On September 14, 2015, a ripple in spacetime that had been traveling towards the earth for over a billion years was picked up by detectors in both Louisiana and Washington. One hundred years after Einstein predicted them, and a billion years after two black holes collided farther away than we could possibly imagine, these gravitational waves reached earth, and put to rest one of the fundamental remaining questions surrounding Einstein’s theory of general relativity.
What are Gravitational Waves and why are we looking for them?
To answer this question, we need to take a quick aside into general relativity, and how it relates to all our previous attempts to make sense of gravity.
Since the 17th century, people have understood gravity through the lens of Newtonian mechanics, the basic formulation of which is that the force exerted between two objects is proportional to their weight and inversely proportional to the square of the distance between them.
What this tells us is that objects fall to the earth because the earth is much more massive than anything on it, and so exerts a force much larger than that exerted upon it.
Newton’s theory allows us to measure these gravitational forces and predict their effects. It doesn’t, however, explain how or why gravity happens. Though not entirely satisfactory, Newtonian gravity was still a vast improvement on mankind’s previous understanding of why objects fall, and took almost two millennia to formulate. Before it, all we had was Aristotle’s theory that objects fall to earth because they’re returning to their natural resting place. What’s more, scientists now had a theory of gravity and motion that could be applied to stellar objects as well. For the first time, they could gaze at the heavens and understand exactly why planetary orbits behaved the way they did. Or almost exactly why.
Fast forward about two hundred years, and people are already starting to find flaws in Newton’s theory. In 1859, french Mathematician Le Verrier noticed that Mercury’s trajectory round the sun did not match up with Newton’s predictions. Newtonian gravity tells us that mercury’s perihelion, or the closest point to the sun in its elliptical orbit, should change by 1.54 degrees per century. The observed offset is actually closer to 1.55 degrees per century. The difference may not seem like much (ratio wise it’s about 2 inches for every mile), but all the other planetary orbits complied exactly. There had to be something else going on.
Instantaneous action at a distance
Fast forward once more to 1905. Einstein has just published a paper on his special theory of relativity, demonstrating that nothing can move faster than the speed of light, and something about Newton’s gravity starts to nag at him. If gravity isn’t mediated by anything, then it’s instantaneous.Take the sun and the earth, for instance. If the sun were to fall out of the sky, Newton tells us that the earth would immediately fall out of its orbit. If the effects of gravity are instantaneous across stellar distances, then it follows that the force of gravity must have infinite speed. But Einstein had just shown that nothing — no object, no signal, no force — could move faster than light. In other words, it should take at least 8 minutes for the earth to notice the changes to its gravitational situation — that’s the amount of time it takes for light to travel between the earth and sun. Until then, it could remain happily oblivious.
Einstein set about trying to figure out how gravity was exerted between two bodies, hoping that the answer would lead him out of this conundrum. If there is nothing but empty space between the earth and sun, he reasoned, then gravity must be exerted by space itself.
The theory that was born of these questions is known as his general theory of relativity, and is staggering in its elegance. Matter causes space to warp around it, Einstein tells us, and the greater the mass, the greater the warp. The resulting shape of space influences the trajectories of nearby bodies because they’re trying to find the shortest possible path along this curved space. Gravity, he realized, is simply a manifestation of objects trying to find the shortest way home.
Einstein went one step further, and realized that matter also causes time to warp. Both space and time are susceptible to gravity. The nearer a clock is to a massive body like the earth, for instance, the slower it will tick. This effect, known as time dilation, has been measured in the lab, and is pronounced enough that it had to be taken into account in the design of GPS satellites.
We can think of spacetime, then, as the fabric of the universe that curves in response to massive objects. It has three spatial dimensions, and one temporal dimension.
Much as a spatial warp can nudge an object’s trajectory (remember that bit about massive bodies changing objects’ trajectories?), so too can a temporal one: Einstein’s math suggests that objects are drawn toward locations where time elapses more slowly. Fundamentally, everything in the universe is looking for a little bit more time.
It took Einstein three years to formulate the mathematical framework to back up his general theory of relativity. But even then, his ideas would only be taken seriously if they could be experimentally validated. The first validation for his theory was that it perfectly predicted Mercury’s weird trajectory around the sun. As the closest planet to the sun, it exists in the most highly curved area of spacetime, and so moves in ways that cannot be explained by Newtonian laws alone.
Another prediction of the theory is that beams of light emitted by distant stars will be deflected as they pass through the warped region of spacetime around the sun. Einstein calculated the exact shape of these trajectories, and waited for the next solar eclipse. Outside of an eclipse, the light from the sun is too bright to enable us to detect anything around it. He didn’t have to wait long: the eclipse of May 1919 was one of the longest of the 20th century, and allowed Sir Arthur Eddington to take pictures of distant stars momentarily visible as the moon eclipsed the sun. On September 22, 1919, Einstein received a telegram announcing that the eclipse observations had confirmed his predictions exactly.
It took us 2000 years to get from Aristotelian gravity to Newtonian gravity, and less than another 300 to Einstein’s gravity. We’re clearly getting better at this.
Throughout the 20th century, experiment after experiment have confirmed the predictions of general relativity. All but one, which brings us back to LIGO.
Stretching spacetime
“There is one remaining experiment, currently more than 20 years in the making, that many consider the final test of the general theory of relativity (GR)”, wrote physicist Brian Greene in an essay marking the centennial of Einstein’s paper. “According to the theory, two colliding objects […] will create waves in the fabric of space, much as two colliding boats on an otherwise calm lake will create waves of water. And as such gravitational waves ripple outward, space will expand and contract in their wake, somewhat like a ball of dough being alternately stretched and compressed.”
Unbeknownst to him, these ripples had already been detected.
But it isn’t just two colliding objects that create waves in the fabric of space. General relativity tells us that any object with mass produces gravitational waves when it accelerates. The waves that we on earth produce, however, are far too small to be detected. We’re simply not massive enough or fast enough. Luckily, the universe is filled with rapidly accelerating supermassive objects, like spinning black holes and neutron stars. We just had to design an experiment sensitive enough to detect them.
And so we did. LIGO, the Laser Interferometer Gravitational Wave Observatory, is a worldwide collaboration managed by Caltech and MIT. It was envisioned over 40 years ago, and has cost upwards of $1.1 bn.
Unlike other kinds of waves we’re used to (microwaves, radio waves, x-rays) gravitational waves are not electromagnetic. They’re not sound waves either. They are ripples in spacetime, causing its very fabric to stretch and contract. Imagine two objects placed at points A and B, 1 mile apart. If a gravitational wave were to pass across them, they would be ever so slightly farther apart for the duration of that wave. The direction perpendicular to them, on the other hand, would be ever so slightly compressed (see visualization below).
LIGO uses these very principles to look for infinitesimal differences in the distance that light must travel along two perpendicular arms of equal length. When a gravitational wave passes by, one arm is stretched while the other is shortened. As a result, the light no longer travels the same distance along both, and this slight variation in distances traveled results in a distinct light pattern on the photodetector known as interference (hence the name interferometer.)
Because it’s trying to measure such small effects (about 10,000 times smaller than an atomic nucleus), LIGO has two separate detectors set up on opposite sides of the country. If both detectors observe identical ripples, we can be sure they weren’t caused by anything in their environments.
And so we have the final major piece of experimental evidence for the theory of general relativity. Does this mean that we can safely assume Einstein’s theory is absolutely correct? Certainly not. There are still some fiddly bits that need sorting out, like the problem of dark energy and general relativity’s refusal to play nicely with quantum mechanics. Just like Newtonian mechanics is not great at explaining objects moving near the speed of light or in high gravitational fields, general relativity doesn’t seem to do well at very small scales. But for now, it’s the best theory we’ve got.
