Your statement that P=mv must be modified is a difficult one to answer. This depends upon the definition of what mass is. Curiously this problem does not have a clear answer. The relativistic transformation of force is based on the assumption that m is an invarient, but in other places the theory contradicts this claim. So it is not at all clear what relativity actually claims regarding this. If you have an answer, I would like to hear it.
I think your ideas on the M-M experiment are correct. The main problem is this. The MM needed an explaination. FitzGerald suggested length contraction and Lorentz made this into a theory. Einstein took Lorentz's theory and modified it by adding a postulate of relativity and then added that the velocity of light is a constant. The funny part is that he then derived a theory which we call relativity which is essentially the same as the Lorentz theory in almost every respect, except that it supposedly was based on a principle of relativity which explained away the MM result. This was very confusing and resulted in misinterpretation. Today we cant make sense of any of it because of the various misrepresentations in textbooks and many other sources of acrimonious dabate and argument. Today few people realise that Einstein's theory is basically exactly the same as the Lorentz theory which was based on the existence of an ether.
What is really curious is that Lorentz's theory is called ad hoc and false because he makes clear that he assumes a length contraction. But Einstein makes the same claim. So why should Lorentz be wrong? No one really says why. If fact it doesn't really seem justified to claim that relativity proves there isn't any ether, because it doesnt really claim this. All it really claims is that the hypothesis of an ether is not necessary within the theory of relativity.But since this is really equivallent to the Lorentz theory based on the existence of an ether, they are really the same in most respects.
What this means is that the postulate that light velocity is constant is really equivalent to the claim that an ether exists. So you are right.
If you would like to read more on this see the papers by H.H. Ricker at
www.wbabin.net
.
