A black hole is a region of space so dense that nothing, not even light, can move quickly enough to escape. At least that was the thinking until the 1970s, when Stephen Hawking calculated that black holes aren’t completely black after all. Instead, Hawking argued, they slowly give off radiation – now known as Hawking radiation – that eventually means the black hole will evaporate.
Hawking’s calculations created a problem. Quantum theory says information can never vanish, so what happens to the information that has fallen into the black hole? Where does it go? This is the black hole information paradox. It has troubled physicists for decades because it highlights the profound disconnect between general relativity, Albert Einstein’s theory of gravity from which black holes were summoned, and the laws of quantum theory that govern the subatomic realm.
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Now, we seem to be on the cusp of a resolution to this, with huge consequences for how we understand the cosmos at its most fundamental. All of which is the subject of a forthcoming book called Black Holes: The key to understanding the universe by and , both particle physicists at the University of Manchester, UK.
New Scientist spoke to them about the latest thinking on the black hole information paradox, what it reveals about where space-time comes from and why the deep structure of the universe looks surprisingly similar to a quantum computer.
Abigail Beall: When most people think of black holes, they probably think of big things in space like collapsing stars and huge forces of gravity. Why are black holes important to particle physicists?
Jeff Forshaw: Black holes are places where quantum physics and general relativity are both relevant and yet we can’t describe, in a consistent way, what happens when black holes evaporate. So, something has got to give. Either quantum mechanics or general relativity is wrong.
Brian Cox: A key point, as well, is that this clash between quantum mechanics and general relativity happens in the vicinity of the event horizon of a black hole, the boundary beyond which light cannot escape. It’s been known for a long time that you would need quantum gravity to explain what happens at a singularity, the point deep inside a black hole where the curvature of space-time becomes so ludicrously extreme and gravity so strong that the equations of general relativity break down. Everything you calculate just goes to infinity.
The real treasure here, though, is that the clash comes in a region where you can’t just throw your hands up and say “it’s something to do with the singularity, so just forget about it”. It’s a region where gravity is not ludicrously strong, so we don’t expect to need quantum gravity.
When he first highlighted this clash, Hawking went against quantum theory by suggesting that radiation escapes from a black hole and that the information it carries disappears. What do we mean by information here?
JF: Imagine everything that falls into a black hole. You could describe it with a long binary sequence of ones and zeros, or bits. And if you’ve got an algorithm that decodes that, it’ll tell you what fell in. The information is the smallest binary string of bits that is sufficient to completely tell you about the thing that fell in, whether it’s a book or a bunch of quantum bits or, you know, a star collapsing.
BC: This is determinism, which is central to physics. If you know everything about a system at one point, then you can predict what it’s going to do in the future and what it was doing in the past.
So what happens to the information when radiation escapes a black hole?
BC: If information is preserved, then, in principle, you could collect all the Hawking radiation and process it in some way. You could wind time back to reconstruct what kind of star collapsed to form the black hole, for example. But that did not appear to be the case because, in Hawking’s original calculation, there is no information in the radiation at all.
JF: The Hawking calculation said that there’s no algorithm that could possibly extract any message from that radiation. That was Hawking’s original calculation – that information is obliterated in a black hole, which violates a key property of quantum mechanics – that information is conserved, and suggests that quantum theory is wrong.
But not everyone agreed with Hawking. What happened?
JF: The theorists Gerard ‘t Hooft and Leonard Susskind said: “Well, let’s suppose that the information does come out and quantum mechanics is good.” Then you’ve got a real problem. The information is coming out from the black hole, but things fall through the horizon of a black hole into the singularity. There’s no mechanism to get anything from the singularity back out again.
What they realised is that, from the point of view of somebody always outside of the black hole, nothing ever actually falls through the horizon. Everything freezes on it, in the sense that it stops. Actually, it’s a very hot membrane and anything that falls on it kind of evaporates off.
If I throw a book into a black hole, from my external perspective, it gets obliterated and burned up and spread all over the horizon of the black hole, then comes back out as Hawking radiation. The book’s kind of burned up on the horizon. But from the point of view of the book, it just falls through the horizon. We could be falling through the horizon of a black hole now, it’s a totally benign experience.
So does the book fall in or does it stay on the horizon?
JF: What ‘t Hooft and Susskind said is that, actually, both happen. This is what is called black hole complementarity. It’s the idea that information simultaneously gets reflected off the black hole and falls smoothly through that horizon.
BC: They’re two perfectly legitimate views of the same thing. Now, modern calculations are showing that this picture is largely correct. Both are legitimate views. Immediately, you can see that challenges our notion of what reality is. How can something have two apparently different fates?
So what actually happens to the information, and what does that tell us about reality?
JF: The first thing you might think would be that the information gets copied on the horizon, so there are two versions. But again, that’s not allowed in quantum mechanics. That pushed ‘t Hooft and Susskind into this idea of holography. They supposed that the information in any region of space is encoded on the boundary of that region of space. Key to this is quantum entanglement, a very non-intuitive connection that can be created between two or more particles. If you cut out a little chunk of space, then the entanglement with the rest of the universe would be sufficient to completely encode for what’s happening inside that region.
Later, Juan Maldacena at the Institute for Advanced Study in Princeton discovered that a particular region of space-time has a completely equivalent description on the boundary of that space-time in terms of a quantum field theory, which describes the movements of subatomic particles. Think of it like the surface of a ball that encodes for general relativity in the interior. In one description of what’s happening, there is no interior space, it is just the surface. That is also an explicit demonstration of the ideas that ‘t Hooft and Susskind brought forward with complementarity. You’ve got the interior space being encoded on the boundary, rather like the information inside of a black hole being encoded on its horizon.
All of which suggests space-time is emergent, but what is it emerging from, exactly, and how?
JF: It’s become clear over the past decade that entanglement is a key feature. Basically, think of the surface of the ball as lots of entangled particles. For every entangled link, think of a little quantum wormhole. There’s a correspondence between entanglement and wormholes – it is as if many-particle entanglement can be thought of in terms of a network of wormholes that weave space-time.
BC: We’re discovering a deeper structure, which doesn’t have space and time in it. And you might say: “Which one is the real description, then? Is it the thing on the boundary or the space inside?” As far as I’m aware, nobody really gets into that discussion. These are equivalent descriptions of the physics.
Who are we to say which is a deeper picture? It’s tempting to do so because it is true that if you look at the temperature of a box full of gas, then you can say that emerges from a description of atoms. I think you would be correct to say the temperature, pressure and entropy – or measure of disorder – of a box of gas has got a deeper description, in terms of moving parts. It becomes philosophical quite quickly. But one super-cool thing is how all this relates to quantum computing, a completely different field, superficially.
How does it relate to quantum computing then?
BC: Quantum computers are made up of qubits, which can exist in not just a state of zero or one, but a mix of the two. These days, one of the big challenges in quantum computing is to store information in a physically robust way because qubits are very delicate things. The answer is to build a network of interconnected qubits in such a way that that network is robust against damage to the fragile quantum states of some of the interconnected qubits.
JF: This network of qubits is a quantum error-correcting code. Now, we are learning that it looks like space is built in much the same way – like a giant quantum computer. If you take some chunk of space-time, the entanglement between that region and the rest of the universe is enough to encode the interior of the region. And that seems to be true for every bit of space everywhere. You can destroy qubits on the boundary and you still don’t destroy the information in the interior. It’s a really clever way of encoding information that’s robust, and one that nature seems to have alighted on.
What does this mean for reality as we know it?
JF: We picture ourselves as being local. Our experience of the world is that we deal with local objects interacting locally with each other. But it appears that there is an equivalent description, which is highly non-local. That already shatters your perception of what you think you are, right?
Space is not fundamental, it is emergent. All that really exists is information. Space and time emerge from a bunch of entangled quantum units that have logical relationships with each other. These units, we’re not quite sure what they are, they could be like qubits or something, but they interact with each other quantum mechanically. And the result of that is the universe we live in.
BC: We really do seem to be saying that space and time emerge from something deeper, which is absolutely fundamental.
