Cosmic amnesia

Listen to this essay 20 minute listen It is 9 am on a warm July Sunday in Cambridge, as I head towards a café in the city centre. The bells of Great St Mary’s church play the familiar melody of the Cambridge Quarters. The sound, now often associated with the chimes of Big Ben in London, was first composed here in 1793. The quarters, named for the melody at each quarter-hour, are an immediately recognisable reminder of the passage of time. Each bell produces a note: a wave with a characteristic frequency that travels through the air and reaches our ears. A hammer strikes the bell, and it oscillates, pushing air molecules back and forth. Those jostling molecules reach our ears and we hear a musical note. Then the bell settles, gives up its energy, and returns to silence. My research here at the University of Cambridge often brings me back to the ringing of a bell. I don’t study the physics of sound, but I do focus on a remarkably similar process, taking place throughout the Universe. I am interested in another object that also rings: a black hole. As I sit down with a coffee, I open my laptop to a wavy signal that gradually fades to a flat line. Two black holes have finished merging – a frenzied process of coalescence – leaving an extremely brief wiggle originating from the remnant black hole. Much like the struck bell, this leftover black hole is ringing in a process called ringdown, and it’s consistent across every merger I investigate. Ringdown allows physicists to test their theories of gravity: did Albert Einstein really have the last word? Just as an off-sounding note from a bell might indicate a design flaw, a discrepancy in the frequencies of a ringing black hole could be the first crack in our understanding of gravity. That’s the scientific rationale for studying ringdown, but what fascinates me equally is what happens next. After the black hole rings, it settles into silence. In that moment, lasting only a few milliseconds, the power and intensity of the merger are lost. From the exterior, almost all of that history suddenly becomes inaccessible, and what is left is featureless. The black hole settles into a simple, peaceful object of pure spacetime, with no trace of the violence that just happened. In some respects, the black holes forget. It seems counterintuitive that something so chaotically created can become so simple. Why do black holes seem to forget their violent histories? These strange objects, scattered throughout the Universe, are unlike anything else we know, yet their forgetfulness does not belong to them alone. Just like their ringing, the underlying physics also governs our world. The same ideas connect black holes and our own journey through time, washing away our histories and resulting in loss. The physics is called entropy. And its central lesson is that, when we zoom out, it is not just black holes that forget, but the world around us too. Much of today’s excitement around black holes concerns their perplexing quantum behaviour. However, I want to tell you about an older, classical understanding of black holes that is strange enough. It traces back to the First World War, when Karl Schwarzschild – a German astronomer serving on the Russian front – uncovered a solution to Einstein’s equations for gravity. His solution described the simplest type of black hole that can exist. Its defining feature is a spherical one-way surface called the event horizon. Things can pass beyond it into the black hole, but they can never leave again, no matter how fast they move or how forcefully they try. That means we can never see what happens beyond this point. However, sometimes objects approaching this boundary can perturb the black hole enough for us to detect it. In 1957, Tullio Regge and John Wheeler wondered what would happen if Schwarzschild’s perfect black hole was disturbed: struck, like a bell, by something falling in. This was 10 years before Wheeler even popularised the term black hole, and almost 60 years before we heard a real one ring. Regge and Wheeler wanted to know whether such an object could survive in a Universe full of stuff. Of course, we now know it can. Regge and Wheeler reached the same conclusion: black holes are stable against small disturbances. But, like a bell, these disturbances set them oscillating for a brief time at predictable frequencies. This is the ringdown. In this way, black holes follow the same rules that govern our seemingly more ordinary world, with its clanging church bells. Yet, whereas a bell sends sound waves through the air, a black hole sends ripples through spacetime itself, called gravitational waves. Some of these waves fall into the black hole, becoming trapped inside the event horizon. Others escape far away, travelling through space at the speed of light. Eventually, some reach Earth, and we detect them. An entire planet like Earth might once have fallen in, and the black hole would show no trace The first gravitational waves we caught arrived at our planet in September 2015, and were detected by the two LIGO instruments, one at Hanford, Washington, and the other at Livingston, Louisiana. Their origin was two black holes colliding and merging, a cataclysmic event 1.3 billion light years away. The black holes had become locked in an inspiral, captured by each other’s gravity, ultimately coalescing into one. For a period of a few milliseconds, the remnant rang, before settling into silence. The result of such a collision is a perfectly smooth, though squashed, spheroid. It carries some rotation from the merging black holes that formed it, causing it to bulge out at the equator. In that sense, it is slightly more complicated than Schwarzschild’s black hole that Regge and Wheeler had originally studied. It is called a Kerr black hole after Roy Kerr who found the solution that describes it. Nevertheless, such black holes are still remarkably simple. From the outside, we can only ever know two intrinsic things about them: how heavy they are, and how fast they spin. (There is also a third quantity, electric charge. However, nature tends to neutralise this as quickly as it appears, so we can safely ignore it.) This feature – that all black holes, no matter their history, can be completely described by mass, spin, charge and nothing more – is called the no-hair theorem, a phrase attributed to Wheeler. Why? From the outside, black holes lack any other distinctive features or ‘hair’ that make them different from each other. That is a departure from our usual experience of things. When I look at my coffee as the bells chime in Cambridge, there is a lot I can say. I can tell you about the mug it is in, its temperature, how strong it is, what kind of milk was used, and so on. The mug gives away a lot of information about its history and its current condition. If I chip the mug’s handle, or dilute the coffee, that information doesn’t go anywhere. The mug keeps a record of things that happen to it. The ringdown allows us to work out the size of the resulting black hole as it’s related to its mass and spin A black hole has an equally, if not far more, complicated history. Yet it reveals almost none of this. It doesn’t matter what kind of star formed it, whether it had planets, or life, or whether it merged once, twice or a hundred times. An entire planet like Earth might once have fallen in, and the black hole would show no trace. Why should this be true? While the analogy of the ringing bell is powerful when describing the ringdown, and close to the underlying physics, it takes us only so far. Ultimately, the no-hair theorem, and the deeper loss that accompanies it, can be explained only by the unique properties of a black hole itself. To see this, let’s return to the moment just after a black hole merger. While some mass is lost as gravitational waves during such a collision, the resulting black hole is always larger. More specifically, the event horizon’s surface area can only ever remain constant or increase. That matters more than it seems. This fact was established long before we had detected a real-life merger, though it is now a prediction that can be tested with gravitational waves. The ringdown allows us to work out the size of the resulting black hole because it is related to its mass and spin. These observations are consistent with the prediction that the newborn entity is indeed larger. As early as the 1970s, this characteristic of black holes attracted the attention of physicists. It introduced an undeniable irreversibility into black hole evolution. The areas of black holes are always increasing, never getting smaller. Black holes were hinting at something: another link between our world and theirs. This link is a quantity called entropy. To see this connection, let’s forget about black holes for a moment and return to Earth. We need to understand what entropy is and how it connects to irreversibility. This link may seem distant at first. But I want to show you how a simple thought experiment takes us from the microscopic world, back to the sizes of black holes, then to the no-hair theorem, and eventually to what black holes forget. Imagine an empty room. Of course, it is not completely empty. Inside are billions of air molecules jostling around, crashing into each other, moving from place to place, in a way that would require an impossible amount of patience, and time, to properly quantify. Thankfully, we don’t ever think about the positions and speeds of individual air molecules. Instead, we think about the sum total of their behaviour. These are quantities like the temperature of the room, or the pressure. For example, we know that temperature is, deep down at the microscopic level, just the motion of air molecules crashing into our skin. At this level, there is no such thing as temperature in the usual sense. It is simply a collection of molecules moving around, imparting energy on the molecules in our body. It is only when we zoom out that we treat the collective behaviour of the molecules as a single quantity. Let’s say we now spray perfume by the entrance to the room. At first, to anyone occupying the space, the location of the perfume is clear. It is localised around the doorway. But over time, the perfume droplets mix with the air molecules until the scent becomes a uniform presence across the room. There will be some point in the future, after the perfume has been sprayed, when there is no more perfume by the door than there is anywhere else in the room. We don’t see particles, we merely sense the bigger picture, like the temperature of the room, or the sound of the bell It might seem obvious that perfume should diffuse in this way. But when we dig deeper, it is strange. It tells us about the passage of time. Perfume always diffuses across the room. It never seems to return to a single corner, or linger by the doorway indefinitely. There is a clear direction; a characteristic that differentiates an earlier time from a later one. The reason is that perfume droplets, like the air molecules, can go anywhere. At any instant, there is a huge number of arrangements they might take. But the overwhelming majority of those arrangements – a molecule here, a droplet there – correspond to perfume spread evenly throughout the room. Only a vanishing few represent it in remaining close to the door. So, while nothing forbids the perfume from gathering back by the bottle, the odds against it are vast. If you were willing to wait an extraordinarily long time (far, far longer than the age of the Universe) you might just witness the perfume returning to the bottle. But I would advise against it. We do not see particles, we merely sense the bigger picture, like the temperature of the room, or the sound of the bell. What we observe is the smell of the perfume, irreversibly moving from a single location to the entirety of the room. This is an example of increasing entropy. We often associate entropy with disorder. I sometimes think about it as how little we know. When the perfume starts by the doorway, we can point to that corner and say ‘The perfume was sprayed here.’ Later, that is no longer possible. The knowledge is lost among the motions of trillions of jostling air molecules. We see only the macroscopic state of the room. From this perspective, the room forgets. This is entropy increasing, and many physicists think this sets a direction through time. While the microscopic laws of physics work the same way backward or forward in time, probability dictates that isolated systems always move from lower to higher entropy. What is true here is also true everywhere: in a room with perfume, or the Universe as a whole. This brings us back to black holes. Wheeler’s student Jacob Bekenstein knew that entropy should always increase, but identified a puzzle. If you take a hot gas cloud full of entropy – molecules in disordered motion, like the perfume – and drop it into a black hole, its entropy appears to simply vanish. What was chaotic becomes simple. That seemed to be a violation of a fundamental law: the entropy of the Universe decreasing. However, Bekenstein realised that a black hole’s area always increases, just like entropy. He concluded that there must be a relationship between entropy and black hole size. So, perhaps black holes are not so simple after all. If black holes are related to entropy, then they must be related to the room I just described. And if Bekenstein’s picture is true, it suggests there must be a world we cannot see, beyond the event horizon, that is filled with abstract states, like the positions of air molecules in the room. The particular nature of these states – how they are arranged, where they are located, and what they are – is still debated. Their microscopic nature demands a quantum theory. Yet, whatever their ultimate nature, they leave us ignorant. The countless possible histories of the black hole become lost. The collapse of a star, the infall of matter, a cataclysmic merger; these details do not survive the final exterior description of the black hole. This was Bekenstein’s understanding of the no-hair theorem: black holes become simple because entropy takes away something we once knew. For our room, we lost the origins of the perfume. For the black hole, we lose everything except the mass and spin. From our vantage point, the black hole forgets. This might trouble you. Is the information really lost, or is it merely inaccessible due to practical limitations? Perhaps the distinction means nothing. After all, what difference is a limitation you cannot overcome to a fundamental rule? But the answer is subtle, and it is here that the black hole and our room part company. Let’s say, for a moment, that we grant ourselves a God’s eye view of the room. We give ourselves full knowledge of the positions and speeds of the particles. The French polymath Pierre-Simon Laplace had a similar idea in his A Philosophical Essay on Probabilities (1814), where he talks about an ‘intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings who compose it.’ In other words, someone who knows everything that can possibly be known about the physical world. Returning to the room, we take stock of every air and perfume molecule. We know their trajectories with perfect precision. With this information we rewind the clock, using the laws of physics to trace the trajectory of each droplet of perfume back to where it originally started. Like pressing rewind on a video, we watch as the air molecules move from place to place. When we do this, the laws of physics run just the same. It would be easy to convince ourselves that the air molecules are moving forwards through time. Yet the droplets betray this illusion. While once spread throughout the room, they gradually converge on a single location: the bottle in the doorway from which they came. At this level, the Universe runs equally well in both directions. We could not accomplish this kind of reversal in practice, of course. Nature does not make it easy. But no law forbids it. We can almost hold on to a memory. Things become hazier over time, but they are never wholly gone. We are unremittingly ignorant of the black hole’s creation. The past becomes inaccessible. The black hole forgets For black holes, the story is different. The event horizon separates a black hole from everything else in the Universe: both figuratively and literally. The event horizon means a black hole is a one-way trip. If you were to venture into the black hole with all-knowing eyes, perhaps you would be able to rewind the clock and see what happened in its past. (Though perhaps not; nobody knows.) Yet in either case, you wouldn’t be able to tell anyone, which for most purposes is the same thing as not finding out. You and your messages would get dragged deeper into the black hole and become scrambled into its long history. On the other hand, from outside the event horizon, we are unable to access the states of the black hole. We never have the opportunity to zoom in and retrace its history like we did with the room. Instead, all we see is the bigger picture, with the details shrouded behind the event horizon. The result of countless microscopic states clustered together to give a few numbers, like the temperature of the room, or the smell of perfume. Except, for the black hole, these are its mass and spin. This is the no-hair theorem twice over. First in the same sense as the room: zoom out, and the fine details wash into a handful of numbers, the history buried among a mass of indeterminate possibilities. But the black hole adds something new. The big picture is the only view we are ever allowed to have. The details disappear behind the event horizon. We therefore remain unremittingly ignorant of the black hole’s creation. The past becomes inaccessible. The black hole forgets. Though, perhaps forgetting is too simple. In our room, the past gets washed away. It may not be permanent, but thermodynamics makes it expensive to recover. And we do not live in this world of particles. We are never Laplace’s intelligence with a God’s-eye view (and why would we want to be?) Instead, we hear chimes, we notice the smell of perfume, we feel the warmth of a room, not the collisions of incomprehensibly many air molecules. We are given these transient experiences as the Universe drifts towards a vast, featureless expanse. This is the compromise nature offers us: something beautiful that must eventually be lost. Black holes are no different. They sing away their history, moving from chaos to silence. They forget nearly everything in the same way that everything eventually does. It is just that they can never reveal anything more. Through the horizon they may still hold something of their lives, albeit in a form impossibly hard to recover. You could call it memory. Perhaps the only way to reach it is to fall in and become part of the history yourself. Again, I’d advise against it. As the clock passes 10 am in the Cambridge café, the bells ring again, before coming to an end. The sound is quickly gone, with only the faint hum of the street below remaining. I sit with my now-cold coffee as I become aware of the hour that has passed since I arrived. This is the world we briefly experience: time marches forward and entropy increases. You must have loss to have existence. Somewhere out there, a black hole rings into silence, too. Space, time and the air around me forget, as will I. Still, I am glad that I am there to hear it.