The Galilean transformation crashes

In the following we will suppose that the Galilean transformation is true. In coordinate system O the time required for light to travel (round-trip) the arm along the 

X axis (71 ) and that required to go perpendicularly to axis (7 ) are the same  

in the O coordinate system, there will be no phase difference between the two beams (one coming from the parallel, the other from the perpendicular arm) and therefore no interference will be observed. Let us consider now a similar measurement in O. In the arm co-linear with x, when light goes in the direction of V, it has to take more time (ti) to get to the end of the arm  

The times tj, and do not equal each other for the moving system and there will be the interference, we were talking about a little earlier. 

Lorentz was forced to put the Galilean transformation into doubt (apparently the foundation of the whole science). 

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