Gravitational Waves

A billion-year-old tremor, caught in a basement#

On 14 September 2015, a signal swept through a detector in Louisiana and, seven milliseconds later, through an identical one in Washington State. It lasted a fifth of a second and rose in pitch like the last note of a slide whistle. It had begun more than a billion years earlier, when two black holes — one about 36 times the mass of the Sun, the other about 29 — finished a long inward spiral and merged into one. In the final instant they converted roughly three solar masses of matter into pure gravitational-wave energy, briefly radiating more power than every star in the observable universe combined.

By the time that convulsion reached Earth it had faded to something almost unimaginably faint. It stretched and squeezed the detector's four-kilometre arms by about $10^{-18}$ metres — less than a thousandth of the width of a proton. And we caught it. That signal, catalogued GW150914, was the first direct detection of a gravitational wave, a full century after Einstein predicted such waves should exist. This is the story of what a gravitational wave actually is, why it is so absurdly weak, and how anyone managed to measure a ripple that small.

What a gravitational wave actually is#

Start with the modern picture of gravity. In Einstein's general relativity (1915), gravity is not a force reaching across space; it is the shape of spacetime. Mass and energy curve the spacetime around them, and objects simply follow the straightest available paths through that curved geometry — the same idea that governs orbits and bends starlight around the Sun, and the backdrop to gravitational time dilation.

Now shake a mass. Because the curvature it produces cannot rearrange itself instantaneously — general relativity forbids any influence travelling faster than light — a disturbance in the geometry propagates outward. That travelling disturbance is a gravitational wave: a ripple in the curvature of spacetime itself, spreading at the speed of light. Einstein worked this out in 1916, one year after the field equations, by studying small ripples on otherwise flat spacetime.

Here is the crucial thing about what the wave does. It is not a wave travelling through space the way sound travels through air or light travels through the electromagnetic field. It is a wave of space — a rhythmic distortion of distance itself. As it passes through a cloud of freely-floating particles, it stretches the distances between them along one direction while squeezing them along the perpendicular direction, then reverses, over and over. Circle becomes ellipse, tall then wide then tall again. These two perpendicular stretch-squeeze patterns are the wave's two polarizations (conventionally called "plus" and "cross"). No particle is pushed anywhere; what changes is the geometry that defines how far apart they are.

Watching the wave stretch space#

The widget below makes the two halves of the story visible at once. On the left, two compact masses orbit and slowly spiral together, radiating waves. On the right sits a ring of free test masses — imagine tiny beads floating in space, feeling nothing but the passing wave.

What to try. Hit play and watch the ring on the right. As each wave crest arrives it stretches the ring horizontally and squeezes it vertically; a half-cycle later the stretch and squeeze swap. That is the "plus" polarization drawn out — and notice the ring is never shoved to one side. It only distends and relaxes, because a gravitational wave changes distances, it does not apply a push. Now watch the two effects that define a chirp. As the orbit on the left decays, the masses whip around faster and closer, so on the right the deformation gets both bigger (louder) and faster (higher-pitched). The strain trace along the bottom shows it directly: a wave whose amplitude and frequency both climb steeply into the merger, then ring down once the two masses become one. "The wave stretches space, and it gets louder and higher as they merge" is not a metaphor here — it is the thing on the screen.

Why they are so extraordinarily weak#

We measure a gravitational wave's strength by its strain — the fractional change in length it produces:

$$h = \frac{\Delta L}{L}$$

A strain of $h = 10^{-21}$ means a length $L$ changes by one part in $10^{21}$. Over LIGO's $L = 4$ km arms that is $\Delta L = h L \approx 4 \times 10^{-18}$ m, thousands of times smaller than a proton. Over the entire $1.5 \times 10^{11}$ m Earth–Sun distance, the same strain would move the two bodies by about the width of a hydrogen atom.

Why so tiny? Because gravity is by far the weakest of the fundamental forces — some $10^{36}$ times weaker than electromagnetism. The same feebleness that lets a small magnet lift a paperclip against the pull of the entire Earth means that even catastrophic motions of enormous masses barely wrinkle spacetime. To make a wave we can detect at all, you need something like two black holes, each dozens of times the Sun's mass, orbiting each other hundreds of times a second at a good fraction of the speed of light — and even that, smeared across a billion light-years, arrives as a strain of $10^{-21}$.

There is a second reason gravitational radiation is weak, built into the physics. An accelerating electric charge radiates dipole electromagnetic waves, but mass comes in only one sign — there is no negative mass — and conservation of momentum forbids gravitational dipole radiation. The leading term is instead the weaker quadrupole: the source must have a changing, non-spherical mass distribution. A perfectly spherical collapse radiates nothing at all; you need the lopsided, tumbling mass configuration of two bodies whirling around each other.

The sources: inspiralling compact binaries#

The loudest sources in the sky are pairs of the densest objects that exist — black holes and neutron stars — locked in a decaying orbit. As two such bodies circle, they continuously radiate gravitational waves, and that radiation carries away orbital energy. Losing energy, the orbit shrinks; shrinking, the bodies speed up and radiate even harder; a runaway that ends in merger. The evolution is captured by a single quantity, the chirp mass $\mathcal{M}$, which sets how fast the frequency sweeps upward:

$$\frac{df_{\text{gw}}}{dt} \;\propto\; \mathcal{M}^{5/3} f_{\text{gw}}^{11/3}$$

The gravitational-wave frequency is twice the orbital frequency (the mass distribution repeats every half-orbit), and as the orbit tightens both the frequency and the amplitude rise together — the rising chirp you saw in the animation. Reading the exact shape of that chirp is how detectors weigh the objects: the sweep rate gives the chirp mass, the amplitude and final frequency pin down the individual masses and the size of the merged remnant. GW150914's chirp told us, with no telescope image at all, that two black holes of about 36 and 29 solar masses had merged into one of about 62 — the missing 3 having flown off as waves. The merging black holes that produce these signals remain the loudest events LIGO hears.

How LIGO detects them#

To catch a strain of $10^{-21}$ you need a ruler that can compare two lengths to better than one part in $10^{21}$. The instrument that does it is a laser interferometer, and its logic is a beautiful bit of judo on the wave's own geometry: since a gravitational wave stretches one direction while squeezing the perpendicular one, build a detector with two perpendicular arms and watch the difference between them.

LIGO — the Laser Interferometer Gravitational-wave Observatory — sends a laser beam into a beam splitter that divides it down two 4 km arms set at right angles. Each beam reflects off a mirror at the far end and returns, and the two are recombined. Light is an electromagnetic wave, so when the returning beams overlap they interfere: the combined brightness depends exquisitely on the difference in the two arms' lengths, because a path difference of even a fraction of the laser's wavelength shifts the crests and troughs into or out of step. When a gravitational wave passes, one arm lengthens by $\Delta L$ while the other shortens by $\Delta L$, and that differential change — twice the strain — moves the interference pattern at the detector.

What to try. Inject a wave and watch the two arms: the horizontal one lengthens exactly as the vertical one shortens, and the photodetector output (gold trace) tracks that differential change — not the length of either arm alone, but the comparison between two perpendicular distances. Slide the strain up and down and read the number underneath: even at a generous $10^{-21}$, the real arms move by about $4 \times 10^{-18}$ m. The mirror motion drawn here is exaggerated by roughly seventeen orders of magnitude so you can see it at all; the achievement of LIGO is measuring the true, invisible version. Getting there took decades of taming everything that could masquerade as a signal — seismic tremors, thermal jitter in the mirrors, even the quantum shot noise of the photons — until the differential arm length could be read to a small fraction of a proton's width.

A whole new way to observe the universe#

Every previous window on the cosmos used light — radio, infrared, visible, X-ray, gamma. Gravitational waves are something categorically different: not electromagnetic radiation at all, but tremors in spacetime, produced by mass in motion and passing almost unimpeded through everything in their path. They let us "hear" events that emit little or no light, like two black holes merging in the dark. LIGO's first detection earned Rainer Weiss, Barry Barish, and Kip Thorne the 2017 Nobel Prize in Physics, and it confirmed in one stroke both that gravitational waves are real and that stellar-mass black-hole binaries exist and merge.

The deepest payoff arrived weeks before that prize. On 17 August 2017, LIGO and its European partner Virgo caught GW170817 — the chirp of two neutron stars spiralling together. Because neutron stars, unlike black holes, are made of matter that shreds and glows on collision, telescopes around the world swung to the patch of sky the detectors pointed to and caught the afterglow across the electromagnetic spectrum, seconds to weeks later. This was the birth of multi-messenger astronomy: the same event read simultaneously in gravitational waves and in light. And what the light revealed was the radioactive glow of freshly minted heavy elements — the debris was forging gold, platinum, and other heavy nuclei by rapid neutron capture, exactly the r-process that builds the elements beyond iron. The gold in a wedding ring, it turned out, is very likely the ash of a collision we can now both see and hear.

The misconceptions, corrected#

Two pictures are worth retiring. The first is that a gravitational wave is a kind of electromagnetic wave, or a sound wave, or any wave that travels through something. It is not. It is a ripple in the geometry of spacetime itself — there is no medium, nothing "waving" except distance. It is emphatically not electromagnetic radiation: it is generated by moving mass rather than moving charge, it carries no electric or magnetic field, and it interacts with matter thousands of times more weakly, which is precisely why it can escape from deep inside cataclysms that light cannot leave.

The second is that gravitational waves push things around the way a normal force does. They don't. A passing wave does not shove an object in the direction it travels; it rhythmically stretches and squeezes the distances between things — the ring in the animation distorts but never lurches sideways. That is why the detector is built as two perpendicular arms whose difference is measured: the wave's signature is a differential stretch, not a push, and reading that differential to a fraction of a proton's width is what let us open an entirely new sense onto the universe.