Help understanding LIGO.?

Question

LIGO measures length change by comparing how long it takes for a LASER to bounce up and down two legs. But it’s not just space that’s squeezing, it’s space-time. Any variation in length is accompanied by an exactly equivalent variation in the time. If the leg gets shorter, the beam travels slower and takes the exact same amount of time to cover the distance. It should read zero even in the presence of large gravity waves. What am I missing?

Update:

*edit* Secondary question. How do they eliminate the overwhelming noise?

neb · Answer

For very low energy gravitational waves in a weak gravitational field, you can assume a linearization  of general relativity. This allows for a somewhat simple transverse gravitational wave solution that propagates at the speed of light.

So, the solution involves trying to find gravitational wave perturbations to the background metric. The background metric defines how space and time are measured so the perturbation gives the modification that describes the effect of the gravitational wave on the metric.

As it turns out with not so simple reasoning and math, a simple transverse gravitational traveling in the z direction (using a flat Minkowski background metrIc) will stretch and compress space in the xy plane (portion of the metric). This stretching and compressing alternates as the wave passes. The time ‘perturbation’ of the background time portion of the metric is zero.

The more general case with strong background curvature and gravitational waves carrying a lot of energy-momentum are a lot more difficult.

LIGO weeds out noise by the fact that there are two LIGO detectors in Washington state and one in Louisiana. They all have to detect the same event so local ‘noise’ can be eliminated for the most part.

Help understanding LIGO.?

1 Answer