The Sagnac Effect
Imagine that we have fastened a fiber-optic cable around the circumference of a ring which is rotating with steady angular velocity ω. We wish to compute the round trip travel time, as measured by a ring-riding observer, for a laser pulse sent clockwise and counterclockwise around the cable. For simplicity, we will ignore the fact that light travels through a fiber optic cable at somewhat less than the speed of light in a vacuum, and will pretend that the world line of our laser pulse is a null curve (but certainly not a null geodesic!).
In the Born line element, let us put . This gives
or
We obtain for the round trip travel time
Putting, we find so that the ring-riding observers can determine the angular velocity of the ring (as measured by a static observer) from the difference between clockwise and counterclockwise travel times. This is known as the Sagnac effect. It is evidently a global effect.
Read more about this topic: Born Coordinates
Famous quotes containing the word effect:
“To speak impartially, the best men that I know are not serene, a world in themselves. For the most part, they dwell in forms, and flatter and study effect only more finely than the rest.”
—Henry David Thoreau (1817–1862)