# A rotating Michelson interferometer from the co-rotating point of view

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## Abstract

The phase shift induced by a uniform rotation in a Michelson interferometer is re-derived in the geometrical framework of the coordinate-free formalism of general relativity from the co-rotating point of view. The effect is second order in the ratio of the interferometer’s speed to the speed of light and further suppressed by the ratio of the length of the interferometer’s arms to the radius of rotation. The relation of the effect to gravitational time dilation is discussed.

## Keywords

Michelson interferometry Speed of light in non-inertial frame of reference Gravitational time dilation Equivalence principle Rotation sensing## Notes

### Acknowledgments

I would like to thank V.I. Ritus for pointing out the analogy between the phase shifts induced by terrestrial gravity and by a uniform rotation in a Michelson interferometer. I am also indebted to G.B. Malykin for having stimulated the re-derivation of the phase shift formula from the co-rotating point of view and to J.-P. Zendri for carefully reading the manuscript and related comments.

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