How does the existence of aether allow for the Galilean transformation? I was reading this and it said that the aether was proposed as a fix to accommodate the Galilean transform because the Laws of Electromagnetism did not remain constant under the Galilean transform. How would the existence of aether have resolved this discrepancy? If aether exists, why would Laws of Electromagnetism suddenly become invariant under the Galilean transform?
 A: An aether with properties like those of an optically dense medium does not fix the lack of invariance; rather, it would have given a physical reason for the lack of invariance of Maxwell's equations with respect to a Galilean boost. This lack of invariance is readily explained if there is a "privileged" frame, i.e. that which is fixed relative to the medium. The wave equation for sound is also not invariant with respect to a Galilean boost, but this lack of invariance is exactly what you'd expect from the presence of the medium: a short pulse from an acoustic source moving in the medium propagates the same way from the a medium-at-rest standpoint independently of whether its source is moving or still relative to the medium. 
A: The ether theory employs the same Lorentz transforms and is also “reciprocal” but there are different reasons for those phenomena known as length contraction and time dilation.
Lorentz theory was an attempt to demonstrate that "existence of ether" was in accordance with invariance of Laws of Electromagnetism.
Null - result of Michelson Morley experiment itself did not shatter that theory.
Albert Einstein noted: “Concerning the Experiment of Michelson and Morley, H.A. Lorentz showed that the result obtained at least does not contradict the theory of an ether at rest”
http://www.relativitybook.com/resources/Einstein_space.html
It is often said, that the Lorentz Ether theory and Special Relativity are empirically equivalent and it is not possible to distinguish between these theories by experiment.
The Lorentz Ether Theory explains null result of ether- drift experiments by means of contraction hypothesis and local time.
The both theories employ the same set of transformations (so – called Lorentz Transformations). Reciprocity of observations in Special Relativity takes place due to physical equivalence of reference frames.
In Lorentz theory moving measuring rod ACTUALLY contracts. However, since moving observer cannot detect his own motion through the Ether, he mistakenly synchronizes clocks in his reference frame by means of Einstein signalling method, admitting that velocity of light in all direction is the same.
This way, thought his own clock runs gamma times slower and measuring rod is gamma times shorter than that one “at rest”, moving observer will make a conclusion, that the rod at rest is gamma times shorter and clock at rest runs gamma times slower.
That leads to full reciprocity of observations in Lorentz ether theory either.
Chapter 3, 3.5.5 The reciprocity of the Lorentz transformation. p. 93
http://www.mpiwg-berlin.mpg.de/litserv/diss/janssen_diss/Chapter3.pdf
Hence, relativity of simultaneity is a part of the Ether theory but not because of physical equivalence of observers, but because of the same synchronization procedure.
But, many scientists consider that Einstein’s interpretation of Lorentz invariance is preferable to Lorentz’s because relativistic phenomenas are simply part of the normal spatio-temporal behavior of systems in Minkowski space-time.
http://www.mpiwg-berlin.mpg.de/litserv/diss/janssen_diss/Chapter4.pdf
