# Spacetime from Euclid to LIGO

In 2015 we first heard the whooping sound made by a pair of colliding black holes.  Two years later it was the unique chirp made by a pair of colliding neutron stars.  Our newfound ability to eavesdrop on cataclysmic events at the far reaches of the universe is thanks to a new generation of gravitational wave detectors.  The gravitational sound show is just beginning, and it promises to reveal the nature of spacetime as never before.

## The quest to understand space

What is space?  We know thinkers have pondered that question at least for as long as there are recorded texts.  The clay tablets left by Ancient Babylonians show they were toying with the nature of triangles.

But, 2300 years ago, the Greek mathematician Euclid revolutionised the science of geometry with systematic thinking that captured the descriptive work of the past and elevated it to the level of universal truths or axioms.

His 13-volume treatise Elements uncovered the perfection of lines and shapes and put it all together in the most influential science book of all time, in print for 2000 years and published in 1000 editions.  It is still taught in schools today.

But are Euclid’s axioms truly universal?

In the early 1800s, German mathematician and physicist Carl Gauss was the first to challenge Euclid’s laws of geometry, especially his fifth axiom, which states that parallel lines can never meet.

Gauss observed that on curved surfaces, parallel lines – such as longitude lines at the earth’s equator – intersect at the poles.   He also realised that space could have shape, and his Egregium Theorem showed that you could measure its shape if you measured distances and angles.

Imagine you’re an ant living on a balloon; your world would seem flat. But an ant familiar with the Egregium Theorem would stretch strings and draw triangles.  If the angles of the triangle added up to more than 180 degrees, the ant would know it’s living on curved space.

Egregium, by the way, is Latin for “exceptional”.

Gauss’ determination to put Euclid’s theorems to the test set the scene for Einstein.

By 1905, he had already come up with his theory of Special Relativity. This was the theory that gave us E=Mc2, which means that energy has mass and mass has energy.

In 1907 Einstein had another revelation that he later described as “the happiest thought of my life”.  He realised that gravity is indistinguishable from acceleration. If you’re riding an elevator with your bathroom scales, you’ll find you’re lighter as the elevator accelerates down and heavier when it decelerates. So, Einstein realised,  gravity is the force you feel when you prevent free fall.

It took eight more years and help from his friends for him to combine this happy thought with Gauss’s thinking about the shape of space, to create his final theory of gravity: General Relativity. Published in 1915, it was based on the revolutionary idea that mass and energy deform space and time, and that deformed spacetime itself has energy. In a certain sense spacetime is an elastic material: immensely stiff but deformable – like a trampoline.

Einstein’s publication gave rise to a succession of remarkable discoveries.

Within months, while serving in the German army, physicist and astronomer Karl Schwarzschild solved Einstein’s equations to reveal how the curvature of space and the warping of time depends on distance from a central mass. The closer the distance and the larger the mass, the more warping there is, and at a certain distance from a central point mass space and time actually come to an end.

He was of course imagining a ‘black hole’, but it would take 50 years before the term was coined.

A few months later, in 1916, Einstein found a solution to his own equations. It predicted the existence of gravitational waves, ripples in spacetime that would travel at the speed of light.

And in the following years, discoveries provided support for the notion that space was a deformable elastic medium – one that could propagate gravitational waves.

In 1919, English physicist Sir Arthur Eddington’s observation of an eclipse from the island of Principe near West Africa proved that space is curved by the Sun. In 1922 Russian scientist Alexander Friedmann showed that Einstein’s equations predicted a dynamic universe in which space itself must either expand or contract. And in 1929 American astronomer Edwin Hubble discovered that the universe was in fact expanding.

When Einstein predicted gravitational waves in 1916 he realised that they could be generated  by pair of stars circling each other. He came up with a formula that describes  how gravitational wave power depends on their masses, the speeds and the spacing – all measurable numbers.

But there was a catch: in his formula, the wave power was divided by an enormous number, a crazy number, that I call Einstein’s number. Algebraically, Einstein’s number is c5/G – the speed of light multiplied by itself five times, divided by G, the tiny number that tells us the weakness of gravity.

Put together, c5/G is more than 1054. If you divide anything by a number this vast, you get next to nothing. Einstein realised this. Nothing he could conceive of could possibly produce measurable gravitational waves. The waves were of academic interest only, he concluded.

What Einstein hadn’t been aware of was that Schwarzschild, who died of an auto-immune disease in 1916, had left him a hidden treasure. The trouble was that Schwarzschild’s solution, which described  a singularity where space and time cease to exist,  was viewed by Einstein and others as a mathematical oddity, not a description of anything that could possibly be real.

But 50 years on, black holes – as these singularities were later dubbed – were the best hypothesis to explain a strange x-ray emitting star called Cygnus X-1.

A tiny object with vast gravity was needed to explain this powerful erratic x-ray emission.  People began to think that black holes might be real.

Then someone took Einstein’s 1916 equation for wave power, and substituted  in Schwarzschild’s black hole formula. A school kid could have done it. The result was miraculous!

With Schwarzschild’s formula, the division by Einstein’s number that made gravitational waves merely academic is transformed into a multiplication by the same number. Suddenly the wave power for a pair of black holes circling each other up-close becomes almost as big as Einstein’s number itself.

This is roughly the power of all the stars in the visible universe!  The catch is it lasts for only an instant. This was Schwarzschild’s hidden treasure.

Schwarzschild’s work tells us that when black holes collide they create a pure gravitational explosion, more powerful than a supernova or a gamma ray burst. Nothing beats it except the Big Bang itself.

However, as an explosion of rippling space, it would pass freely through you. Even if it happened as nearby to Earth as the Sun, you would feel no more than a tiniest shudder. Yet each such gravitational explosion would in principle be detectable across the entire universe.

## Harnessing inertia to build a gravitational wave detector

I was inspired to join the quest to detect colliding black holes by the eccentric pioneer of gravitational wave astronomy, American physicist Joseph Weber. Back then, we reasoned that explosions so vast must be detectable. We thought that if we worked hard at inventing a gravitational detector, we might pick up a signal by Christmas! That was in 1973.

Our ability to detect gravitational waves relies on the concept of inertia – the tendency of matter to continue in its state of motion unless acted on by an external force.

Scientists have been relying on inertia to detect relative motion for nearly 2000 years.  In 132 AD, Chinese scientist Zhang Heng harnessed inertia to build the first seismometer.

Inside a big bronze urn he suspended a mass so that it could swing freely in the horizontal plane. If the ground moved, so would the urn, but the mass, anchored to space by the law of inertia, would stay in place.

Inside, the movement dislodged a ball from the mouth of one of eight dragons that marked the cardinal directions. The ball rolled out and was caught in the mouth of a bronze toad.  This way he detected an earthquake hundreds of kilometres away.

Heng’s seismometer allowed him to detect the motion of the earth against unchanging space. But what if space suddenly stretches? You won’t feel a thing, and nor will a seismometer, just as you do not feel the universe expanding. But, you might notice that a distant object has just moved away from you. It did this because inertia caused it to follow expanding space.

Modern day gravitational wave detectors like the Laser Interferometer Gravitational-Wave Observatory (LIGO) in the US detect the stretching and shrinking  of space  caused by a passing wave  by suspending two 40 kilogram masses four kilometres apart.

These masses are coated with near-perfect mirrors, so changes in the distance between them can be measured by using a beam of laser light as a ruler. The catch is the minuscule size of the change. Like ripples in a pond, gravitational waves diminish as they expand away from the source.

Even though LIGO was aiming to measure the space distortion created by colliding black holes – the biggest dynamic distortion possible – the ripples they create reduce to half every time you double the distance.

By the time the wave reaches the Earth from a black hole collision a billion light years away, the stretching and shrinking of space in a LIGO detector has reduced to a hundredth of a billionth of a billionth of a metre – much smaller than the size of a proton.

## A dream fulfilled

It took more than 40 years and several generations of detectors, before, finally, the pair of advanced LIGO detectors were ready to begin listening for the sounds of gravitational waves. The new detectors were three times more sensitive than previous ones, but still three times below their ultimate design specification. We were hopeful but not optimistic.

On September 14, 2015, a few days before the official start date, the first signal came in. Was it a hoax? Was it accidental? A short rapidly rising pitch, from two octaves below to middle-C made a brief whoop sound. It was heard in two detectors 3000 kilometres apart and had a time delay just right for a wave travelling at the speed of light. After months of investigation there was no doubt that it was real.

All our dreams were finally fulfilled on February 11, 2016, when gravitational wave astronomers announced in a Washington press conference, that they had indeed detected a pair of black holes spiralling together and merging into a single black hole.

And since that first detection, more whoops from other colliding black holes have followed.

You might think that detecting the collision of a pair black holes would be a hard act to follow. Yet a year and a half after that announcement, the world was again thrilling to the news of another type of cosmic cataclysm.

We had not been optimistic about detecting colliding black holes because we had very little idea how many pairs of black holes might exist. Instead we had placed our hopes on something we knew much more about: neutron stars.

Neutron stars are one step away from becoming a black hole. Many exist as pulsars: rapidly spinning remnants of supernova explosions that emit powerful flickering beams of radio waves. They have a dimeter of about 20 kilometres, are composed of neutrons, and are denser than an atomic nucleus.

Thousands of them are known in the Milky Way, and the predictions were that out in the distant universe we might be able to detect one or two of them merging every year.

Little did we know that we were already detecting those events.

During the 1980s astronomers were puzzling over vast bursts of gamma rays being detected by orbiting gamma ray telescopes, on average one every day.

In 1989 a paper published in Nature by Hebrew University physicist Tsvi Piran proposed these bursts were created by merging neutron stars, spiralling together at 10% of light speed, and flinging some of their nearly pure neutron matter out into space. Here it would go off like an enormous nuclear fission bomb, giving off bursts of gamma rays. The process would also be a forge for heavy elements in the universe like platinum and gold.

Since the advanced LIGO detectors started working in 2015, our 1000-strong team comprising researchers based at more than 80 universities around the world were hoping for all of this: a long slow chirp of gravitational waves as a pair of neutron stars spiralled together, a burst of gamma rays produced when they collided, and an atomic explosion where we might see the signature of gold production.

Most of us thought the chances of all of this was very small. The gamma ray beam might miss the earth. The explosion, called a macronova or kilonova, is much weaker than a supernova and would be hard to detect.

However, more than 100 telescopes around the world had already signed up to receive alerts from the LIGO detectors on either side of the US, and the European Virgo detector in Pisa, Italy, in the event of a gravitational wave signal.

On August 17, 2017, all of our Christmases came at once.

It was exactly what we had dreamed of. The gravitational wave signal was loud and clear in the two LIGO detectors in the US, but very weak in the European Virgo detector because of its orientation.

The non-detection by Virgo told us roughly where to look in the sky. The Fermi gamma ray observatory out in space detected a burst of gamma rays 1.7 seconds later, coming from the same region of sky. A few hours later the Swope telescope in Chile detected the fading glow of a vast explosion, in that same region, at the edge of a known galaxy, 130 million light years away.

Before long 100 telescopes across the southern hemisphere were watching it. The colours in the light indicated the presence of heavy elements like gold and platinum.

## The future

We called this the birth of multi-messenger astronomy: the gravity wave messenger and the electromagnetic messenger worked in unison. This discovery was a stupendous example of scientific prediction. It confirmed Einstein’s 102 year-old prediction that gravity waves travel at the speed of light, and Piran’s 28 year-old prediction that gamma ray bursts were the signature of colliding neutron stars,  and that gold and platinum were formed in this explosion.

From these recent discoveries we can predict what lies ahead. As sensitivity improves, we’ll  exponentially increase our reach into the universe. Increase the sensitivity by two and you’re reaching into a volume 23 times larger, which means eight times as many signals.

In the next few years the world’s existing three detectors, plus two more under construction in Japan and India, should be tuning in to the sounds of  hundreds of black hole and neutron stars collisions every year.

More detectors will help to pinpoint the source of the signals, but the biggest pay-off comes from increasing sensitivity. Just a four-fold increase in sensitivity would expand our horizon to more than half of the visible universe. A 10-fold improvement would give us the whole universe! Detectors with this capability have been suggested for Australia, China, Europe and the USA.

The legacy of Einstein, the recent Nobel Prize winners and the huge international LIGO and Virgo team, will be the ability to listen to the symphony of the universe. It will be in a minor key because the truth is that our universe is winding down as black holes form, grow and gobble up each other.

But I can’t end on a melancholy note. Rather I want to sing in celebration of gravitational waves as humanity’s new set of ears. We are no longer deaf to the sounds of space. And we can be pretty certain that our cosmic ears will give us deeper understanding of the nature of space.

We are still groping to understand its microstructure and its reason for being. Is it a quantum foam inhabited by strings, or is it something else?

Stay tuned for surprises, unforeseen revelations, and an avalanche of discoveries as our remarkable new technology develops.