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Gravitational waves, as the LIGO-India project puts it, are predicted as an essential element of Einstein's theory of general relativity, yet the first direct detection came only in 2015. The change LIGO measured was a few billionths of a billionth of a metre. This post explains what was measured, works through the numbers, and shows why India is building its own detector.
What was the first detection?
The discovery paper, Observation of Gravitational Waves from a Binary Black Hole Merger (2016), reports that on 14 September 2015 at 09:50:45 UTC both LIGO detectors in the United States recorded the same short signal. It swept upward in frequency from 35 to 250 Hz, with a peak strain of 1.0 × 10⁻²¹. The waveform matched general relativity's prediction for two black holes spiralling together and merging. In the source frame the two black holes were about 36 and 29 times the Sun's mass, the final black hole about 62, and about 3.0 solar masses of energy were radiated as gravitational waves. The source was about 410 megaparsecs away.
The Nobel Prize in Physics 2017 went to Rainer Weiss, Barry C. Barish and Kip S. Thorne "for decisive contributions to the LIGO detector and the observation of gravitational waves".
Worked example 1: how small is a strain of 10⁻²¹?
Strain h is the fractional change in length, ΔL/L, so it has no units. The LIGO-India detector page describes LIGO's interferometer arms as 4 km long.
ΔL = h × L = 1.0 × 10⁻²¹ × 4,000 m = 4.0 × 10⁻¹⁸ m.
A femtometre is 10⁻¹⁵ m, so the arm changed by about four thousandths of a femtometre. The detectors compare the lengths of two arms at right angles using laser light, which is why they are called interferometers.
Worked example 2: how much energy did the merger release?
The paper says 3.0 solar masses were converted to gravitational-wave energy. Use E = mc², with the Sun's mass of 1.9884 × 10³⁰ kg from NASA's Sun fact sheet.
m = 3.0 × 1.9884 × 10³⁰ = 5.97 × 10³⁰ kg.
c² = (3.0 × 10⁸)² = 9.0 × 10¹⁶ m²/s².
E = 5.97 × 10³⁰ × 9.0 × 10¹⁶ ≈ 5.4 × 10⁴⁷ J.
Check the masses: 36 + 29 = 65, and 65 − 62 = 3. The missing mass is the radiated energy, consistent within the paper's stated uncertainties.
Why does India need its own detector?
LIGO Laboratory's LIGO-India page explains the reason. Two detectors that sense the same polarisation, like the two US sites, are enough to confirm that a signal is real, but they cannot pin down where on the sky it came from or reveal the wave's polarisation. A network of three gives a sharp sky location for only about half of all possible directions. Locating a source anywhere on the sky needs at least four comparable detectors operating at the same time.
Because detectors are sometimes offline, a network needs more than four. Virgo in Italy and KAGRA in Japan are part of it, and LIGO Laboratory calls LIGO-India "the all-important fifth". The project is a collaboration between LIGO Laboratory and three Indian institutes: RRCAT in Indore, the Institute for Plasma Research in Ahmedabad, and IUCAA in Pune. The page shows the planned site in Maharashtra.
The LIGO-India project site says the detector received the Government of India's in-principle approval in February 2016, and LIGO Laboratory records a memorandum of understanding signed in March 2016. For construction progress and timelines, check the project site directly.
Worked example 3: how timing locates a source
Gravitational waves travel at the speed of light. Suppose two detectors are 3,000 km apart. The largest possible gap in arrival time is
t = d/c = 3.0 × 10⁶ m ÷ 3.0 × 10⁸ m/s = 0.010 s, or 10 ms.
A measured gap smaller than this tells you the angle between the source direction and the line joining the detectors, but that angle traces out a ring on the sky. A third detector gives a second ring, and the rings cross at two points. Further detectors, far from the others, shrink the uncertainty. A detector in India, a long way from the US and Europe, adds long baselines in new directions.
What mistakes do students make with these ideas?
Treating strain as a distance. Multiply by the arm length to get ΔL.
Using the total mass in E = mc². Only the 3.0 solar masses that went missing were radiated.
Thinking one detector can find direction. It cannot; timing between sites is what locates a source.
Radio astronomers are hunting gravitational waves in another way, by timing pulsars; our post on the Giant Metrewave Radio Telescope describes that goal.
What can a student take from this work?
The LIGO story is about measuring something almost too small to imagine, and the LIGO-India plan is about a network rather than a single instrument. Both carry a lesson for study: precision comes from careful comparison, and some answers need more than one viewpoint.
If interference of light is the part that loses you, the Fermi Concept Library has every concept in physics, chemistry, biology, mathematics and computing with its own lesson, so you can revise it before tackling interferometers.
Work out ΔL for a strain of 1.0 × 10⁻²¹ on a 3 km arm, then explain in one sentence why longer arms help.
