the aether was the gravitational field and this in turn was simply spacetime. 
In short, the aether was needed but it was wrongly conceptualised. 
A: 
  
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*Does the experiment prove that the (luminiferous) aether does not exist?
  

No, it just proved that the luminiferous aether is not needed. The wikipedia article is correct. Physicists were working on the problem of the apparent conflict between Maxwell's electrodynamics and Newtonian mechanics  prior to Einstein's development of special relativity. There is an alternative to special relativity, Lorentz ether theory. The latter says that the ether does exist, but that it is not observable. There is no difference between the two theories in terms of predicted experimental outcomes. There is a huge difference between the two in terms of the assumptions those theories make.
Einstein simply took Maxwell's equations at face value: That the speed of light is the same to all inertial observers, with all the repercussions that has with regard to the limitations of Newtonian mechanics. The modern view is of course that the luminiferous aether is not needed, bolstered by the fact that photons do just fine in vacuum


  
*Why was the aether not observed in the MM experiment?
  

Because it doesn't exist.
Physicists at that time looked at electromagnetic radiation as being a wave phenomenon, somehow analogous to other wave phenomena known at that time. All wave phenomena known at that time needed some kind of medium to transport the waves. Physicists at that time did not know about quantum mechanics. Photons do just fine in vacuum.
A: Matter is always in motion. Aether is a non-baryonic form of matter and thus is always in motion as is baryonic matter. The concept of a stationary aether is as absurd as the concept of a stationary planet.The Michelson-Morley (MM) experiment did not detect the presence of stationary aether, just as no experiment is ever going to detect any stationary planet. To conclude from the MM experiment that aether does not exist, is unjustified. 
