Two gravitational-wave detectors

Why is a perfectly clear signal in one detector treated as no detection at all?

Suppose I hand you a strip chart from a gravitational-wave observatory, and on it sits a beautiful rising chirp — exactly the shape theory predicts for two black holes spiralling together. Clean. Unmistakable. And the collaboration says: we have nothing.

That seems perverse, does it not? The signal is right there. So let me ask what looks like a naive question: what would you have to believe about the instrument before you were allowed to call that chirp a detection?

Start with what the instrument is being asked to do. LIGO measures a change in the length of a four-kilometre arm of about one part in 10^21 — a mirror displacement thousands of times smaller than a proton. Anything that nudges a mirror produces a wiggle. A truck on a nearby road, a distant storm driving microseism through the ground, a scattered laser beam bouncing off a vibrating surface, a bit of electronics glitching. The data stream is not quiet with occasional signals in it; it is a continuous mess with structure everywhere.

Now here is the step that matters. If the noise were pure Gaussian hiss, you could compute how often chance alone would fake your chirp, and the answer would be reassuringly tiny. But the noise is emphatically not Gaussian. Real interferometers produce "glitches" — short, loud, transient excursions that occur far more often than Gaussian statistics allow, and some of them look uncomfortably like real signals. So what happens to your confidence when the population of impostors is much larger than the theory of pure chance predicts?

It collapses. Not because the chirp is unconvincing to the eye, but because you have no honest way to say how often the instrument produces convincing-looking chirps on its own.

So how would you get that number back? Ask yourself what an independent copy of the instrument buys you. There are two detectors, one at Hanford in Washington State and one at Livingston in Louisiana, about 3,000 km apart. A truck in Louisiana does not shake a mirror in Washington. Their glitch populations are essentially uncorrelated. So if you demand that both see the same waveform, the chance of a coincidental fake is roughly the product of two small numbers rather than one — and a product of small numbers gets very small very fast.

But mere coincidence is not enough, is it? Two glitches will occasionally land near each other by luck. So the demand is tightened: the two must agree in shape, in amplitude consistent with one source and two antenna orientations, and above all in timing. A gravitational wave travels at the speed of light, so it cannot arrive at the two sites more than about ten milliseconds apart. That window is the filter. In GW150914, the first detection, the wave reached Livingston roughly seven milliseconds before Hanford — comfortably inside it, and itself a crude bearing on the sky.

And here is the move I find most elegant, because it turns the requirement into a measuring instrument. If you want to know how often the pair fakes a coincidence, slide one detector's data in time by much more than ten milliseconds and look for coincidences again. Any real signal is destroyed by the shift; anything you now find is pure background. Repeat over thousands of shifts and you have empirically measured the false-alarm rate rather than assumed it. For GW150914 that procedure returned a rate below one in 200,000 years — a number no single-detector chirp, however pretty, could ever have earned.

Do you see what has quietly happened? The second detector is not there to see the wave better. It is there to let you count how often you are wrong.

Two refinements keep this honest. First, "no detection at all" is a little too absolute. A single-detector trigger is not discarded; it is reported as a candidate with a far weaker significance, because the background can only be estimated by less direct means. GW190425, a likely neutron-star merger, was essentially a one-detector event, published as such and treated with corresponding caution.

Second, coincidence is not only about confidence — it is about knowing anything at all. A single interferometer is nearly omnidirectional; it cannot say where a wave came from. Arrival-time differences across a network are what localise a source on the sky, and that is what let telescopes chase GW170817 to its host galaxy hours later. With Virgo in Italy and KAGRA in Japan added, the network triangulates rather than merely corroborates.

So redundancy here is doing double duty: it converts an unauditable claim into a measurable one, and it converts a yes-or-no into a direction.

• How time-slide background estimation compares with the analytic false-alarm rates used in particle physics.
• Why a detector network's sky localisation improves so sharply with the third and fourth site.
• Whether pulsar timing arrays, which use dozens of "detectors", face the same correlated-noise problem in a different guise.

Every term the collection defines is gathered in the glossary.