The effect of rotations on Michelson interferometers

•Rotations induce a phase shift in Michelson interferometers.•Earth’s rotation induces a constant bias in Michelson interferometers.•Michelson interferometers can be used to sense center and radius of rotations.

In the contest of the special theory of relativity, it is shown that uniform rotations induce a phase shift in Michelson interferometers. The effect is second order in the ratio of the interferometer’s speed to the speed of light, further suppressed by the ratio of the interferometer’s arms length to the radius of rotation and depends on the interferometer’s position in the co-rotating frame. The magnitude of the phase shift is just beyond the sensitivity of turntable rotated optical resonators used in present tests of Lorentz invariance. It grows significantly large in Earth’s rotated kilometer-scale Fabry–Perot enhanced interferometric gravitational-wave detectors where it appears as a constant bias. The effect can provide the means of sensing center and radius of rotations.