Does Michelson-Morley experiment really disprove the existence of aether? In the MM experiment, the speed of one light beam was supposed to slow down as it moved against the flow of aether, but when it bounced off the mirror, it would be moving in the opposite direction--with the flow of aether and therefore should be moving faster. The average speed of light on that arm of the experiment should have been exactly the same as the light flowing across the current of aether as the aether flow terms cancel each other.
Why isn't this the same as a high school physics problem involving boats in a current or people on a moving sidewalk where the current term just drops out because you add speed in one direction and subtract it in the reverse direction?
It seems like a properly adjusted MM apparatus, would always measure the speed of light on the 2 axes as being the same REGARDLESS of whether there is aether or not.
What am I missing?
 A: The point of the experiment is that in the aether, light along one arm of the interferometer will return at a different time than light along the other arm.
Forget about light for now and think of one of those moving walkways that you find in an airport (https://en.wikipedia.org/wiki/Moving_walkway). If I walk to one end of the walkway and back, that meaning I get a constant increase in speed going one way, and a constant decrease in speed coming back, will I have taken the same amount of time as if I didn't use the walkway at all? It turns out that the answer is no. 
To see this, suppose the length of the walkway is $d$ and I walk with a speed $v$. If the walkway moves with a speed $v_w$, then I will be moving at a speed $v+v_w$ when I walk with the walkway, and a speed $v-v_w$ when I walk against it. The time it takes me to walk there and back is therefore $$\Delta t = \frac{d}{v+v_w} +\frac{d}{v-v_w}$$ as long as $v_w<v$ (which is has to be or I would never get back). This is in contrast to the time it would take with no walkway at all
$$\Delta t' = \frac{d}{v}+\frac{d}{v}$$
which is always less than the time it takes on the walkway whenever $v_w \neq 0$. So in fact, the average velocities are not the same as it takes me a longer time to walk the same distance on the walkway.
It is the same idea with the Michelson-Morley experiment. If the aether existed, the light ray that is parallel to the flow of the aether would experience a speed-up in one direction, and a slow-down in the other, which means it would take longer to return than the beam perpendicular to it. This time delay would cause the two beams to interfere when recombined, and this interference pattern can be viewed on a screen. Notice that the only solution to the equation $\Delta t = \Delta t'$ is when $v_w=0$, meaning that no interference pattern implies that there is no walkway, which in this case means no aether that changes the relative speed of light.
A: At the time, the experiment did not disprove the existence of the "aether". What it did was demonstrate by experiment that if the aether did indeed exist, it would have to possess some extremely peculiar properties: on the one hand, it would have to allow material objects to pass through it without resistance (so as to not interfere with the motion of planets), while at the same time it also had to be somehow dragged along with an object that was moving through it (so as to yield a null result in the M-M experiment).
The "aether drag" hypothesis was seriously considered within the physics community as a way to preserve the aether and escape the consequences of the M-M test, but it did not get very far.  
