A. The Michelson-Morley experiment.----[ Return home ]

The result of the Michelson-Morley experiment is due to the Lorentz'contaction alone, but we have also obtained a new interesting physical fact that the round-trip speed of light is always c in a moving frame whatever its motion velocity, particularly in the direction of motion or in the plane Y'Z' orthogonal to this direction.

Here, we are going to show that the round-trip speed of light is isotropically c in any frame and thus that no phase shift may be detected even from any of the arms of the Michelson-Morley interferometer.

First we have to calculate the length of one arm of the interferometer, when it make the angle with the X axis of motion of the frame.

We see immediatly from the figure below that x1 = x2.sqrt(1-bb) with b=v/c.

Thus, and with: we obtain the result:.

It is the contracted arm L when the non-contracted (at rest) is Lo.

Now we have to consider the velocities along the arm in the positive and in the negative way.

These velocities have already been calculated for the wave structure of the electron.

According to the figure below:

the velocities obtained are: and .

As the length of the arm is still L, the time needed for the light for a round trip is:.

As this time delay doesn't change whatever the angle , no phase shift is expected between the arms of the interferometer and whatever its orientation in space.

Finally as the time delay in the moving frame is t'=t.sqrt(1-bb) with t the time delay in the rest frame, we have t'=2Lo/c. Thus, as Lo is also the measure of the length (unchanged) of each arm in the moving frame, the round-trip speed of light is isotropically c in the moving frame.

But, obviously to obtain it, we need a mirror whose real distance changes in the rest frame.

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