Static Spacetimes I am reading Wolfgang Rindler's Relativity. At the beginning of the chapter on stationary or static spacetimes he says:
"We now define the stationarity of a lattice by the following light-circuit postulate: if light is sent around any lattice polygon ABC . . . A, then a standard clock at rest at A always measures the same transit time. If, in addition, that time is independent of the sense in which the polygons are traversed, we call the lattice static. The spacetime itself is called stationary (or static) if it contains at least one lattice that is stationary (or static).
As an example of a stationary but not static lattice, consider one rigidly attached to the rotating earth. It is easy to see that a sufficiently large lattice triangle in the equatorial plane will be traversed by light more slowly in the sense of the rotation than in the opposite sense, simply because relative to the underlying quasi-inertial background the first circuit is the longer."
I don't understand how the circuit is longer if the light begins travelling in the direction of rotation. Its going have to travel against the rotation as it is reflected back, so doesn't this negate the increase in path length when it is travelling in the sense of the rotation? 
 A: Think of this polygon as an interferometer, where each vertex is a mirror and the lines are paths the light travel. Here light traveling clockwise meets light traveling counterclockwise and we measure the interference. If light travels around the polygon either way in equal time, it also means that as an interferometer photons traveling one direction interfere with those traveling the other way with no phase shift. This would be a static spacetime. 
Now consider a rotating frame. Think of light traveling around an interferometer that is rotating. Once light travels around the interferometer it has shifted its angular position a little bit. This means the light recombines with some shift in relative phase. Another way to see this is to imagine a fiber optic around the equator of the Earth. Light takes about $1/8$ of a second to orbit the Earth, but by the time it does the Earth will have shifted its angular position. Light traveling east will have a small distance, about $11$km additional to move, while light traveling west will have about the same less to move. This means there will be a phase change in the split beam of light. This is the Sagnac effect. The rotation of the frame emulates the frame dragging of a rotating mass. This is the Lense-Thirring effect. If this phase shift is constant it means the frame dragging is constant. This is a stationary spacetime.
The LIGO interferometer is really based on a similar idea, but is meant to detect a transient change in the phase shift of light traveling the two arms. The transient change in the phase measures a nonstationary spacetime, which is the gravitational wave passing through.
