Hi

The Michelson-Morley experiment and similar linear interferometers are
actually rotating when they are in use. They are thus similar to
Sagnac-interferometers.

A rotating Michelson-Morley interferometer looks like in the attached
picture.
[image: image.png]
The black interferometer in this picture rotates and thus has different
positions at different times. The light-ray however is moving along a
straight line and hits the end of the interferometer at time t0+dt and is
reflected back at the origin at t0+2dt. As is seen in the picture the light
is moving a somewhat shorter distance than the length of the interferometer.
The path length of the light ray can be easily calculated.

With angular velocity omega and length L of the interferometer and speed of
light c the light ray path l becomes
l = L*cos(omega*L/(2*c))
or relative to the interferometer length
l/L = cos(omega*L/(2*c)) = sqrt(1-sin(omega*L/(2*c))^2) which for small
angles approximates to sqrt(1-(omega*L/(2*c))^2)

Compare this with the Lorentz-contraction
L/L0 = sqrt(1-v^2/c^2)

The expresions are definitely similar. They imply that v = omega*L/2. For an
11 meter long interferometer, the length that Michelson and Morley used in
later experiments, v becomes 7.3 *10^-5 *11/2 = 4 * 10^-4 m/s which is a
very low speed. Much lower than is detectable with such an interferometer.

<http://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment#Early_experiments>The
null result of the Michelson-Morley-interferometer is explained by Lorentz
contraction:
http://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment#Length_contraction

So, would you say that the interferometer is shortened as special relativity
says or that the light rays are shortened as shown above?

David

David Jonsson, Sweden, phone callto:+46703000370

<<image.png>>

<<attachment: rotating_interferometer.png>>

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