«In my previous lecture I left you on a cliffhanger: a paradox about the nature of black holes, the incredibly dense objects created by the collapse ...»
Transcript of Stephen Hawking’s second Reith lecture
Lecture broadcast on 02.02.2016
With annotations by BBC Science Editor David Shukman
Stephen Hawking, the "world's most famous scientist" is giving this year's BBC Reith Lectures. As a
guide for the "interested but perplexed", I have added a few notes (in italics below) to the transcript
of Prof Hawking's second lecture, in the same way I did last week.
In my previous lecture I left you on a cliffhanger: a paradox about the nature of black holes, the incredibly dense objects created by the collapse of stars. One theory suggested that black holes with identical qualities could be formed from an infinite number of different types of stars. Another suggested that the number could be finite. This is a problem of information, that is the idea that every particle and every force in the universe contains information, an implicit answer to a yes-no question.
Because black holes have no hair, as the scientist John Wheeler put it, one can't tell from the outside what is inside a black hole, apart from its mass, electric charge, and rotation.
This means that a black hole contains a lot of information that is hidden from the outside world. If the amount of hidden information inside a black hole depends on the size of the hole, one would expect from general principles that the black hole would have a temperature, and would glow like a piece of hot metal. But that was impossible, because as everyone knew, nothing could get out of a black hole. Or so it was thought.
This problem remained until early in 1974, when I was investigating what the behaviour of matter in the vicinity of a black hole would be, according to quantum mechanics.
DS: Quantum mechanics is the science of the extremely small and it seeks to explain the behaviour of the tiniest particles. These do not act according to the laws that govern the movements of much bigger objects like planets, laws that were first framed by Isaac Newton. Using the science of the very small to study the very large was one of Stephen Hawking’s pioneering achievements.
To my great surprise I found that the black hole seemed to emit particles at a steady rate.
Like everyone else at that time, I accepted the dictum that a black hole could not emit anything. I therefore put quite a lot of effort into trying to get rid of this embarrassing effect.
But the more I thought about it, the more it refused to go away, so that in the end I had to accept it. What finally convinced me it was a real physical process was that the outgoing particles have a spectrum that is precisely thermal. My calculations predicted that a black hole creates and emits particles and radiation, just as if it were an ordinary hot body, with a temperature that is proportional to the surface gravity, and inversely proportional to the mass.
DS: These calculations were the first to show that a black hole need not be a one-way street to a dead end. No surprise, the emissions suggested by the theory became known as Hawking Radiation.
Since that time, the mathematical evidence that black holes emit thermal radiation has been confirmed by a number of other people with various different approaches. One way to understand the emission is as follows. Quantum mechanics implies that the whole of space is pairs of virtual and anti particles, filled with pairs of virtual particles and antiparticles, that are constantly materializing in pairs, separating, and then coming together again, and annihilating each other.
DS: This concept hinges on the idea that a vacuum is never totally empty. According to the uncertainty principle of quantum mechanics, there is always the chance that particles may come into existence, however briefly. And this would always involve pairs of particles, with opposite characteristics, appearing and disappearing.
These particles are called virtual because unlike real particles they cannot be observed directly with a particle detector. Their indirect effects can nonetheless be measured, and their existence has been confirmed by a small shift, called the Lamb shift, which they produce in the spectrum energy of light from excited hydrogen atoms. Now in the presence of a black hole, one member of a pair of virtual particles may fall into the hole, leaving the other member without a partner with which to annihilate. The forsaken particle or antiparticle may fall into the black hole after its partner, but it may also escape to infinity, where it appears to be radiation emitted by the black hole.
DS: The key here is that the formation and disappearance of these particles normally passes unnoticed. But if the process happens right on the edge of a black hole, one of the pair may get dragged in while the other is not. The particle that escapes would then look as if it’s being spat out by the black hole.
A black hole of the mass of the sun, would leak particles at such a slow rate, it would be impossible to detect. However, there could be much smaller mini black holes with the mass of say, a mountain. A mountain-sized black hole would give off x-rays and gamma rays, at a rate of about ten million megawatts, enough to power the world's electricity supply. It wouldn't be easy however, to harness a mini black hole. You couldn't keep it in a power station, because it would drop through the floor and end up at the centre of the Earth. If we had such a black hole, about the only way to keep hold of it would be to have it in orbit around the Earth.
People have searched for mini black holes of this mass, but have so far not found any. This is a pity, because if they had I would have got a Nobel Prize. Another possibility, however, is that we might be able to create micro black holes in the extra dimensions of space time.
DS: By ‘extra dimensions’, he means something beyond the three dimensions that we are all familiar with in our everyday lives, plus the fourth dimension of time. The idea arose as part of an effort to explain why gravity is so much weaker than other forces such as magnetism – maybe it’s also having to operate in parallel dimensions.
According to some theories, the universe we experience is just a four dimensional surface in a ten or eleven dimensional space. The movie Interstellar gives some idea of what this is like. We wouldn't see these extra dimensions because light wouldn't propagate through them but only through the four dimensions of our universe. Gravity, however, would affect the extra dimensions and would be much stronger than in our universe. This would make it much easier to form a little black hole in the extra dimensions. It might be possible to observe this at the LHC, the Large Hadron Collider, at CERN in Switzerland. This consists of a circular tunnel, 27 kilometres long. Two beams of particles travel round this tunnel in opposite directions, and are made to collide. Some of the collisions might create micro black holes. These would radiate particles in a pattern that would be easy to recognize. So I might get a Nobel Prize after all.
DS: The Nobel Prize in Physics is awarded when a theory is “tested by time” which in practice means confirmation by hard evidence. For example, Peter Higgs was among scientists who, back in the 1960s, suggested the existence of a particle that would give other particles their mass. Nearly 50 years later, two different detectors at the Large Hadron Collider spotted signs of what had become known as the Higgs Boson. It was a triumph of science and engineering, of clever theory and hard-won evidence. And Peter Higgs and Francois Englert, a Belgian scientist, were jointly awarded the prize. No physical proof has yet been found of Hawking Radiation.
As particles escape from a black hole, the hole will lose mass, and shrink. This will increase the rate of emission of particles. Eventually, the black hole will lose all its mass, and disappear. What then happens to all the particles and unlucky astronauts that fell into the black hole? They can't just re-emerge when the black hole disappears. It appears that the information about what fell in is lost, apart from the total amount of mass, and the amount of rotation. But if information is lost, this raises a serious problem that strikes at the heart of our understanding of science.
For more than 200 years, we have believed in scientific determinism, that is, that the laws of science determine the evolution of the universe. This was formulated by Pierre-Simon Laplace, who said that if we know the state of the universe at one time, the laws of science will determine it at all future and past times. Napoleon is said to have asked Laplace how God fitted into this picture. Laplace replied, “Sire, I have not needed that hypothesis.” I don't think that Laplace was claiming that God didn't exist. It is just that he doesn't intervene to break the laws of science. That must be the position of every scientist. A scientific law is not a scientific law if it only holds when some supernatural being decides to let things run and not intervene.
In Laplace's determinism, one needed to know the positions and speeds of all particles at one time, in order to predict the future. But there's the uncertainty relationship, discovered by Walter Heisenberg in 1923, which lies at the heart of quantum mechanics.
This holds that the more accurately you know the positions of particles, the less accurately you can know their speeds, and vice versa. In other words, you can't know both the positions and the speeds accurately. How then can you predict the future accurately? The answer is that although one can't predict the positions and speeds separately, one can predict what is called the quantum state. This is something from which both positions and speeds can be calculated to a certain degree of accuracy. We would still expect the universe to be deterministic, in the sense that if we knew the quantum state of the universe at one time, the laws of science should enable us to predict it at any other time.
DS: What began as an explanation of what happens at an event horizon has deepened into an exploration of some of the most important philosophies in science - from the clockwork world of Newton to the laws of Laplace to the uncertainties of Heisenberg – and where they are challenged by the mystery of black holes. Essentially, information entering a black hole should be destroyed, according to Einstein’s Theory of General Relativity while quantum theory says it cannot be broken down, and this remains an unresolved question.
If information were lost in black holes, we wouldn't be able to predict the future, because a black hole could emit any collection of particles. It could emit a working television set, or a leather-bound volume of the complete works of Shakespeare, though the chance of such exotic emissions is very low. It might seem that it wouldn't matter very much if we couldn't predict what comes out of black holes. There aren't any black holes near us. But it is a matter of principle. If determinism, the predictability of the universe, breaks down with black holes, it could break down in other situations. Even worse, if determinism breaks down, we can't be sure of our past history either. The history books and our memories could just be illusions. It is the past that tells us who we are. Without it, we lose our identity.
It was therefore very important to determine whether information really was lost in black holes, or whether in principle, it could be recovered. Many scientists felt that information should not be lost, but no one could suggest a mechanism by which it could be preserved.
The arguments went on for years. Finally, I found what I think is the answer. It depends on the idea of Richard Feynman, that there isn't a single history, but many different possible histories, each with their own probability. In this case, there are two kinds of history. In one, there is a black hole, into which particles can fall, but in the other kind there is no black hole.
The point is that from the outside, one can't be certain whether there is a black hole or not.
So there is always a chance that there isn't a black hole. This possibility is enough to preserve the information, but the information is not returned in a very useful form. It is like burning an encyclopaedia. Information is not lost if you keep all the smoke and ashes, but it is difficult to read. The scientist Kip Thorne and I had a bet with another physicist, John Preskill, that information would be lost in black holes. When I discovered how information could be preserved, I conceded the bet. I gave John Preskill an encyclopaedia. Maybe I should have just given him the ashes.
DS: In theory, and with a purely deterministic view of the universe, you could burn an encyclopaedia and then reconstitute it if you knew the characteristics and position of every atom making up every molecule of ink in every letter and kept track of them all at all times.
Currently I'm working with my Cambridge colleague Malcolm Perry and Andrew Strominger from Harvard on a new theory based on a mathematical idea called supertranslations to explain the mechanism by which information is returned out of the black hole. The information is encoded on the horizon of the black hole. Watch this space.
DS: Since the Reith Lectures were recorded, Prof Hawking and his colleagues have published a paper which makes a mathematical case that information can be stored in the event horizon. The theory hinges on information being transformed into a two-dimensional hologram in a process known as supertranslations. The paper, titled Soft Hair on Black Holes, offers a highly revealing glimpse into the esoteric language of this field http://arxiv.org/pdf/1601.00921v1.pdf and the challenge that scientists face in trying to explain it.
What does this tell us about whether it is possible to fall in a black hole, and come out in another universe? The existence of alternative histories with black holes suggests this might be possible. The hole would need to be large, and if it was rotating, it might have a passage to another universe. But you couldn't come back to our universe. So although I'm keen on space flight, I'm not going to try that.
DS: If black holes are rotating, then their heart may not consist of a singularity in the sense of an infinitely dense point. Instead, there may be a singularity in the form of a ring. And that leads to speculation about the possibility of not only falling into a black hole but also travelling through one.