The following is an extract from our Lost in Space-Time newsletter. Each month, we hand over the keyboard to a physicist or mathematician to tell you about fascinating ideas from their corner of the universe. You can sign up for Lost in Space-Time for free here.
From our current vantage point, gravitational waves appear to be a ubiquitous phenomenon in the cosmos. The first detection of these ripples in space-time came in September 2015 at the Laser Interferometer Gravitational-Wave Observatory (LIGO). The waves captured were the by-product of a merger of two black holes, 1.3 billion light years away, each with the mass of approximately 30 suns.
Since that time, there have been roughly 100 other detections associated with similarly violent events 鈥� collisions between two black holes or two neutron stars and even a fateful encounter between a black hole and a neutron star. And just last year, we discovered that our universe appears to be immersed in a low-frequency background of gravitational radiation 鈥� the cumulative and ever-present residue of thousands (perhaps even a million) black hole crashes throughout cosmic history.
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Although scientists now have plenty of gravitational wave data to sift through, this was not always the case. In fact, 99 years elapsed between the time that Albert Einstein raised the prospect of gravitational waves and when the first direct evidence of their existence was obtained. During that lengthy interim, much of what we learned about this phenomenon came from mathematics.
It occurred to Einstein in 1916 that the acceleration of matter through space and time 鈥� the milieu we all inhabit called space-time 鈥� could cause ripples to form, like those produced by a boat in a calm pond, except they would emanate in all directions from the point of origin.
This was more than just an idle thought that crossed his mind. Einstein described such waves and the properties they would possess explicitly using mathematics. Nevertheless, he had profound doubts as to whether gravitational waves truly existed. And if they did exist, he was not sure they could ever be detected.
He wavered on this point for years, and by 1936, two decades after his initial suggestion, he had determined that any solution to the equations of general relativity that would give rise to gravitational waves would also contain a singularity 鈥� a discontinuity in space-time whose presence could throw his entire theory into disarray. To avoid such a dire contingency, he concluded that gravitational waves could not exist and prepared to present that case in a talk at Princeton University that same year. After a colleague alerted Einstein to a flaw in his reasoning, he adopted a more equivocal stance in his lecture, saying, 鈥淚f you ask me whether there are gravitational waves or not, I must answer that I don鈥檛 know. But it is a highly interesting problem.鈥�
Given what we know now, Einstein was right to have left the matter open. He was also correct in surmising that gravitational waves would be hard to detect. If it would take a truly cataclysmic event to produce a discernible signal, that posed a challenge. Solutions to the equations of general relativity were very hard to come by and the earliest ones involved comparatively simple situations, such as the case of a perfectly spherical star, stationary in space and unchanging in time. A scenario that could produce gravitational waves, involving massive bodies that are moving exceedingly fast and poised to smash into each other, would be much more complicated.
It was not immediately clear whether one could solve the Einstein equations under these messier and more demanding conditions. Eventually, there was progress. In 1952, the mathematician Yvonne Choquet-Bruhat proved that the Einstein equations had a stable solution that allowed for gravitational waves 鈥� but she only managed to show that such a solution existed for a short while into the future. In 1969, she joined forces with the mathematical physicist Robert Geroch to extend that result, showing that a stable solution could last for an arbitrarily long time.
That was a critical milestone because it meant you could rely on general relativity to predict the kind of waves that would be produced, for instance, if two black holes smashed into each other. Conversely, you could start from the opposite direction, relying on the same equations to work out details regarding the original objects that generated the waves, like their mass or if they are rotating and how fast.
While mathematicians and physicists were approaching this subject from the theoretical end, experimentalists started to build small gravitational wave detectors in the early 1970s. These were eventually scaled up, leading to the start of construction of LIGO in 1994; preliminary operations began eight years later. The resulting observatory is an engineering marvel, capable of detecting changes in distance between its mirrors that are 10,000 times smaller than the width of a proton. These fluctuations indicate that ripples in space-time are passing through.
But a computational challenge still loomed. Before they could have any hopes of spotting gravitational waves, scientists at LIGO and its European counterpart, Virgo, would have to know what to look for 鈥� the shape, amplitude and frequency of the waves they expect to find. This was a difficult problem that took many years to solve.
A major advance occurred in 2005 when the physicist Frans Pretorius realised that the calculations that Choquet-Bruhat had developed during her work in the 1950s could be used in computer simulations of black hole mergers. This was one of many key steps that contributed to the detection a decade later of the first gravitational waves 鈥� and those that have since followed.
One might say that, in this instance, researchers simultaneously proved Einstein both right and wrong. Proving him wrong merely indicated that Einstein was cautious 鈥� not a terrible quality for a scientist to have and surely better than the trait of hubris. Proving Einstein right was a testament to his greatness and that of the brilliant idea he conceived in 1916. One consequence of that insight, among many that could be mentioned, is the fact that gravitational wave astronomy offers a new 鈥� and still largely unexplored 鈥� avenue for probing the universe. Unsurprisingly, it also happens to be one of the fastest growing areas in astronomy.
