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§ Phase xv · Stellar Quanta · Chapter 06

Gravitational waves

Einstein wrote down a theory in 1915 that said heavy things in motion should send ripples through the geometry of the universe, and then spent the next two decades half-believing his own arithmetic. A hundred years later, on a quiet September morning in Louisiana, an instrument the size of a small town heard the last fifth of a second of two black holes falling into each other from more than a billion light-years away. The signal lasted two-tenths of a second. Its discovery rewrote what counts as an astronomical instrument and opened a sense modality we did not previously have.

In June 1916, six months after he finished general relativity, Albert Einstein sat down in Berlin to ask a follow-up question. If gravity is the curvature of spacetime, and curvature can change as the matter that causes it moves, then waves of curvature ought to propagate the same way ripples propagate across a pond. He linearised his field equations, treated the metric as a small perturbation on top of flat space, and out came a wave equation. The solutions travelled at the speed of light. They were transverse. They had two independent polarisations, rotated by forty-five degrees rather than ninety, a peculiar signature of the spin-two field that carries gravity. Einstein wrote the paper, called the waves Gravitationswellen, and put it out into the world.

He then proceeded to disbelieve them, on and off, for the next twenty years. The trouble was a stubborn technicality. Some of the wave solutions in the linearised theory looked like coordinate artefacts, mathematical fictions that you could erase by choosing a different set of axes. Einstein could not always tell which solutions carried real energy and which were sleight of hand. By 1936 he had convinced himself, with his Princeton assistant Nathan Rosen, that the whole business was a mistake. He submitted a paper titled “Do gravitational waves exist?” to the Physical Review, with the conclusion that they did not. The anonymous referee, the cosmologist Howard Robertson, pointed out a sign error. Einstein, furious at having been refereed at all, withdrew the paper and never published in the Physical Review again. He sent a corrected version to a different journal, with a footnote thanking a colleague for “drawing attention” to an error, and quietly returned to believing in his waves.

The mathematical question of whether gravitational waves carry real energy was not fully settled in the physics community until 1957, at a conference in Chapel Hill, North Carolina, organised by Cecile Morette-DeWitt and Bryce DeWitt. Richard Feynman, sitting at the back, proposed a now-famous thought experiment. Imagine two beads strung on a rigid rod, free to slide. A passing gravitational wave will stretch and squeeze the rod’s length scale faster than the rod itself can adjust, and the beads will scrape along the rod, dissipating heat from friction. If heat is dissipated, energy must have been deposited by the wave. The waves are real. Feynman’s “sticky bead” argument finally cleared the conceptual fog. The next question was experimental. If the waves are real, can a person on Earth actually catch one?

The first serious attempt was made by an electrical-engineer-turned-physicist named Joseph Weber at the University of Maryland. Through the early 1960s, Weber designed and built large aluminum cylinders, about two metres long and half a metre in diameter, suspended in vacuum and instrumented with piezoelectric strain sensors. The idea was simple. A passing gravitational wave at the right frequency would set the bar ringing like a tuning fork, and the piezoelectric crystals would register the vibration. In 1969 Weber announced that two of his bars, one in Maryland and one at Argonne National Laboratory near Chicago, had registered coincident events at a rate of about one per day. He interpreted them as gravitational waves coming from the centre of the Milky Way. The astronomy community paused.

The pause lasted about four years. By 1973, half a dozen groups around the world had built bars of their own, copying Weber’s design as closely as they could. None of them saw the coincident signal Weber had reported. Weber kept insisting his apparatus was correctly calibrated and that the others had subtle backgrounds. The argument went on for years. Eventually the field arrived at a quiet consensus that whatever Weber had seen, it was not gravitational waves. He had been honest, persistent, and probably wrong. But he had also done something durable. He had founded experimental gravitational-wave physics as a discipline, and he had convinced a generation of younger physicists that the problem was worth taking seriously. Among the people he convinced was a Princeton-trained theorist named Kip Thorne at Caltech, who began to wonder whether a different sort of detector might actually work.

While the bar detectors argued, the universe quietly handed astronomers a second route to the same answer. In 1974 a Princeton graduate student named Russell Hulse, working at the giant Arecibo radio telescope in Puerto Rico under his advisor Joseph Taylor, found a pulsar with an unusual property. A pulsar is a rapidly spinning neutron star that emits a narrow beam of radio waves, sweeping past the Earth like a lighthouse and arriving in our antennas as a pulse train of stunning regularity. The pulsar Hulse and Taylor found, catalogued as PSR B1913+16, had a period that wobbled in a strict eight-hour cycle. The wobble was the unmistakable signature of orbital motion. The pulsar was one half of a binary system, locked in a tight orbit with another neutron star, the two of them whirling around their common centre of mass at speeds approaching a thousandth of the speed of light.

Such an orbit is exactly the kind of accelerating mass distribution that general relativity says should radiate gravitational waves. As energy leaks away into the waves, the orbit should slowly tighten, the two stars spiralling in toward each other on a precisely calculable schedule. Taylor and his collaborators began timing the pulses with painful care. Within a few years, they had measured the orbital period decay. The orbit was shrinking at a rate of about seventy-five microseconds per year. General relativity predicted seventy-five microseconds per year. The agreement, refined over the next two decades, eventually reached one part in a thousand. The waves were real, the energy was real, and the universe was helpfully demonstrating both. Hulse and Taylor were given the Nobel Prize in 1993.

The indirect detection vindicated Einstein’s arithmetic, but it left the experimentalists hungry. To hear an actual wave, you needed a detector that could measure a length change of about one part in ten to the twenty-first, that is, a stretch of one proton’s diameter across the diameter of the Earth, or, equivalently, the breadth of a human hair across the distance to the nearest star. No existing apparatus came close. Joseph Weber’s bars were sensitive to maybe one part in ten to the sixteenth. The gap was five orders of magnitude.

Rainer Weiss, an experimental physicist at MIT who had grown up listening to his radio-engineer father describe wartime interferometers, had an idea. Take a powerful laser, split its beam in two with a half-silvered mirror, send each half down a long evacuated tube to a mirror at the far end, bounce the light back, and recombine the two beams at the original splitter. The recombined light will interfere. If the two arm lengths are exactly equal, the geometry of the interference pattern is fixed. If a passing gravitational wave changes the length of one arm relative to the other (even by a tiny fraction of a wavelength), the interference pattern shifts and a photodetector at the output reads a change in intensity. Weiss worked out the noise budget in a 1972 technical report and concluded that with arms a few kilometres long and enough laser power, the device could in principle reach the strain sensitivity required to hear astrophysical sources. Kip Thorne, who had been thinking about gravitational-wave sources for a decade, became Weiss’s theoretical partner. Together with the Scottish experimentalist Ronald Drever, who had developed exquisitely precise optical-cavity techniques at Glasgow, they conceived what eventually became LIGO: the Laser Interferometer Gravitational-Wave Observatory.

The decision to build LIGO was not an easy sell. The National Science Foundation was being asked to commit hundreds of millions of dollars to a device that would search for a signal nobody had ever directly seen, using a method that had never measured anything close to the required sensitivity, to hunt sources whose predicted rates spanned six orders of magnitude in the literature. The skepticism was reasonable. Through the 1980s and early 1990s, the LIGO project survived an internal crisis (Drever and Weiss disagreed publicly enough about the design that the management was overhauled, with Barry Barish brought in from particle physics to professionalise the construction), a near-cancellation by Congress, and a series of technical problems whose solutions required inventing new branches of optics and seismic isolation. The first version of the detector, LIGO-I, ran from 2002 to 2010 with arm-length sensitivity good enough to see a strain of about ten to the minus twenty-one over a useful frequency band. It saw nothing. The project then shut down for a five-year rebuild. The upgraded instrument, Advanced LIGO, came online in September 2015.

On the morning of September 14, 2015, at 09:50:45 Coordinated Universal Time, the strain channels at the LIGO Livingston site in Louisiana registered a transient. Seven milliseconds later, the LIGO Hanford site in Washington state, three thousand kilometres away, registered the same waveform with a delay consistent with the speed of light. Both detectors saw the same pattern: a low-amplitude oscillation at about thirty-five Hertz that rose in frequency and amplitude over the next two-tenths of a second, peaked at a few hundred Hertz, and then died away in a brief ringing tail. The engineers on shift recognised that the signal was real well before they understood what it meant. The amplitude was huge by detector standards, twenty-four times the typical noise floor in a matched-filter analysis. The bigger problem was the opposite. The signal was so clean and so obviously a match to general-relativistic predictions that nobody believed it was unblinded data.

The collaboration spent five months verifying that the event was not a hardware injection, not a calibration test, not malicious mischief, before announcing it to the world on February 11, 2016. The event was named GW150914, after its date. The waveform matched, with parameters extracted by careful template-fitting, the inspiral and merger of a binary black-hole system with component masses of about thirty-six and twenty-nine solar masses, at a luminosity distance of about 410 megaparsecs (roughly 1.3 billion light-years). The final black hole was sixty-two solar masses, with three solar masses worth of energy radiated as gravitational waves in the last quarter of a second. At its peak, the source emitted gravitational-wave power exceeding the combined electromagnetic power output of every star in the observable universe. None of that energy was visible to any telescope.

The 2017 Nobel Prize in Physics was awarded to Rainer Weiss, Barry Barish, and Kip Thorne. Ronald Drever had died earlier that year and was therefore ineligible. The citation read, with unusual precision for the Nobel committee: “for decisive contributions to the LIGO detector and the observation of gravitational waves.” It was the first Nobel ever given for an observation made by a single instrument designed and built within the lifetime of its honourees.

What happened next made the first detection seem like a warm-up. On August 17, 2017, at 12:41 UTC, the LIGO detectors and their European counterpart Virgo registered a long, slow chirp lasting about a hundred seconds. The signal pattern said this was not a black-hole binary. The chirp ended at a few hundred Hertz and trailed off without the abrupt merger-peak that black-hole pairs produce. The component masses, extracted from the chirp’s evolution, were in the range of 1.1 to 1.6 solar masses, the unmistakable signature of two neutron stars. The event was named GW170817. Two seconds after the wave peak, the Fermi gamma-ray satellite registered a short gamma-ray burst from the same patch of sky. Eleven hours later, the Swope optical telescope in Chile, scanning the LIGO error region, found a new point of light in the galaxy NGC 4993, forty megaparsecs away. Over the following two weeks, telescopes on every continent and in orbit followed the source as it brightened, reddened, and slowly faded. The spectrum of its dying glow contained features that could only be explained by the radioactive decay of freshly synthesised heavy elements: lanthanides, the trans-iron metals, possibly the first directly observed signature of where the universe makes its gold and platinum. The merger of two neutron stars, predicted on paper for decades, had been caught in the act and listened to in every electromagnetic and gravitational channel at once.

h ≈ (G M / c² D) · (v / c)²

P_GW ≈ (32 / 5) · (G⁴ / c⁵) · M⁵ / r⁵

The Hulse-Taylor pulsar is still in orbit, still losing energy to its waves, still on track to merge in a few hundred million years. LIGO and Virgo and the newer Japanese detector KAGRA have now catalogued more than ninety gravitational-wave events, mostly binary black holes, occasionally neutron-star pairs, once a black-hole-neutron-star pair. The third LIGO observing run added events at a rate of more than one per week. The next generation of detectors (the European Einstein Telescope, the American Cosmic Explorer, the space-based LISA mission) will catch tens of thousands per year and will be able to hear the in-spirals of supermassive black holes in the centres of distant galaxies. The pulsar-timing arrays, using a different technique that watches pulsars across the galaxy for correlated wobbles, have already detected the long-wavelength gravitational-wave background that may come from supermassive black-hole binaries spiralling through the cosmic web.

Einstein, who half-doubted his own waves for two decades and once tried to publish a paper saying they did not exist, was wrong about that and right about almost everything else. The geometry of the universe really does ring when it is struck. The ring is faint, almost ridiculously so, but it carries information that no photon can carry. It travels through opaque clouds of dust, through nuclear-burning interiors, through epochs of the universe so early that ordinary light was still trapped in plasma and could not escape. Every black-hole inspiral we record is a clean measurement of a system with no electromagnetic counterpart at all. Every neutron-star merger throws gold and platinum into space at a measurable rate. The chapter is open, the instruments keep improving, and the universe is, for the first time in its history, audible to one of its own species.