Sagnac effect

In a Sagnac interferometer, a source is split into two beams that travel in opposite directions around a closed path and then recombine. When the apparatus rotates, the path and the recombination point move during the beams' travel. The counter-propagating waves therefore accumulate a relative phase difference; for a stationary apparatus the rotation-induced contribution vanishes. For a uniform rotation and a loop with oriented area vector A, the optical phase shift is proportional to the component of angular velocity Ω normal to the loop and to the enclosed area. Increasing the area or rotation rate increases the signal. The effect is not limited to a circular ring: it applies to closed paths generally, with the enclosed oriented area determining sensitivity.

French physicist Georges Sagnac reported an observation in 1913 using a rotating optical interferometer. The experiment showed a shift of the interference fringes when the apparatus rotated. A later large-area experiment by Michelson, Gale and Pearson reported a measurement of the rotation effect in 1925. Modern experiments have tested the same area-and-rotation relationship with non-optical waves. In 2022, a cesium-atom interferometer measured the phase shift due to Earth's rotation and reported agreement with the theoretical prediction at 25 parts per million accuracy.

In a ring-laser gyroscope, counter-propagating laser waves circulate in a closed cavity; rotation changes their relative phase and produces a measurable frequency difference. A fiber-optic gyroscope guides the two waves in opposite directions through a long coil of optical fiber and detects their phase difference on recombination. These instruments can measure rotation without relying on a spinning mechanical rotor, and are used in inertial navigation and geophysical measurement. Their sensitivity depends in part on the effective enclosed area, which can be increased by using many turns of fiber or a larger optical cavity.

The Sagnac effect is sometimes presented as an early test of competing accounts of light propagation, but it should not be treated as proof of a stationary ether. Its prediction is consistent with special relativity when signals are analyzed in a rotating reference frame. In such a frame, assigning synchronized clocks around a closed rotating path leads to a synchronization offset; this helps explain why counter-propagating signals do not return simultaneously. The measured phase difference is a physical observable, whereas descriptions of the effect can depend on the coordinate framework used.