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  • Arpan Dey

Has The Black Hole Information Paradox Been Solved?

Updated: Dec 27, 2022

You must have heard of this famous paradox in physics: the information paradox (more precisely, the black hole information paradox). To start with, what is the significance of the information paradox? Well, this paradox arises out of the "combination" of general relativity and quantum mechanics – the two pillars of modern physics. Further research on the information paradox might reveal the link between these two theories and might lead to a theory of everything – a single theoretical framework that can explain all possible interactions in this universe. The information paradox is a fundamental paradox in physics. And recently (not so recently), there has been some excitement in the physics community because of some new insights into the paradox. Indeed, recent research indicates that radically new physics might not be necessary to resolve the paradox, however, at the same time it must be emphasized that the paradox has not yet been resolved completely.

What's this paradox, anyway? I will assume you know that particle-antiparticle pairs can pop up in vacuum. However, they must soon annihilate each other to not violate the law of conservation of energy. Now consider that a particle A and its antipartner B emerge near the event horizon in such a manner that A falls inside a black hole, while B remains outside the black hole. Now, before the particles have a chance to annihilate each other, A is sucked in by the black hole. But then, who annihilates B? Who accounts for the energy of B? Doesn’t that violate the law of conservation of energy? Hawking concluded that the black hole contributes part of its own energy. The black hole emits a radiation: the Hawking radiation. And after a very long amount of time, the black hole evaporates away completely.

Now, information. In some sense, information helps us tell things apart. On the other hand, black holes suck in things and crush them into the singularity. Or in other words, the difference between a pen and a pencil, as they fall into a black hole, is lost in the sense that inside a black hole, we have no means to differentiate a pen and a pencil. As far as we know, there is no way to retrieve information from a black hole. If you fall through a black hole, your existence is simply "deleted." This means that the information associated with you is lost. (In fact, over time, when every star in our universe will either become a black hole, or be sucked into one (and all planets will be destroyed), if the information associated with objects that fall into black holes is indeed lost, all the information associated with this universe will be deleted entirely.) But what exactly is paradoxical about all these? Well, information can’t be destroyed. This is a fundamental law. The information associated with a particle can’t be destroyed. Every object in the universe is composed of particles with unique quantum properties. And no matter how much we try to destroy these objects, the quantum information related to them can never be entirely deleted. In theory, it is even possible to recreate the object. (Like in quantum teleportation, you can, in theory, transfer all the quantum information about an object to a different place, where it can be reassembled.) But we can't retrieve information from a black hole. However, the information must be present somewhere. Oh well, maybe we can’t perceive this information. But it exists inside the black hole alright. After all, no one has ever been inside a black hole. But once we learn that even black holes are not permanent, they radiate energy, the possibility of the information resting peacefully in there gets ruled out, too. And as far as we know, the Hawking radiation contains no information about the objects that fell into the black hole. So where does the information go? This is the information paradox.

The information paradox might be a result of our misunderstanding of how general relativity and quantum field theory interact. Many proposals have been made to resolve the paradox. Perhaps black holes pass on the information to baby universes, which store the information. (It has been speculated that black hole singularities might give rise to new baby universes, which are hidden from us by the black hole's event horizon.) Or maybe, the information is contained in the Hawking radiation in such a manner that we can’t perceive it.

Now, since we are discussing the information paradox, I can't resist talking about a very important and relevant principle: the holographic principle. The only thing I will assume is that you have some idea about entropy. Jacob Bekenstein proposed that black holes must have some entropy. If a black hole sucks everything inside, the surrounding entropy definitely decreases. But the total entropy must increase. Bekenstein, from this, concluded that the black hole has some entropy which increases as it sucks in matter. You may ask what property of the black hole gives rise to this entropy. Well, string theory provides an answer to that, but we won't discuss it here. Anyway, so maybe the event horizon of the black hole contains this entropy, and so the information. Gerard ’tHooft demonstrated that particles falling into black holes cause gravitational deformation and "bumps" on the event horizon. This can contain the information of the particle. So essentially, the black hole can be treated as a hologram. This is because the information of the three dimensional object falling into the black hole is stored on a two dimensional surface: the event horizon. Similarly, the universe can also be considered to be a hologram. Thus, we can consider gravity as nothing but a projection of quantum mechanics in a higher dimension. The interesting idea explaining all these is the holographic principle (first proposed by Juan Maldacena). Holography can explain and link two entirely different kinds of theories in physics. Holographic duality is also referred to as AdS/CFT correspondence, where AdS refers to Anti de-Sitter spaces (AdS are spaces with negative curvature), while CFT refers to Conformal Field Theory. All this is technical, but the concept is really simple. Imagine a sphere. CFT is related to the boundary, while the AdS space sits inside the sphere. Everything in the AdS space has a counterpart in the CFT boundary. It is crucial to understand that a hologram is two dimensional, but it can contain all the information about all three dimensions of the object it represents. Think of it like this. A three dimensional universe contains black holes and strings (see this) governed solely by gravity, whereas the two dimensional boundary of this three dimensional universe contains ordinary particles governed solely by standard quantum field theory. This means it is possible to relate gravity to a quantum field theory which has no gravity, and this may prove to be of great help when trying to reconcile general relativity and quantum field theory. The AdS/CFT correspondence can somewhat resolve the black hole information paradox. The information is contained in the two dimensional event horizon of the black hole.

And finally, what was the recent excitement about? According to classical physics, black holes are simple objects. According to recent research, however, black holes are more complex than we originally thought. The "lost" information is present in the gravitational field of the black hole at the quantum level (quantum hair). Objects falling into a black hole will leave a mark in its gravitational field, and the information is not lost. Black holes of the same mass and same radius, but which sucked in different objects, will have very slight differences in their gravitational fields. The information, thus, is preserved. But this only shows that it is possible to retrieve some of the apparently-lost information. This still does not solve the problem of reconciling general relativity with quantum mechanics. And we need to reconcile them because physics can't be different at different scales. So, I would say it is too early to claim that the information paradox has been solved. However, there have been some great insights into the subject, and I urge you to explore these ideas on the Internet.

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