Gravitational Waves: Measuring a Ripple Smaller Than a Proton

Spacetime that rings

General relativity treats gravity not as a force but as the curvature of spacetime caused by mass and energy. When massive objects accelerate asymmetrically — two black holes orbiting each other, for instance — the changing curvature propagates outward at the speed of light as a gravitational wave. Unlike an electromagnetic wave, it does not push charges around; it stretches space along one axis while squeezing it along the perpendicular axis, alternating as the wave passes — the "plus" and "cross" polarisations. The amplitude is a dimensionless quantity called strain, h = ΔL/L, and it is almost absurdly small: LIGO's first detection measured h ~ 10⁻²¹.

The quadrupole formula and the runaway inspiral

Einstein's quadrupole formula gives the power radiated by a binary system of masses m₁ and m₂ separated by a:

P = -(32/5) · G⁴/c⁵ · (m₁m₂)²(m₁+m₂) / a⁵

df/dt = (96/5) · π^(8/3) · (G·M_c/c³)^(5/3) · f^(11/3)   // frequency sweep

Because P scales as 1/a⁵, energy loss to radiation shrinks the orbital separation, which raises P further still — a runaway feedback loop that inevitably ends in a merger within a finite time. This is why the Hulse–Taylor binary pulsar's slow orbital decay, measured over decades, matched general relativity so precisely it earned the 1993 Nobel Prize. The single number that best characterises a binary's waveform is the chirp mass M_c = (m₁m₂)^(3/5)/(m₁+m₂)^(1/5), which controls how fast the frequency rises; GW150914 had M_c ≈ 28.3 solar masses.

How LIGO hears it

LIGO (Laser Interferometer Gravitational-Wave Observatory) is a Michelson interferometer with two perpendicular 4 km arms. A laser beam splits, bounces roughly 280 times between suspended mirrors in each arm — power-recycled up to about 100 kW circulating — and recombines to interfere. A passing wave stretches one arm and compresses the other by a few thousandths of a proton diameter, shifting the interference fringe by an amount the detector can resolve. The 40 kg fused-silica mirrors hang from quadruple pendulums to isolate them from ground vibration below about 10 Hz; above that, quantum shot noise sets the limit at high frequency and thermal noise dominates the middle band. Two LIGO sites (Hanford, Livingston — 3,000 km apart) plus Virgo in Italy and KAGRA in Japan give both coincidence confirmation and sky localisation by triangulating arrival-time differences.

Reading the chirp: inspiral, merger, ringdown

A binary black hole signal has three acts. The inspiral sweeps upward in frequency as the orbit tightens — LIGO only catches the last fraction of a second of a process that began millions of years earlier. The merger, lasting milliseconds, is when the event horizons touch and strain peaks. The ringdown is the newly formed black hole settling into a stationary Kerr solution, radiating away its distortion in exponentially damped quasi-normal modes — from which its final mass and spin can be read off. Because general relativity predicts the exact waveform shape as a function of masses and spins, LIGO detects real events by matched filtering: cross-correlating the noisy data stream against roughly 100,000 precomputed template waveforms and flagging anything crossing a signal-to-noise threshold of about 8 in each detector.

GW150914, GW170817 and multi-messenger astronomy

GW150914, announced in February 2016, was a 36+29 solar-mass black hole merger about 430 megaparsecs away — the first direct detection, confirming a century-old prediction Einstein himself thought might never be testable. GW170817, a year later, was a binary neutron star merger only 40 Mpc away, and this time light arrived too: a short gamma-ray burst 1.7 seconds after the gravitational-wave signal, then weeks of optical and infrared afterglow — a kilonova — showing the radioactive decay of freshly synthesised heavy elements including gold and platinum, roughly 10 Earth-masses' worth in that one merger. That combination of gravitational and electromagnetic signals from the same event launched multi-messenger astronomy, and gave an independent "standard siren" measurement of the Hubble constant using the gravitational-wave distance together with the host galaxy's redshift. As of the third LIGO/Virgo/KAGRA observing run, over 90 compact-binary mergers have been catalogued, including GW190521 — an 85+66 solar-mass merger producing a ~142 solar-mass remnant that falls squarely in the "pair-instability gap" stellar evolution alone cannot explain, hinting at hierarchical mergers of earlier black holes.

Frequently asked questions

Try it live

Open Gravitational Waves to watch a binary black hole spiral inward, hear its chirp waveform grow in frequency and amplitude, and see how a simplified LIGO interferometer would register the passing wave — modelled on GW150914 itself.