Matematician Hadi Godazgar on the Big Bang, black holes, and the Information Paradox
Hawking radiation is a phenomenon associated with black holes. Black holes are the most extreme objects in nature. To describe black holes, imagine standing on the surface of the Earth and jumping up. So you jump up and then you fall back down because gravity pulls you down to Earth. Imagine you jump even harder, so the speed at which you are jumping is higher. What will happen is that you’ll jump up further, you’ll go higher, but again you’ll fall back to Earth. Now there’s a particular speed called escape velocity and if you jump at that speed you’ll manage to escape Earth’s gravity and go into outer space. This is what rockets do, for example. At that speed, and higher than that speed, you’ll manage to escape the body, in this example, Earth, and go into outer space.
But there is a particular object called the black hole, such that the escape velocity, the velocity, the speed at which you have to jump or to fire your rocket to escape that object, is actually higher than the speed of light. That’s called the black hole. That is why people say that not even light can come out of the black hole. As I said before, black holes are extremely strange objects and hard to imagine, precisely for this reason. To give you an idea of how extreme these objects are, imagine if the Earth was a black hole. What would it look like?
For Earth to be a black hole, you have to take everything on Earth, the whole Earth, and squash it into a ball of approximately one and a half centimeters in diameter. So if you put all of Earth into just this little ball, that would be a black hole.
It is an object so dense that gravity is becoming strong. Or to put it another way, if you want to keep the size of the Earth fixed, for the Earth to be a black hole its mass has to be two thousand times the mass of the Sun. And the reason for that is that the gravity is, again, very strong.
What I’ve said so far is all classical, but we also know that there’s the quantum regime particles at the very microscopic length scales described by quantum physics. The reason why quantum physics should play a role here is that black holes, as I said, are extreme, and they lie in the regime where both gravity and quantum physics are appreciable – we can’t neglect either. There’s strong gravity, but the distances are so small that we expect quantum physics to play some role as well. And this is where Hawking radiation comes in. Hawking radiation is perhaps the most famous example of the interplay between gravity and quantum physics. And this is one reason why black holes are sometimes referred to as laboratories for quantum gravity.
Besides the Big Bang, which gave rise to the universe, black holes are the only objects we have in nature where we can test our ideas on quantum gravity.
So what’s Hawking radiation? Well, imagine you have a black hole, and Hawking radiation is simply the statement that I said before: classically nothing comes out of a black hole, but once you put quantum physics into the picture, in fact, black holes radiate. They give off energy and that’s Hawking radiation. Before I said: “the black hole, nothing can come out of a black hole”, now I’m saying something can come out of a black hole. Where’s the explanation for this Hawking radiation? The explanation is that in quantum physics you have a way of describing what the energy of a particle is, and before the star collapses you have one way of prescription, of defining energy. After the star collapses or forms a black hole, your space has changed. It’s no longer the same space. The star has changed into a black hole, and that means that in the latter picture when you have a black hole what you mean by energy is different to what you meant by the energy of the particle before the black hole formed. And this relation about what you meant by energy before collapse and what you meant by energy after collapse is precisely what gives rise to Hawking radiation. So you can think of this as a particle lying at the center of a seesaw, and in quantum physics this particle will fluctuate, and you can think of black hole formation as the seesaw suddenly being changed into a different shape. Those oscillations of this little particle will change because you’re changing the surrounding space. That’s essentially the explanation of Hawking radiation and where it comes from.
This poses a theoretical question. Things went into the black hole. The black hole radiates, and the only thing we know about this radiation is the temperature, which is just a single number. And we don’t now anything else, and then the black hole disappears. But this poses a problem, and the reason this poses a problem is that things go into the black hole, information goes in, but all we get out is a single number and the mass of the black hole.
So we know the total energy of what went in plus a single number that’s the temperature. And in quantum physics this can’t happen. In quantum physics we should be able to recover the information that went in. This is called Unitarity. And the puzzle associated with this lack of information is called the Information Paradox.
A current area of research is to precisely explain what happens to the information, and there are various proposals recently. One being that interaction of particles is important, and this changes the picture. The simple scenario that I gave is modified by interactions. Another proposal is that there are other charges besides the mass, there are other descriptions of the black hole that play a role. And this is current research regarding Hawking radiation.