# How is LIGO so sensitive? [duplicate]

My understanding is that interferometers can detect distance changes on the order of the wavelength of light being used. LIGO uses 808 nm light but has a sensitivity of 10^-18 m. Where do those 11 orders of magnitude come from?

LIGO is an 'L' shaped installation that splits a laser beam into two parts and fires it down each leg of the L.

After an equivalent of approximately 75 trips down the 4 km length to the far mirrors and back again, the two separate beams leave the arms and recombine at the beam splitter. The beams returning from two arms are kept out of phase so that when the arms are both in resonance (as when there is no gravitational wave passing through), their light waves subtract, and no light should arrive at the photodiode. When a gravitational wave passes through the interferometer, the distances along the arms of the interferometer are shortened and lengthened, causing the beams to become slightly less out of phase, so some light arrives at the photodiode, indicating a signal.

(...)

Note that the effective length change and the resulting phase change are a subtle tidal effect that must be carefully computed because the light waves are affected by the gravitational wave just as much as the beams themselves

LIGO Wikipedia entry

If you can keep the two beams perfectly out of phase under nominal conditions, any shift in space-time will upset this precisely tuned destructive interference. They are not using the wavelength of the light to directly measure the gravitational waves, but rather using the light as an indicator that the test platform has been disturbed. The sensitivity of LIGO is a reflection on how accurately we can detect phase shifts.

*I am not a trained physicist, so this is about a detailed answer as I can give. If you were looking for direct knowledge and/or the maths to back it up, I apologize.

• Okay, but the formula for the intensity of the interference is: $$1/2 (E1+E2)^2=r^2t^2[1−cos(4π * (L1−L2)/λ)]$$ The value of the L1-L2/λ term is ~10^-11. The cosine of that to first order is ~ 1 - 10^-121! I have a hard time believing we can measure the intensity of light with an accuracy of 1 part in 10^121. Feb 11 '16 at 17:48