The Magicians

by Marcus Chown

  It is perfectly possible that the pair of black holes had been orbiting each other for billions of years, all the while radiating gravitational waves, which sapped them of orbital energy, causing them to gradually spiral together. But it was only during the final ten or so orbits, each lasting about a hundredth of a second, that the convulsions of space–time were violent enough to create gravitational waves strong enough to be detectable on Earth.

  Although the tenth-of-a-second-long pulse had been travelling for 1.3 billion years, it would have been missed had Advanced LIGO been turned on a month later. It seems that the collaboration was extraordinarily lucky. But physicists do not believe in luck. The fact that LIGO caught its quarry so soon after the instrument was turned on can mean only that black hole mergers are common. And this has proved to be the case.

  Since the first black hole merger, eight more have been detected. Most significant was the detection on 17 August 2017 of a much weaker and longer-duration pulse of gravitational waves from a merger of two ‘neutron stars’. Such stars, also spawned by supernova explosions, are formed when the core of a star is not massive enough for its gravity to crush it all the way down to a black hole. Typically, a neutron star is about the size of Mount Everest and so dense that a sugar-cube-sized volume of its material would weigh as much as the entire human race.

  The crucial difference between a neutron star and a black hole is that it is not simply a bottomless pit in space–time but an object made of actual ‘stuff’. Whereas a black hole merger produces nothing but gravitational waves – all matter in the vicinity having long ago been vacuumed up by each hole – a neutron star merger generates not only gravitational waves but a fireball of blisteringly hot matter. The radiation from the fireball was observed in the days after 17 August 2017 by about seventy ground-based and space-based telescopes, sensitive to different types of light. Most significant of all was the detection of an intense flash of high-energy gamma rays. This solved several cosmic mysteries in one go.9

  In the late 1960s, the Americans launched satellites into orbit to detect the gamma rays from clandestine Soviet nuclear tests. To their shock and surprise, they discovered that around once a day there was a flash of gamma rays coming not up from the ground but down from space. The discovery of ‘gamma-ray bursters’ was not revealed to the astronomical community until the 1980s, and it was not until the 1990s that it became clear that they were at immense distances. It was then suggested that the most common type might be the result of a merger between two neutron stars. This theory was dramatically confirmed with the discovery of a gamma ray burst from the gravitational wave source detected on 17 August 2017.

  But the gamma rays also revealed something else. The cores, or ‘nuclei’, of different atoms produce gamma rays at discrete energies, which provide a unique fingerprint for each kind of atom. And what gamma-ray astronomers saw was the sudden appearance of the fingerprint of gold; forged in the fireball was a mass of gold equal to about twenty times the mass of the Earth.

  Astronomers have long known that all the elements heavier than hydrogen and helium were forged in the nuclear furnaces of stars, which, when they exploded, spewed them into space to be incorporated into successive generations of stars. But although nuclear astrophysicists had successfully identified the origin of pretty much all the ninety-two naturally occurring elements, they did not know the origin of gold. Now, at last, they do. Can there be a more striking connection between the mundane and close to home and the cosmic and far away? If you have a gold ring or necklace, its atoms were forged long before the Earth was born, in a fireball caused by the cataclysmic coalescence of two neutron stars.

  The LIGO–Virgo team had predicted that 2017 would be the year its detector would reach the sensitivity to pick up a signal from the first neutron star merger, and it was proved to be correct. However, what the team failed to realise was that there existed a class of black hole mergers out there that was much more powerful and which they would easily spot with a less sensitive detector as early as 2015.

  All the discoveries had been made with an extraordinary instrument. Although each LIGO site boasted a four-kilometre ruler made of a laser of light whose stretching and squeezing revealed a passing gravitational wave, in fact each site possessed two identical rulers, arranged in the shape of an ‘L’. These were the arms of an ‘interferometer’, so called because it exploits the phenomenon of ‘interference’ to measure tiny changes in the paths taken by light.

  When two waves – which could be waves of light, water or anything else – overlap, and the peaks of one coincide with the peaks of the second, they boost each other, in a process known as constructive interference. When the peaks of the first wave coincide with the troughs of the second, they cancel each other out, in a process known as destructive interference.

  At each LIGO site, laser light is split in two, and half is sent down the evacuated tube of one arm of the interferometer and the other half down the other one. At the end of each arm, a suspended mirror reflects the light back the way it has come. The two halves are then combined and the brightness of the light measured. The key thing is that if one of the arms has been stretched relative to the other, the two light waves will not exactly match. If the peaks of one wave coincide with the troughs of the other, they will cancel each other out and the brightness measured will be zero. In fact, if the two light waves are even slightly out of step with each other, they will create an obvious change in the brightness of the light on recombination. In this way, it is possible to discern changes in the length of one arm relative to the other of a mere fraction of the ‘wavelength’ of the laser light – that is, a fraction of a thousandth of a millimetre.

  Although measuring such a small change in the length of a four-kilometre-long arm may seem impressive, the detection of the gravitational waves on 14 September 2015 required measuring a hugely smaller change. Each arm was alternately stretched and squeezed not by a fraction of a thousandth of a millimetre but by a hundred-millionth of the diameter of a single atom. When you realise that it takes ten million atoms laid end to end to span the full stop at the end of this sentence, you will begin to appreciate the astonishing achievement of detecting gravitational waves.§ ‘The signals are infinitesimal. The sources are astronomical. The sensitivities are infinitesimal. The rewards are astronomical,’ writes Janna Levin in Black Hole Blues.10

  Given the scale of the achievement, it was no accident that the 2017 Nobel Prize in Physics was awarded for the discovery of gravitational waves. The three founding fathers of LIGO were considered to be Weiss, Thorne and a Scottish experimental physicist. Ronald Drever had Alzheimer’s disease and was in a care home near Glasgow.11 Sadly, he died only months before the awarding of the Nobel Prize, and Weiss and Thorne instead shared the prize with Barry Barish.

  The aim now is not only to improve the sensitivity of the LIGO detectors but to bring online more detectors around the world, to better locate the source of any burst of gravitational waves. The European Virgo instrument became operational soon after Advanced LIGO and participated in some of its discoveries, such as that of the neutron star merger. The Kamioka Gravitational Wave Detector (KAGRA) in Japan is set to join the network in 2020, and one in India will join by 2025.

  The merger of neutron stars and black holes did not surprise the LIGO and Virgo experimenters, who had hoped to detect them. But what is most exciting about the gravitational wave ‘window’ they have opened up on the universe is the possibility of seeing things nobody expects and of being utterly surprised. ‘The discoveries, made by our thousand-strong international team, are just the start,’ says Sheila Rowan, LIGO physicist and Scientific Advisor to the Scottish Government. ‘There should be lots more amazing stories to come.’

  We can learn a lesson from light. Once upon a time, we knew only about the light we could see with our eyes. Then we discovered that this is merely a tiny fraction of the ‘electromagnetic spectrum’ and that in addition to the colours of the rainbow, th
ere are a million other ‘invisible colours’. When we learnt to look at the universe with artificial eyes that could see such colours – gamma rays, X-rays, ultraviolet, infrared, radio waves, and so on – we discovered all kinds of unexpected things. We discovered gamma-ray bursters and ‘pulsars’. We discovered ‘quasars’ and supermassive black holes. We discovered the relic ‘afterglow’ of the Big Bang fireball and planets around other stars – more than four thousand of them at the last count.

  Now, with the success of LIGO and Virgo, we stand at the dawn of a new era in astronomy. ‘We know about black holes and neutron stars, but we hope there are other phenomena we can see because of the gravitational waves they emit,’ says Weiss.

  It is as if we have been deaf and have now gained a sense of hearing, but at present our hearing is crude and rudimentary. At the very edge of audibility, we have heard a sound like a distant rumble of thunder, but we have yet to hear the equivalent of birdsong, of a baby crying or of a piece of music. As LIGO and Virgo and other gravitational wave experiments around the world increase their sensitivity, who knows what wonderful things we will discover as we tune into the cosmic symphony?

  Notes

  1 Indirect evidence of the existence of gravitational waves was actually discovered in 1975. It came from the ‘binary pulsar’, PSR B1913+16, a system in which two super-compact ‘neutron stars’ are spiralling together. Careful observations by Russell Hulse and Joseph Taylor revealed that the stars lose orbital energy at exactly the rate expected if they are radiating gravitational waves. For their discovery, the two American astronomers won the 1993 Nobel Prize in Physics.

  2 To be precise, the gravitational force between an electron orbiting a proton in an atom of the lightest element, hydrogen, is about 1040 times weaker than the electromagnetic force between the particles.

  3 ‘On Gravitational Waves’ by Albert Einstein and Nathan Rosen (Journal of the Franklin Institute, vol. 223, issue 1, January 1937, p. 43).

  4 I am conflating things here, but the story of Einstein asking to use a bulldozer is true. A family friend, Loretta Donato, tells of her uncle working on a building site in Princeton. ‘For several days a little old man was sitting on a bench watching my uncle work,’ says Donato. ‘One day the old man asked my uncle if he would show him how to use the bulldozer, and my uncle agreed. The little old man was Einstein … My uncle taught Einstein how to use a bulldozer. But the family joke is that my uncle taught Einstein at Princeton!’

  5 ‘Einstein Versus the Physical Review’ by Daniel Kennefick (Physics Today, vol. 58, issue 9, 2005, p. 43: https://doi.org/10.1063/1.2117822).

  6 ‘Observation of Gravitational Waves from a Binary Black Hole Merger’ by B. P. Abbott et al., LIGO Scientific Collaboration and Virgo Collaboration (Physical Review Letters, vol. 116, 11 February 2016, p. 061102).

  7 The gravitational signal from the merger of two black holes would have been impossible to predict had it not been for a breakthrough made by South African–Canadian physicist Frans Pretorius in 2005. Although exact ‘solutions’ to Einstein’s equations of gravity are notoriously difficult to obtain, Pretorius defied the odds and found one for two black holes in orbit about each other (‘Evolution of Binary Black Hole Spacetimes’ by Frans Pretorius (Physical Review Letters, vol. 95, 14 September 2005, p. 121101: https://arxiv.org/pdf/gr-qc/0507014.pdf)).

  8 Gravity can shrink an interstellar cloud of gas and dust to form a compact star if the cloud can shed its internal heat, since the force of hot gas pushing outwards stymies gravity. This happens when molecules radiate energy in the form of far-infrared light, which is able to escape a gas cloud. However, molecules consist of heavy atoms such as carbon and oxygen, which have been built up from hydrogen inside stars since the Big Bang 13.82 billion years ago. In the beginning, there were no such molecules; consequently, bigger masses with bigger gravity were required to overcome the internal heat of gas clouds and spawn stars. This is why the first-generation stars would have been giants by today’s standards.

  9 The gamma rays, after travelling 130 million light years across space from the elliptical galaxy NGC 4993, arrived just 1.7 seconds after the burst of gravitational waves. From this, physicists deduced that the speed of gravitational waves is within one part in a million billion of the speed of light (‘GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral’ by B. P. Abbott et al. (Physical Review Letters, vol. 119, 16 October 2017, p. 161,101)).

  10 Black Hole Blues: And Other Songs from Outer Space by Janna Levin (The Bodley Head, London, 2016).

  11 The Ascent of Gravity: The Quest to Understand the Force that Explains Everything by Marcus Chown (Weidenfeld & Nicolson, London, 2017).

  * A ‘field’ is simply something that has a value at every point in space. That may be a number, as in the case of air, where each point possesses a number of a certain magnitude to represent the pressure. Or it could be a ‘vector’, as in the case of a magnetic field, where each point possesses a number representing the magnitude of the force and an arrow representing its direction. Think of it as a field of arrows.

  † The location of a town might be specified as thirty kilometres north of London and thirty kilometres east of London, or it could be specified as 42.4 kilometres in a northeast direction. Both are examples of ‘coordinate systems’.

  ‡ The irony is that Einstein did not believe in another prediction of his theory of gravity: black holes. Being the most compact possible objects, they can whirl around each other in much closer proximity than stars, creating much greater distortions of space–time and radiating far more intense gravitational waves.

  § Einstein predicted the laser. How astonishing, then, that a prediction of Einstein’s (gravitational waves) that confirmed another prediction of Einstein’s (black holes) was confirmed by an instrument that used yet another prediction of Einstein’s (the laser)!

  10

  The poetry of logical ideas

  The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.

  EUGENE WIGNER

  Pure mathematics is, in its way, the poetry of logical ideas.

  ALBERT EINSTEIN

  The stories I have recounted have, I hope, illustrated the central magic of science – its ability to predict the existence of things that, when people go and look for them, turn out to exist in the real world. It is an ability that is so magical that even the exponents of science can scarcely believe it. As mentioned before, the question of why it is so hard for physicists to believe the predictions of their own theories was pondered by Steven Weinberg in his book, The First Three Minutes.1 What puzzled him about the birth of the universe was why the prediction of the afterglow of the Big Bang in 1948 had been ignored and the cosmic background radiation stumbled upon by accident only in 1965. ‘The problem is not that we take our theories too seriously,’ he concluded, ‘but that we do not take them seriously enough.’

  It is easy to see why physicists find it so hard to believe their theories. After all, how is it possible that arcane mathematical formulae scrawled across blackboards or whiteboards can have anything whatsoever to do with real things in the real world? How can it be that the universe out there has a mathematical twin down here, which mimics it in every conceivable way?

  This remarkable fact was apparent even to Galileo in the seventeenth century: ‘Philosophy is written in the grand book – I mean the universe – which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles and other geometric figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering about in the dark labyrinth.’2

  Isaac Newton, who was born in the year Galileo died, was successful in expressing the laws of motion an
d of gravity as precise mathematical formulae. And in the years that followed, mathematics scored more and more successes in describing ever greater tracts of physical reality. In the nineteenth century, this success was exemplified by the triumph of Maxwell’s equations of electromagnetism, and in the twentieth century by the equations of quantum theory and Einstein’s theory of gravity – the general theory of relativity.

  Undoubtedly, however, the most powerful demonstration of the deep connection between mathematics and the physical universe was the Dirac equation. Despite the fact that his triumphant description of the electron, compatible with both quantum theory and Einstein’s special theory of relativity, was conjured out of thin air purely for mathematical consistency, it nevertheless predicted the existence not only of quantum spin but of a hitherto unsuspected universe of antimatter. Dirac, as amazed as everyone else, concluded, ‘God used beautiful mathematics in creating the world.’3