So what? In his book The Black Hole War, Leonard Susskind describes the moment in a small seminar room in an attic in San Francisco in 1983 when Hawking first made the claim that information is destroyed by black holes.37 The soon-to-be Nobel Prize winner Gerard ’t Hooft ‘stood glaring’ at the blackboard for an hour after Hawking’s talk. ‘I can still see the intense frown on Gerard’s face and the amused smile on Stephen’s.’ ’t Hooft was glaring because the laws of physics as we currently understand them preserve information. If we know the precise state of something at a given moment in time then, in principle, we can predict precisely what it will do in the future and know what it was doing in the past. This is determinism, the fundamental idea that the Universe evolves in a predictable way. All the known laws of physics deliver deterministic evolution. They take a system, be it a box of gas or star or galaxy, and evolve it uniquely into a single, well-defined configuration at some time in the future. And because things evolve in a unique and predictable way, the laws also allow us to calculate precisely what the system was like at any time in the past.§ But what of a Universe that contains black holes? Galaxies contain supermassive black holes at their cores, and those black holes swallow things. If the black hole subsequently disappears in a puff of information-free Hawking radiation, then it would be impossible in the far future to reconstruct any details about anything that had fallen in. It would in fact be impossible to deduce that the black hole ever existed at all, because it would have erased all trace of itself. This problem has become known as the black hole information paradox.
Figure 11.1 shows a Penrose diagram that illustrates the problem. It is obtained by sewing together two spacetime geometries: the Schwarzschild spacetime corresponding to the period that the black hole exists (Figure 8.3) and flat (Minkowski) spacetime when the black hole has gone. The singularity disappears with the black hole and the wavy line representing the end of time therefore ends before future timelike infinity at the upper tip of the diagram. We have no idea what happens at the rightmost point of the singularity, since this is the event where the black hole disappears and quantum gravity effects are important. But as we’ll see, and contrary to the expectations of many experts in the field until very recently, it turns out that we don’t need to know to solve the information paradox.
The shaded region of the diagram corresponds to times after the evaporation of the black hole, where spacetime is flat and there appears to be no trace of anything that crossed the event horizon. To see this, draw a light ray (a 45-degree line) from any point inside the event horizon and you’ll see that it ends on the singularity. The region behind the horizon remains a prison from which there is no escape because it is causally disconnected from the Universe outside; there is no spacetime directly above the singularity in Figure 11.1. The only thing that survives into the future when the black hole has disappeared is Hawking radiation. We’ve drawn a wiggly arrow to indicate the worldline of the last Hawking particle to be emitted as the black hole vanishes – it heads off happily to future lightlike infinity.
Figure 11.1. Penrose diagram for an evaporating black hole. The singularity disappears after the last Hawking particle (orange). The blue line is the worldline of a book thrown into the hole and in red is another Hawking particle. Both Hawking particles follow their respective dotted worldlines and end up at future lightlike infinity.
According to Hawking, the radiation is featureless and the black hole therefore erases all trace of everything that fell into it. Where did everything go? If the hole did not evaporate, we could at least offer the vague statement that ‘it fell into the singularity and we don’t really understand that place’. But after the hole evaporates, there isn’t any singularity anymore – there is no hiding place.
Black hole complementarity offers an apparently simple resolution to the paradox, at least from the point of view of an outside observer. Since nothing is ever seen to fall through the horizon, nothing is ever lost. Let’s think again about the book we tossed into the black hole, we have drawn its worldline in blue on the figure. From the perspective of the outside observer, according to complementarity, the book is incinerated on the horizon and its ashes are returned to the Universe as Hawking radiation (as illustrated by the red wiggly arrow). This is no different to burning a book on a campfire. If we burn a book, the information contained within can in principle be recovered if we make precise enough measurements of all the ashes and gases and embers that emerge. In practice, this is not possible, but practicality is not a word that concerns theoretical physicists. The point is that it is possible in principle. The information contained in the book got scrambled up during the burning process, but it wasn’t destroyed. We would claim that nothing has disappeared, it has just been converted from words on a page into particles in space. It’s clear from the Penrose diagram that as long as the book burns up before it crosses the horizon, it is possible to draw worldlines that link every atom in the book to future timelike or lightlike infinity.
Contrast this with the view from inside the black hole. The book is spaghettified as it approaches the singularity. Though we don’t know what happens at the singularity, the fact that it lies behind the horizon implies that the book is not able to get back out again. It is destroyed at the end of time inside the horizon. But that is OK because from the external viewpoint information is preserved. The stories in the book are written in the Hawking radiation and will always be there, in principle, for the super-beings of the future to read. If we accept complementarity, both the internal and external viewpoints are true.
What are the consequences for physical reality? We tend to think, based on our experience of the world, that large physical objects like books or astronauts can only be in one place at once and only a single fate can befall them. Quantum theory destroys this picture when we ask questions about the behaviour of sub-atomic particles, and complementarity appears to be an even more radical challenge to our intuition. It asks us to accept that there are two equally valid views of what happens to a big thing like an astronaut – you, for instance – freely falling towards a black hole. You are both spaghettified (inside) and vaporised (outside). This suggests that the relationship between the inside of a black hole and the outside is not the same as the relationship between ‘here’ and ‘over there’ according to our everyday experience. There is also a small but persistent fly in the ointment: Stephen Hawking’s calculation, which says that the Hawking radiation contains no information. In the history of the subject, attacking this sharp, well-defined problem in Hawking’s calculation turned out to be extremely fruitful in the quest to place complementarity on a rigorous footing, because the question is simple and easy to state: if the information is to come out, where did Stephen Hawking go wrong?
* Choosing a large black hole means that tidal effects are small at the horizon.
† Often called the Fulling–Davies–Unruh effect to acknowledge the earlier work in 1973 by Stephen Fulling.
‡ You can see this directly from Hawking’s formula – the temperature of a black hole is inversely proportional to its mass.
§ This is also true for the quantum evolution of the state of a system, even though the outcomes of individual experiments are not determined.
12
The Sound of One Hand Clapping
‘Entanglement is iron to the classical world’s bronze age.’
Michael Nielsen and Isaac Chuang38