Michelson and Morley's experiment- Special Relativity?

- How is there a fringe pattern? It says that the there is a path difference yet the distance to either mirror is exactly the same.

- Why does rotating it 90 degress cause a shift in the fringes?

http://myslu.stlawu.edu/~jmil/physics/labs/104_lab/gifs/michelson.gif

see diagram. The difference in path length in a typical michelson-morley interferometer is different which is why they are useful.

However... in the thought experiment if we have both arms the same length then the arm that is in the direction of motion will experience a different effective length to the other arm and rotating 90 degrees would cause a shift in the fringe pattern.

Also, there will still be a fringe pattern even if it is the same length because it is basically Young's double slit experiment. (In fact even a single beam has a fringe pattern due to diffraction!)