**Theoretical introduction.**

**True constancy of the round-trip speed of light ( MMX ).**

The Galileo's Transformations With Metric Change [GTWMC] as an obvious and immediate consequence of my classical electron theory leads to the rigorous conclusion that the Michelson-Morley experiment will never present the slightest phase shift (frange displacement).

To show that I consider a frame K' in motion relatively to the rest frame and of velocity v.

If the the axis of the rest frame (K) and K' are orientated as they are ordinarily in " relativity ", the GTWMC are: x'=[x-vt]/sqrt(1-bb), t'=t.sqrt(1-bb), y'=y, z'=z, with b=v/c.

It is impotant to remind here that these transformations are fully equivalent to the facts that the frequency of a clock in motion in ether, decreases according to

F'=Fo.sqrt(1-bb) [time dilation] and that the lengths contracts in the direction of motion according to L'=Lo.sqrt(1-bb) [Lorentz' contraction].

Thus if a light wave energy is in motion along the X axis of K in the positive way, its motion equation is in K: x(t)=c.t.

But in K' the equation is according to GTWMC:

[x'(t')/t']=[x(t)/t -v]/(1-bb)=[c-v]/(1-bb).

In the negative way, the equation in K is x(t) = -c.t and thus in K':

[x'(t')/t'] = -[c+v]/(1-bb).

Now for the distance D' between the halfsilvered mirror (beam splitter)and a main one (X' axis), the time needed for a round-trip is: D'{1-bb}.{1/[c-v] + 1/[c+v]}= 2.D'/c.

And more the light velocity needed for a round-trip along this 2.D' is:

2.D'/[2.D'/c]= c !, incredibly for any velocity of the moving frame in space.

To derive the velocities along the Y' and Z' axis of K', we consider the components of the velocities for the axis Y and Z of K.

For the Y' axis, we have in K: [dy/dt]= sqrt[c.c-v.v].

But in K', according to GTWMC: [dy'/dt']={dy/[dt.sqrt(1-bb)]} = c !!!

Here the one-way and the round-trip velocities are both c, whatever the velocity v of the frame in space. And that means that the round-trip time is still 2.D'/c for the same arm of the interferometer. I have to say here, that we have not to consider again the Lorentz ' contraction which is already contained in the GTWMC.

Conclusion: as the round-trip time doesn't vary for any of the two arms of the interferometer, it is a loss of time to try to detect a phase shift between the two path during a rotation of the apparatus which, clearly, will be always nil.

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