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Today I met a man who was claiming that the Sagnac effect, particularly in the case of light moving in a circular pattern with a rotating observing "arm" as in the first figure in the link, is contrary to special relativity. He claimed that since the wave will hit the observing arm at a rate of c+v or c-v, that this contradicts the constancy of c.

Now, in my head, I am thinking that this speed of c+v is what we observe from our inertial system which holds the axis of the roation constant, but that an actual observation device placed on the arm would still observe the incoming light as having a speed of 3*10^8 m/s.

Is this to be explained by a slight time dilation, making the time difference in the frame of the observer located on the moving arm equal to the time difference observed by us in the reference frame holding the axis constant?

[tex]y = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}[/tex]

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# Sagnac Effect and Special Relativity

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