Presets
Playback
Detector
Source and demo wave
Model checks
The science
Fringe shift
A wave of strain h changes the differential arm length by ΔL = hL, so the round-trip phase difference is Δφ = 4πΔL/λ and the light leaving the dark port is I = I0 sin2(Δφ/2). For h = 10-21, L = 4 km and λ = 1064 nm this is 0.047 picoradians, far below one fringe, which is why the arms are Fabry-Perot cavities (signal gain 2F/π) and why noise decides everything.
Noise budget
Shot noise hshot = (λ/4πL) √(2ℏω0/P) (π/2F) √(1+(f/fp)2) falls with laser power P; radiation-pressure noise grows with P and falls as 1/(mΩ2). The two meet at the standard quantum limit √2 √(hshothrp), independent of power. A steep seismic wall limits low frequencies and a fixed thermal curve the middle band. The inspiral signal h(f) = √(5/24) π-2/3 (G Mc)5/6 f-7/6 / (c3/2d) gives the matched-filter SNR2 = 4∫|h(f)|2/Sn df.
Honest simplifications: a lossless Michelson-like model with prefactors of order unity in the radiation-pressure term, no squeezing or signal recycling, one fixed thermal curve, one detector, Newtonian-order inspiral up to the innermost stable circular orbit (no merger or ringdown), no sky-position or polarisation factors. The numbers are illustrative; they are not the real sensitivity curve of any observatory.
What to try
- Press Black-hole merger or Neutron-star merger and compare the red signal line with the white noise curve.
- Raise the laser power: shot noise drops but radiation pressure rises at low frequency.
- Press 40 m prototype and see why long arms matter.