Focus of Week 5 The information loss paradox in black holes, an example of scientific controversy

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1 Focus of Week 5 The information loss paradox in black holes, an example of scientific controversy Our Focus of this week 5 allows you to better understand elements of a controversy which has agitated quite a few black hole theorists for the last four decades. Media have at times relayed such debates. Make you own idea and then participate to the Discussion! According to you, is there or isn t there loss of information in black holes? But let us start by presenting the elements of the debate : Stephen Hawking raises the question Information disappears in black holes: if I drop a box of sugar into the horizon of a black hole, all the information contained in this box (the trademark, the number of sugar cubes, their shape, their nature) is in principle lost, for ever. It is at least what one thought until Stephen Hawking discovered the phenomenon called (since then) Hawking radiation: as we have seen in the course, when one takes into account the quantum fluctuations close to the horizon, one deduces that the black hole emits particles, and thus loses energy. Ultimately, it should have lost all its mass energy and thus disappeared. This is the process called black hole evaporation. In a famous article of 1976, entitled «Breakdown of predictability in gravitational collapse», Stephen Hawking asks the following question: if the black hole fully disappears into Hawking radiation, is the information that had vanished into the black holes reappearing? His own answer is no: the spectrum of Hawking radiation is what one qualifies as thermal, which means that its characteristics are such that they depend only on a temperature, and this temperature is determined only by the overall mass of the black hole (this is another illustration of the no- hair theorem: a black hole is only

2 characterized by its mass, charge and spin). Hence Hawking radiation cannot restore the information about the box of sugar: it is lost for ever : When physicists start to bet The conclusion reached by Hawking was not to the liking of everyone. The controversy it generated is well illustrated by the bet that Stephen Hawking and the great specialist of black holes, Kip Thorne, made with another theorist John Preskill. John Preskill was opposing the following. to the conclusion reached by Hawking, himself supported by Thorne, The Hawking radiation phenomenon is related to the quantum creation of particle- antiparticle pairs: one member of the pair disappears inside the black hole, the other remains on our side of the horizon but can no longer find its match to disappear again into the vacuum. But even in this situation, the two remain highly correlated. In the language of quantum mechanics, they are said to be entangled. It is therefore contrary to the laws of quantum mechanics that information disappears: the particles that form the Hawking radiation outside the black hole remains entangled with the particles that disappeared inside. In 2004, S. Hawking admitted that he had lost the bet. The calculations he had just made led him to think that the horizon fluctuated and let information seep through. He offered Preskill an encyclopedia on baseball, but considering that the information that comes out of a black hole is as useful as that obtained from the ashes of an encyclopedia, he remarked that he could just as easily have offered him the book in ashes. Kip Thorne and other physicists were not convinced by the "surrender" of S. Hawking. The controversy continued.

3 Black hole complementarity Leonard Susskind, a theorist from Stanford, has introduced the notion of complementarity in black holes, according to which no observer sees any violation of the laws of Nature. More precisely, we should not consider black holes from the perspective of an omniscient observer who can see both inside and outside the black hole, but as an observer who is either inside the horizon, or outside of the horizon, or who passes from outside to inside. Susskind proposed several thought experiments that illustrate his point. One of them shows why the quantum principle of no- cloning is observed in black holes. According to this principle, one cannot duplicate, i.e. identically reproduce, a quantum state 1. The rest of this paragraph is a bit complex (although there is still no formula) but it shows you the kind of thought experiments that feed today the reflections of theorists. If it makes your neurons bubble, do not risk a blackout of your nervous system and proceed to the next section. Let us imagine the following experiment (see Figure next page). Alice is inside a vessel that falls freely into the horizon of a black hole. Bob, who does not know Alice, is in a spaceship that is maintained at a distance outside the black hole horizon. Bob then observes Hawking radiation and, if we follow John Preskill who thinks Hawking radiation contains information on what goes on inside of the black hole, Bob is able to decode this information and learn some facts about Alice, for example the colour of her eyes. Some time later, Bob spacecraft falls into the horizon of the black hole: Alice can then send directly to Bob information on the colour of her eyes. If Alice's eyes were quantum (replace "eye colour" with "a quantum property of one atom of Alice s eyes), 1 To understand this principle, arm yourself with a (good) dose of imagination. This principle is directly related with the principle of linearity, which is a pillar of quantum mechanics. According to this principle, if we have two quantum states A and B, we can combine them to obtain a new quantum state, noted A + B. Consider two quantum states, a dog A and a cat B (assumed to be microscopic in order to be of a quantum nature) and assume that we can clone them. Let's start by combining them: it is difficult to imagine a quantum superposition A + B of a dog and a cat, say a being which has sometimes the head of a dog, sometimes the head of a cat. Now we clone this strange being: sometimes we see two dog heads, sometimes two cat heads, other times a dog s head and a cat's head. Or let s do the opposite: we clone separately dogs and cats, then superimpose the two cloned dogs and two cloned cats. We get another weird being but one which is likely to be different from the previous one because the heads are necessarily two dogs or two cats! This means that the quantum cloning is incompatible with the sacrosanct principle of linearity. We have proved by contradiction that quantum cloning is not possible.

4 there is thus duplication, or cloning, of the information on a quantum property, which is prohibited by the laws of Nature. Isn t there a contradiction? Well actually, the second message will never reach Bob. The reason is as follows. Once Bob has entered the horizon of the black hole, he will quickly fall to the central singularity. Alice must then hurry up to sends the "quantum" information about her eyes. But, in quantum physics, information is carried out by quanta, and time and energy are connected: the shorter the emission time is, the larger the energy of the emitted quantum. The calculation shows that, for the quantum message to reach Bob in time, the message must be carried by a quantum of energy higher than the total mass of the black hole. It is obviously impossible! In other words, regardless of how she does it, Alice cannot send a quantum message to Bob fast enough for him to receive it before being crushed into the central singularity of the black hole. The laws of Nature are safe: there will be no duplication of quantum information. I gave you detail reasoning to show, in this example, how arguments based on gravity (the black hole and the presence of a horizon) and quantum mechanics (the flow of information and related laws ) combine to reach the conclusion.

5 Maldacena conjecture In 1997, an important theoretical breakthrough, due to the Argentinian theorist Juan Maldacena, came reinforce the idea that no information is lost in black holes. Maldacena discovered a correspondence between theories with gravity and theories without gravity in a space one less dimension. This result, technically called "AdS / CFT correspondence" is actually just a guess, but it has been verified in a number of cases, particularly in the context of string theory. One often refers to holography when speaking of Maldacena s conjecture: a 3- dimensional gravity theory is described by a theory without gravity in 2 dimensions, just as the reality of our 3- dimensional space is represented by a hologram that is a surface in 2 dimensions. All this should not surprise you: remember that, for a black hole, it is as if the information entered into the black hole was stored on the surface of its horizon. This means in particular that, in the case of universes where the correspondence conjectured by Maldacena is exact, one can mathematically describe the black hole and the space- time around it with a non- gravitational theory, that is to say, a quantum theory. Information should thus be conserved.

6 The firewall Everything seemed almost said when in 2012 Joseph Polchinski and colleagues (Ahmed Almheiri Donald Marolf and James Sully) emphasized that making a number of assumptions "reasonable", it could be shown that conservation of information is inconsistent with one of the basic principles of general relativity: the equivalence principle which says that an observer in free fall does not see gravitational effect. The solution they propose is radical. Recall that, as we have seen in the course, in the context of classical general relativity an astronaut in free fall through the horizon is observed nothing special. According to Polchinski and his colleagues, when we take into account quantum effects, the astronaut will encounter energy fluctuations which become increasingly large as he get closer to the horizon (to distances of the order of the Planck length). In other words, he faces a firewall that will burn him to death. This means in particular that we must then give up the equivalence principle of general relativity, at least in the vicinity of the horizon of the black hole. This sparked a lively discussion, particularly to see whether the assumptions made were as "reasonable" as it seemed, and if one should not reject some of them, rather than discard the principle of equivalence. Latest developments Most recently in February 2016, Stephen Hawking, Andy Strominger and Malcolm Perry proposed a new solution to the problem: the proliferation of vacuums. They use soft gravitons, that is to say, zero energy gravitons. Recall that the quantum vacuum is the lowest energy state. If I add a soft graviton, I do not change the energy of this state, so I get another vacuum. And so on... So we have a multiplicity of vacuums with different configurations (typically the number of soft gravitons). Each different configuration can be regarded as information. This would be where the information buried into the black hole is hiding... The multiplicity of solutions shows that we have not yet obtained the definitive solution. It is likely that the latter will only appear once we have solved the problem of reconciling the theory of gravity with quantum mechanics. But conversely, we can say that understanding black holes and what happens near the horizon will lead us to identify the characteristics of the theory that will unify the whole. And that's why these questions fascinate theorists. Here you are closer to science in motion, and, in addition, to some of the most fundamental issuse in physics. If your neurons have not failed you, you may now turn to the Discussion!