Okay. This will probably sound like everything everyone has heard in ATM before, but I'll post it anyway.
In the MM experiment, two beams of light were separated perpendicular to each and brought back together so their difference in times could be measured between that in the line of motion through the ether and that cross-wise to it. That in the line of motion is found to be t=d/(c-v)+d/(c+v)=2dc/(c^2-v^2) for the sum of the back and forth times and that cross-wise is found to be t=2dc/sqrt[c^2-v^2]. Lorentz noticed that if the distance were to shrink in the line of motion by the ratio of these two times, then that would produce a null result, as was found to be the case. Einstein also used a thought experiment with the same setup to come to the same conclusion, whereby gamma=sqrt[1-(v/c)^2] in relativity was born.
Now, there are two things about this. First, finding the speed of light in each direction should not have been c-v and c+v as were used for this, but c*(c+vo)/(c-vs) and c*(c-vo)/(c+vs) for Doppler, where vo is the velocity of the observer and vs is the velocity of the source. For some reason, the velocity of the source was not considered for this. This only applies for after the point of separation and before they reunite, however, but as long as all of the mirrors used are travelling at the same speed in the same direction in respect to one another, one will recieve a null result every time. So that causes relativity to become unsubstantiated right off the bat.
But I want to go a little further with this. Both the actual experiment and thought experiment used beams that travelled perpendicular to each other. So what I want to know is if we use a different angle between the beams, will we still find that the component of the distance in the line of motion must still be contracted by a factor of gamma in order for the times to match, or would it be something else. The experiment would still work fine and should still produce a null result, otherwise we could gain positive results this way. If it is gamma every time, then that would strengthen the case for relativity. But if not, then it is probably blown out of the water, and back to Doppler we go.
Of course, I had to do it in exactly the same way they did, using c+v and c-v for the velocities, to see if I come to the same results, and then compare for different angles. So we designate some angle we are finding for, figure the light is travelling over the resultant angle, so the distance there is ct, (sin L)d+vt along the line of motion, x along the original angle, and therefore (cos L)x for the base. From this we get
C=cos L, S=sin L
Separating the component for that which contracts along the line of motion with G (some value for gamma), then
Factoring in for d, we now have
Expanding this and solving for the exponents of x using the quadratic formula, this becomes
x=t*[-Sv+sqrt((Sc)^2+c^2/z-v^2/z)]/(1/z+S^2), where z=1+(GS/C)^2
Finally, solving for t, we get
Alright. But that is only the time travelling to the reflecting mirror. We still need the time for coming back. By going through the same method as before, one finds this to be
which turns out to be almost the same formula, since only the value for S changes sign. Adding these two times together and reducing a little gives us the total time for a beam travelling along some angle. So this is
Finally, since we are actually looking for the formula in terms of d instead of x here, we can substitute back in for x and get
Okay. It's looking good. There's a couple of gammas already in there if they will only hold up. So let's find out. For the cross-wise beam, the angle is zero degree, so S=0 and C=1, so z=1. That gives us
t=2(d/c)*sqrt[1-(v/c)^2]/(1-(v/c)^2)=2(d/c)/sqrt[1-(v/c)^2], so that works out.
For along the line of motion, the angle is 90 degrees, so S=1, C=0, so z=infinity, and we have
t=2(d/c)*sqrt[1-(v/c)^2]/(1-(v/c)^2)=2(d/c)/sqrt[1-(v/c)^2], when G=gamma=sqrt[1-(v/c)^2], so that works out also.
Now let's try it for some angle in between, say 45 degrees, using the same G=gamma=sqrt[1-(v/c)^2] in the line of motion for the Lorentz contraction and v=.6c. So
Finding for the same values at zero or 90 degrees, which come out to the same thing either way, we find
It is not the same time for other angles! That means the value of gamma must be changed depending on the angle between the beams. Therefore, the value of gamma is not always G=sqrt[1-(v/c)^2] for the contraction in the line of motion, and relativity does not hold for this. Since this is what relativity is based on from the get-go, it looks like we might be looking back at Doppler to explain the effects we observe.
Of course, before I make such a conviction, and pass the point of no turning back for relativity, starting to treat it as Doppler instead, I will need every person that can to run through these equations and make sure I haven't made any errors. After all, it was starting to look good there for a minute, with gamma actually carrying through in the calculations themselves, but it is the end result that matters. If they are difficult to follow, maybe somebody can re-perform the same calculations their own way to see if they come to the same conclusions and post it here.