Black Holes: The Key to Understanding the Universe

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A Brief History of Black Holes

‘A knowledge of the existence of something we cannot penetrate, of the manifestations of the profoundest reason and the most radiant beauty – it is this knowledge and this emotion that constitute the truly religious attitude; in this sense, and in this alone, I am a deeply religious man.’

Albert Einstein

At the heart of the Milky Way, there is a distortion in the fabric of the Universe caused by something 4 million times more massive than our Sun. Space and time are so warped in its vicinity that light rays are trapped if they venture closer than 12 million kilometres. The region of no return is bounded by an event horizon, so named because the Universe outside is forever isolated from anything that happens within. Or so we used to think when the name was coined. We have named it Sagittarius A* and it is a supermassive black hole.*

Black holes lie where the most massive stars used to shine, at the centres of galaxies and at the edge of our current understanding. They are naturally occurring objects, inevitable creations of gravity if too much matter collapses into a small enough space. And yet, although our laws of Nature predict them, they fail to fully describe them. Physicists spend their careers looking for problems, conducting experiments in search of anything that cannot be explained by the known laws. The wonderful thing about the increasing number of black holes we have discovered dotted across the sky is that each one is an experiment conducted by Nature that we cannot explain. This means we are missing something deep.

The modern study of black holes begins with Einstein’s General Theory of Relativity, published in 1915. This century-old theory of gravity leads to two startling predictions: ‘First, that the fate of massive stars is to collapse behind an event horizon to form a “black hole” which will contain a singularity; and secondly, that there is a singularity in our past which constitutes, in some sense, a beginning to the universe.’ This remarkable sentence appears on the first page of a seminal textbook on general relativity, The Large Scale Structure of Space-Time, written in 1973 by Stephen Hawking and George Ellis.1 It introduces evocative terms – black hole, singularity, event horizon – which have become part of popular culture. It also says that at the end of their lives, the most massive stars in the Universe are compelled by gravity to collapse. The star vanishes, leaving an imprint in the fabric of the Universe. But behind a horizon, something remains. A singularity, a moment rather than a place when our knowledge of the laws of Nature breaks down. According to general relativity, the singularity lies at the end of time. There is also a singularity in our past, which marks the beginning of time: the Big Bang. We are asked to accept the profound idea that our scientific description of gravity, the familiar force that governs the behaviour of cannon balls and moons, is at its heart concerned with the nature of space and time.

It’s not obvious that gravity should be related to space and time, let alone that seeking to describe it in a scientific theory might lead one to contemplate the beginning and end of time. Black holes take centre stage in exploring this deep relationship because they are gravity’s most extreme observable creations. They are so intellectually troublesome that well into the 1960s many physicists felt that while black holes are a feature of the mathematics of general relativity, Nature would surely find a way to avoid creating them. Einstein himself wrote a paper in 1939 in which he concluded that black holes ‘do not exist in physical reality’.2 Einstein’s illustrious contemporary Arthur Eddington put it in rather pithier terms: ‘There should be a law of Nature to prevent a star from behaving in this absurd way.’ Well, there isn’t, and they do.

We now understand that black holes are a natural and unavoidable phase in the lives of stars a few times more massive than our Sun, and since there are many millions of such stars in our galaxy, there are many millions of black holes. Stars are large clumps of matter fighting gravitational collapse. In the early stage of their lives, they resist the inward pull of their own gravity by converting hydrogen into helium in their cores. This process, known as nuclear fusion, releases energy which creates a pressure that halts the collapse. Our Sun is currently in this phase, converting 600 million tonnes of hydrogen into helium every second. It’s easy to skim over very large numbers in astronomy, but we should pause and marvel at the terrifying difference in scale between the stars and the objects of everyday human experience. Six hundred million tonnes is the mass of a small mountain, and our Sun has been steadily burning through a mountain’s-worth of hydrogen every second since before the Earth formed. Not to worry; it has enough hydrogen left to continue its tussle with gravity for another 5 billion years. The Sun can do this because it is big; a million earths would fit comfortably inside. It is 1.4 million kilometres in diameter; a passenger jet would have to fly for six months to circumnavigate it. And yet the Sun is a small star. The largest known stars are a thousand times larger, with diameters in the region of a billion kilometres. Placed at the centre of our solar system, such stars would engulf Jupiter. Monsters like these will end their lives in catastrophic gravitational collapse.

Gravity is a weak but inexorable force. It only attracts, and in the absence of any stronger counteracting forces, it attracts without limit. Gravity is trying to pull you through the floor towards the centre of the Earth, and it’s pulling the ground in the same direction. The reason everything doesn’t collapse to a central point is that matter is rigid; it’s built out of particles that obey the laws of quantum physics and repel each other when they approach too closely. But the rigidity of matter is something of an illusion. We fail to perceive that the ground below us is essentially empty space. The dancing electron clouds surrounding atomic nuclei keep atoms apart and fool us into thinking that solid objects are densely packed. The reality is that the atomic nucleus occupies only a tiny fraction of the volume of an atom and that the ground below our feet is as insubstantial as vapour. The repulsive forces inside matter are nevertheless very powerful and they are capable of keeping you from falling through the floor, and of stabilising dying stars up to twice the mass of the Sun. But there is a limit, and that limit is explored by neutron stars.

A typical neutron star has a radius of just a few kilometres and a mass around 1.5 times that of the Sun. A million ‘Earths’ squashed into a region the size of a city. Neutron stars tend to spin very fast, emitting bright beams of radio waves that illuminate the Universe like a lighthouse. The first observation of such a neutron star, known as a pulsar, was made by Jocelyn Bell Burnell and Antony Hewish in 1967. So regular is the pulse, which sweeps over Earth every 1.3373 seconds, that Bell Burnell and Hewish christened it Little Green Men-1. The fastest pulsar yet discovered, known as PSR J1748-2446ad, rotates 716 times every second. Neutron stars are extremely energetic celestial objects. On 27 December 2004, a burst of energy hit the Earth, blinding satellites and expanding our ionosphere. The energy was released by the rearrangement of the magnetic field around a neutron star called SGR 1806-20, which lies 50,000 light years from Earth on the other side of the galaxy. In a fifth of a second the star radiated more energy than our Sun emits in a quarter of a million years.

The gravitational pull at the surface of a neutron star is 100 billion times that of Earth. Anything that falls onto the surface is flattened in an instant and transformed into nucleon soup. If you were to fall onto the surface of a neutron star, the particles that were once a part of your voluminous atoms would be transformed into neutrons and squashed together so tightly that they would be jiggling around at near light speed in an attempt to avoid each other. This jiggling can support a neutron star with a mass of around two solar masses, but no more. Beyond this limit, gravity wins. If a little more mass were poured onto its surface, the city-sized star would collapse to form a spacetime singularity. Georges Lemaître, a Catholic priest and one of the founders of modern cosmology, described the Big Bang singularity at the origin of our Universe as a day without a yesterday. A singularity formed by gravitational collapse is a moment with no tomorrow. What remains outside is a dark imprint of what once shone: a black hole.

Today, we have concrete observational evidence that our Universe is populated by black holes. The images shown in Figure 1.1 were obtained by the Event Horizon Telescope Collaboration, a network of radio telescopes located across the Americas, Europe, the Pacific, Greenland and Antarctica. The left-hand image shows the central supermassive black hole in the galaxy M87, which lies 50 million light years from Earth. As is so often the case in science, this fuzzy image from far away grows increasingly wonderful as you learn more about what you are looking at.

This black hole has a mass 6.5 billion times that of our Sun and lies within the dark central region of the image, known as the shadow. This region is dark because gravity is so strong that light cannot escape, and since nothing can travel faster than light, nothing can escape. Inside the shadow lies the event horizon of M87’s black hole, a sphere in space of diameter 240 times the distance from the Earth to the Sun. It shields the external Universe from the singularity. The bright disk surrounding the shadow is formed mainly by rays of light emitted from gas and dust spiralling around and into the black hole, their paths twisted and forged into a distinctive doughnut shape by the hole’s gravity.

Figure 1.1. Left: The supermassive black hole at the centre of the galaxy M87. Right: Sagittarius A*, the black hole at the centre of our own galaxy. Both as imaged by the Event Horizon Telescope Collaboration. (European Southern Observatory/EHT Collaboration/Science Photo Library)

The right-hand image is the supermassive black hole at the centre of our own galaxy, Sagittarius A*. At a mere 4.31 million solar masses, it is a minnow by comparison. The glowing disk would fit comfortably within the orbit of Mercury. Its presence was first inferred indirectly, by observing the orbits of stars around it. These stars are known as the ‘S Stars’. The star S2 orbits particularly close to the black hole, with a period of just 16.0518 years. The precision is important, because the detailed observations of S2’s orbit were compared with the predictions of general relativity and used to infer the presence of a black hole well before it was photographed. S2 was observed to make its closest approach to Sagittarius A* in 2018, when it passed within just 120 Astronomical Units of the event horizon.† At closest approach, it was travelling at 3 per cent of the speed of light. Reinhard Genzel and Andrea Ghez received the 2020 Nobel Prize for these high-precision observations performed over many years. They were proof that there is a ‘supermassive compact object at the centre of our galaxy’, in the words of the Nobel Prize committee. They shared the prize with Sir Roger Penrose for his mathematical demonstration ‘that black hole formation is a robust prediction of the general theory of relativity’.

We’ve also detected numerous smaller, stellar mass black holes by detecting the ripples in space and time caused when they collide with each other. In September 2015, the LIGO gravitational wave detector registered the ripples in spacetime caused by a collision between two black holes that occurred 1.3 billion light years from Earth. The black holes were 29 and 36 times the mass of the Sun and collided and merged in less than two tenths of a second. During the collision, the peak power output exceeded that of all the stars in the observable Universe by a factor of 50. By the time the ripples reached us, over a billion years later, they shifted the distance measured along LIGO’s 4-kilometre-long laser ruler arms by one thousandth of the diameter of a proton in a fleeting, wiggling pattern that exactly matched the predictions of general relativity. LIGO and its sister detector Virgo have since detected a host of mergers between black holes. The 2017 Nobel Prize in Physics was awarded to Rainer Weiss, Barry Barish and Kip Thorne for their leadership in designing, building and operating LIGO. The known ‘Stellar Graveyard’ of stellar mass black holes and neutron stars at the time of writing is shown in Figure 1.2.

Taken together, these observations, using different telescopes and techniques, demonstrate beyond reasonable doubt that neutron stars and black holes exist. Science fiction becomes science when experimental observations confirm theories, and as our theoretical voyage takes us along ever stranger paths into ever more tangled intellectual terrain, we should keep reminding ourselves that these absurd things are real. They are a part of the natural world, and we should therefore attempt to understand them using the known laws of Nature. If we fail, we have the chance to uncover new laws of Nature, and this has most assuredly turned out to be the case, beyond even the wildest dreams of the early pioneers.

Figure 1.2. The known stellar mass black holes and neutron stars arranged with the smallest mass objects at the bottom. The smallest circles are the neutron stars and the arrows indicate observed collisions and mergers between pairs of black holes or neutron stars. The numbers on the left are solar masses (mass of Sun = 1 solar mass).

Attempting to avoid the absurd

Black holes were first proposed in 1783 by the English rector and scientist John Michell and independently in 1798 by the French mathematician Pierre-Simon Laplace. Michell and Laplace reasoned that, just as a ball thrown upwards is slowed down and pulled back to the ground by the Earth’s gravity, it is conceivable that there exist objects that exert such a strong gravitational pull they could trap light.

An object flung upwards from the surface of the Earth must have a speed in excess of 11 kilometres per second to escape into deep space. This is known as Earth’s escape velocity. The gravitational pull at the Sun’s surface is much stronger, and the escape velocity is correspondingly higher at 620 kilometres per second. At the surface of a neutron star, the escape velocity can approach an appreciable fraction of the speed of light.‡ Laplace calculated that a body with a density comparable to the Earth but with a diameter 250 times larger than the Sun would have a gravitational pull so great that the escape velocity would exceed the speed of light, and therefore ‘the largest bodies in the Universe may thus be invisible by reason of their magnitude’.3 This was a fascinating idea and ahead of its time. Imagine a spherical shell in space touching the surface of one of Laplace’s giant dark stars. The escape velocity from the shell would be the speed of light. Now make the star a little denser. The stellar surface would shrink inwards, but the imaginary shell would remain in place, marking out a boundary in space. If you hovered on the shell, now above the surface of the star, and shone a torch outwards, the light would go nowhere. It would remain forever frozen, unable to escape. This boundary is the event horizon. Inside the shell, the torchlight would be turned around and pulled back onto the star. Only outside of the shell could light escape.

Michell and Laplace imagined these dark stars as huge objects, perhaps because they could not conceive of the alternative. But an object doesn’t have to be big to have a strong gravitational pull at its surface. It can also be very small and very dense; a neutron star, for example. For an object of any mass, one can use Isaac Newton’s laws to calculate the radius of the region of no escape that would form around it if it were compressed sufficiently:

where G is Newton’s gravitational constant, which encodes the strength of gravity, and c is the speed of light. If we crush anything with mass M into a ball smaller than this radius, we will have created a dark star. Putting the mass of the Sun into this equation, we find that the radius is approximately 3 kilometres. For the Earth, it’s just under 1 centimetre. It is difficult to imagine the Earth being crushed to the size of a pebble, which is probably why Michell and Laplace didn’t consider the possibility. Fantastical as they are, however, there would seem to be nothing particularly troublesome or absurd about dark stars, should they exist. They would trap light but, as Laplace pointed out, that would just mean that we wouldn’t be able to see them.

This simple Newtonian argument gives us a feel for the idea of a black hole – gravity can get so strong that light cannot escape – but Newton’s law of gravitation is not applicable when gravity is strong and Einstein’s theory must be used. General relativity also allows for objects whose gravitational pull is so great that light cannot escape, but the consequences are very different and most definitely troublesome and absurd. As in the Newtonian case, if any object is compressed below a certain critical radius, it will trap light. In general relativity this radius is known as the Schwarzschild radius, because it was first calculated in 1915, very shortly after general relativity was published, by the German physicist Karl Schwarzschild. Coincidentally, the expression for the Schwarzschild radius in general relativity is precisely the same as the Newtonian result above. The Schwarzschild radius is the radius of the event horizon of a black hole.

We will learn more about the Schwarzschild radius in Chapter 4, when we have the machinery of general relativity at our disposal, but we can catch a glimpse of some of the absurdities to come. We will learn that black holes affect the flow of time in their vicinity. As an astronaut falls towards a black hole, their time will tick more slowly as measured on clocks far away in space. That’s interesting, but not absurd. The absurd-sounding result is this: according to the far away clocks, time grinds to a halt on the event horizon. As viewed from the outside, nothing is ever seen to fall into a black hole, which means an astronaut falling towards a black hole will remain frozen on the horizon for all eternity. This also applies to the surface of a star collapsing inwards through the horizon to form the black hole. At first sight, it seems the theory of general relativity predicts a nonsense. How can a star collapse through the event horizon to form a black hole if its surface is never seen to cross the horizon? Observations like this troubled Einstein and the early pioneers, and this is only one in a blizzard of apparent paradoxes.

For Einstein, and the majority of physicists until the 1960s, such worries led to the conclusion that Nature would find a way out, and research into black holes was primarily concerned with demonstrating that they could not exist. Perhaps it is not possible to compress a star without limit and thereby generate an event horizon. This doesn’t seem unreasonable, given that a sugar-cube-sized lump of neutron star material would weigh at least 100 million tonnes. Perhaps we don’t fully understand how matter behaves at such extreme densities and pressures.

Stars are large clumps of matter fighting gravitational collapse, and when they run out of nuclear fuel their fate depends on their mass. In 1926, Eddington’s Cambridge colleague R. H. Fowler published an article ‘On Dense Matter’ in which he showed that the newly-discovered quantum theory provided a way for an old collapsing star to avoid forming an event horizon due to an effect known as ‘electron degeneracy pressure’.4 This was the first glimpse of the ‘quantum jiggling’ we referred to earlier in the context of neutron stars. His conclusion appeared to be an unavoidable consequence of two of the cornerstones of quantum theory: Wolfgang Pauli’s Exclusion Principle and Werner Heisenberg’s Uncertainty Principle.

The Exclusion Principle states that particles like electrons cannot occupy the same region of space. If lots of electrons are squashed together by gravitational collapse, they will separate themselves into their own individual tiny volumes inside the star in order to stay away from each other. Heisenberg’s Uncertainty Principle now comes into play. It states that as a particle is confined to a smaller volume, its momentum becomes larger. In other words, if you confine an electron it will jiggle around, and the more you try to confine it, the more it will jiggle. This creates a pressure in much the same way that the heat from nuclear fusion reactions earlier in the star’s life causes its atoms to jiggle and halt the collapse. Unlike the pressure from fusion reactions, however, electron degeneracy pressure requires no energy release to power it. It seemed a star could resist the inward pull of gravity indefinitely.

Astronomers knew of such a star, known as a white dwarf. Sirius B is a faint companion of Sirius, the brightest star in the heavens. Sirius B was known to have a mass close to that of our Sun, but a radius comparable to the Earth. Its density, using the measurements of the time, was estimated to be around 100 kg/cm3, which, as Fowler notes ‘has already given rise to most interesting theoretical considerations’. In his book The Internal Constitution of Stars, Eddington wrote, ‘I think it is generally considered proper to add the conclusion “which is absurd”.’ Modern measurements put the density over ten times higher. Absurd as this exotic planet-sized star appeared, however, Fowler had discovered a mechanism that explained how it could resist gravity. This seems to have offered a great deal of relief to the physicists of the day because it stopped the unthinkable happening. Thanks to Fowler, it appeared that stars end their lives as white dwarfs. Supported by the quantum jiggling of electrons, they will not collapse inside the Schwarzschild radius and an event horizon will not form.

The sense of relief didn’t last long. In 1930, during an 18-day voyage from Madras to work with Eddington and Fowler in Cambridge, a 19-year-old physicist named Subrahmanyan Chandrasekhar decided to calculate just how powerful electron degeneracy pressure could be. Fowler had not placed an upper limit on the mass of a star supported in this way, and it seems most physicists assumed there should be none. But Chandrasekhar realised that electron degeneracy pressure has its limits. Einstein’s theory of relativity says that no matter how confined an electron becomes, the speed of its jiggles cannot exceed the speed of light. Chandrasekhar calculated that the speed limit will be reached for a white dwarf with a mass around 90 per cent that of the Sun.5 A more accurate calculation reveals that the Chandrasekhar limit, as it is now known, is 1.4 times the mass of the Sun. If a collapsing star exceeds this mass, the electrons no longer provide enough pressure to resist the inward pull of gravity because they are moving as fast as they can, and gravitational collapse must continue. Eddington was unimpressed. He felt that Chandrasekhar had incorrectly meshed relativity with the then-new field of quantum mechanics and, when done correctly, the calculation would show that white dwarf stars could exist up to arbitrarily large masses. The subsequent argument between the young Chandrasekhar and the venerable Eddington affected Chandrasekhar deeply. Decades after Eddington’s death in 1944, Chandrasekhar still described this time as ‘a very discouraging experience … to have my work completely discredited by the astronomical community’. Chandrasekhar was ultimately proved correct, and he received the Nobel Prize for his work on the structure of stars in 1983.

Chandrasekhar’s result, published in 1931, was not regarded as definitive evidence that black holes must form. Einstein was still concerned about the apparent freezing of time on the event horizon in 1939. Perhaps there is some other process that can provide support for a collapsing white dwarf when electron degeneracy pressure fails? In the late 1930s, the American physicist Fritz Zwicky and the Russian physicist Lev Landau suggested, correctly, that there may be even denser stars than white dwarfs that are supported not by electron degeneracy pressure but by neutron degeneracy pressure. Under the extreme conditions found in gravitational collapse, electrons can be forced to fuse together with protons to form neutrons and lightweight particles called neutrinos, which escape the star. Neutrons, just like electrons, jiggle around as they are squashed close together, but because they are more massive than electrons, they can provide more support. These objects are neutron stars.

It’s not unreasonable to wonder whether this fate might be the end of the road for all supermassive stars, even though the experience with white dwarfs suggests that neutron degeneracy pressure should also have its limits. Maybe the most massive stars eject material into space as they collapse, or maybe they bounce and explode as they reach neutron star densities. These possibilities were not easily dismissed at the time – nuclear physics was a very new field and the neutron itself was only discovered in 1932.

By 1939, J. Robert Oppenheimer and his student George Volkov, building on work by Richard Tolman, had established what is now called the Tolman–Oppenheimer–Volkov limit, which places an upper limit on the mass of a neutron star at just under three times the mass of the Sun. Oppenheimer and another of his students, Hartland Snyder, subsequently showed that, under certain assumptions, the heaviest stars must collapse behind an event horizon to form a black hole.6 This landmark paper begins: ‘When all thermonuclear sources of energy are exhausted a sufficiently heavy star will collapse. Unless fission due to rotation, the radiation of mass, or the blowing off of mass by radiation, reduce the star’s mass to the order of that of the Sun, this contraction will continue indefinitely.’ The final lines of the introduction detail the consequences for the flow of time at the horizon that so worried Einstein: ‘The total time of collapse for an observer comoving with the stellar matter is finite, and for this idealized case and typical stellar masses, of the order of a day; an external observer sees the star asymptotically shrinking to its gravitational radius.’§ In other words, it takes around a day for a star not very much bigger than the Sun to collapse out of existence from the point of view of someone riding inwards on the surface of the collapsing star, but an eternity for anyone watching from the outside. This is the puzzling behaviour of time we noted previously. Oppenheimer and Snyder accepted this basic result of general relativity and showed that it leads to no contradiction. We will explore these intriguing results in more detail in the following chapters.

At this point, World War II intervened, and the thoughts of the world’s physicists turned to supporting the war effort. In the United States, the expertise in nuclear physics honed by the study of stars was particularly relevant to the development of the atomic bomb, and Oppenheimer famously became the scientific leader of the Manhattan Project. When the war ended and the physicists returned, a new generation was poised to take up the mantle. In the United States, that generation was nurtured by John Archibald Wheeler. It was Wheeler who first coined the term black hole at a lecture in the West Ballroom of the New York Hilton on 29 December 1967. In his autobiography, Wheeler describes his intellectual struggles with black holes throughout the 1950s.7 ‘For some years this idea of collapse to what we now call a black hole went against my grain. I just didn’t like it. I tried my hardest to find a way out, to avoid compulsory implosion of great masses.’ He recounts how he eventually became convinced that ‘nothing can prevent a large-enough chunk of cold matter from collapsing to a dimension smaller than the Schwarzschild radius’. Wheeler’s intellectual conversion culminated in a 1962 paper with his student Robert Fuller in which they conclude that ‘there exist points in spacetime from which light signals can never be received, no matter how long one waits’.8 These are the points inside the event horizon from which the Universe beyond is forever isolated. Black holes, it seems, are unavoidable. Any remaining theoretical concerns were dispelled in 1965 by Sir Roger Penrose’s Nobel Prize-winning paper ‘Gravitational Collapse and Space-Time Singularities’, a three-page tour-de-force in which Penrose proves that, in Wheeler’s words, ‘for just about any description of matter that anyone has imagined, a singularity must sit at the centre of a black hole’.9

A profound glow

Our brief history of black holes brings us to 1974 and a paper by Stephen Hawking, which led to an apparently simple question that has driven black hole research for half a century since its publication.

By the 1970s the existence of black holes was widely accepted by theorists, although they were yet to be sighted by astronomers, and the attention of the small group still interested in them turned to the conceptual challenges they pose. Hawking’s paper, published in the journal Nature, is colourfully titled ‘Black Hole Explosions?’10 Hawking showed that the presence of an event horizon has a dramatic effect on the vacuum of space in its vicinity. Quantum theory tells us that empty space is not empty. It is filled with fields that are constantly fluctuating, and these fluctuations manifest themselves as the potential to create particles: photons, electrons, quarks, any particles, in fact. The vacuum has a structure. In common or garden empty space, these fluctuations come and go; one might picture so-called virtual particles continually popping into and out of existence, but the net result is that no real particles ever appear miraculously out of nothing. The presence of the horizon disrupts this balance, with the result that the fleeting virtual particles can become real. These particles, known as Hawking radiation, stream out into the Universe carrying a tiny fraction of the black hole’s energy with them. Over unimaginable time scales, vastly longer than the current age of the Universe, a typical black hole will evaporate away and, ultimately, explode. Black holes, to use Hawking’s famous phrase, ain’t so black. They glow gently like faint coals in the cold sky. Very faint coals. The temperature of a solar mass black hole is 0.00000006 degrees Celsius above absolute zero, which is far colder than the Universe today.¶ Sagittarius A* is even colder: 4.31 million times colder to be precise. But the temperature of a black hole is not zero, and that matters enormously. It means, as we’ll discover, that black holes obey the laws of thermodynamics – the same laws that govern glowing coals and steam engines and stars – and it means they are not immortal. One day in the far, far future, they will all be gone.

A profound question arises as a result of this faint glow. When the black hole has gone, what has happened to everything that fell in? Because of the unique production mechanism of Hawking radiation, plucked as it is out of the vacuum in the vicinity of the event horizon, the radiation would seem to have nothing to do with whatever has fallen into the black hole during its lifetime. It is very difficult therefore to see how any information about anything that fell in, or indeed the star that collapsed to form the black hole in the first place, could be preserved, imprinted somehow, in the radiation. Indeed, Hawking’s original calculation appeared very clear on this point. The radiation, the remnants of the black hole, contains no information at all.

One of the pioneers of modern black hole research, Leonard Susskind, tells the story of a meeting in a small San Francisco attic room in 1983 at which Hawking first raised this question and answered it, incorrectly as it turns out. Susskind’s first-hand account of the tremendous intellectual struggle Hawking’s question generated is called The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics. Susskind has a way with titles. He once co-authored a paper called ‘Invasion of the Giant Gravitons from Anti-de Sitter Space’. He writes that ‘Stephen claimed that information is lost in black hole evaporation, and worse, he seemed to prove it. If that was true … the foundations of our subject were destroyed.’

Susskind was referring to one of the pillars of modern physics: determinism. If we know everything about a system, be it a simple box of gas or the Universe, we can predict how it will evolve into the future and how it looked in the past. This is an ‘in principle’ statement of course. It’s not possible in practice to know everything about the past and future, because we always have incomplete information about any real physical system. But in science, unlike modern-day politics, principles matter. If Hawking was right, black holes would render the Universe fundamentally unpredictable and the foundations of physics would crumble.

We now know that Stephen Hawking was wrong – information is not destroyed and physics is safe – as Hawking himself came to accept with delight, not regret, not least because the ongoing programme of research stimulated by his original claim continues to propel us towards a new understanding of space and time and the nature of physical reality.

In the last edition of A Brief History of Time, Hawking writes that he eventually changed his mind in 2004 and conceded a bet he’d made with John Preskill (whose work we’ll meet later). After a further argument about the merits of cricket and baseball, which he also lost, Hawking gave Preskill an encyclopaedia of baseball. At the time of writing, Hawking notes, nobody knew how the information gets out of the black hole – just that it does. What was clear, however, is that the information would be very hard to decode. ‘It’s like burning a book,’ he writes. ‘Information is not technically lost, if one keeps the ashes and the smoke – which makes me think again about the baseball encyclopaedia I gave John Preskill. I should perhaps have given him its burnt remains instead.’

Beyond the horizon

Imagine you find a watch lying on the ground. On close inspection you are compelled to marvel at its delicate sophistication and exquisite precision. The mechanism was surely designed; there must have been a creator. Transpose ‘watch’ for ‘Nature’ and this is the argument for God presented by clergyman William Paley in 1802. We now understand that the argument is seriously undermined by the overwhelming evidence in support of Darwin’s theory of evolution by natural selection. The watchmaker is Nature, and it is blind. ‘There is grandeur in this view of life,’ wrote Darwin, ‘with its several powers, having been originally breathed into a few forms or into one; and that, while this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved.’

But what of the fixed law of gravity, a prerequisite for the existence of the planets on which the endless forms evolved? Or the laws of electricity and magnetism which glue the animals together? Or the menagerie of subatomic particles out of which we are made? Who or what laid down the laws; the framework within which everything cycles on?

The story of modern physics has been one of reductionism. We do not need a vast encyclopaedia to understand the inner workings of Nature. Rather, we can describe a near-limitless range of natural phenomena, from the interior of a proton to the creation of galaxies, with apparently unreasonable efficiency using the language of mathematics. In the words of theoretical physicist Eugene Wigner, ‘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. We should be grateful for it.’11 The mathematics of the twentieth century described a Universe populated by a limited number of different types of fundamental particles interacting with each other in an arena known as spacetime according to a collection of rules that can be written down on the back of an envelope. If the Universe was designed, it seemed, the designer was a mathematician.

Today, the study of black holes appears to be edging us in a new direction, towards a language more often used by quantum computer scientists. The language of information. Space and time may be emergent entities that do not exist in the deepest description of Nature. Instead, they are synthesised out of entangled quantum bits of information in a way that resembles a cleverly constructed computer code. If the Universe is designed, it seems, the designer is a programmer.

But we must take care. Like Paley before us, we are in danger of over-reaching. The role of information science in describing black holes may be pointing us towards a novel description of Nature, but this does not imply we were programmed. Rather we might conclude that the language of computing is well suited to describing the algorithmic unfolding of the cosmos. Put in these terms, there is no greater or lesser mystery here than Wigner’s miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics. Information processing – the churning of bits from input to output – is not a construction of computer science, it is a feature of our Universe. Rather than spacetime-as-a-quantum-computer-code pointing to a programmer, we might instead take the view that earth-bound computer scientists have discovered tricks that Nature has already exploited. Viewed in this way, black holes are cosmic Rosetta Stones, allowing us to translate our observations into a new language that affords us a glimpse of the profoundest reason and most radiant beauty.

* Sagittarius A* is pronounced ‘Sagittarius A-star’.

† 1 Astronomical Unit is (approximately) equal to the distance of the Earth from the Sun.

‡ The speed of light is 299,792,458 metres per second.

§ By ‘gravitational radius’ they mean the Schwarzschild radius.

¶ The temperature of the cosmic microwave background radiation today is 2.725 degrees Celsius above absolute zero.