Wednesday, July 09, 2008

First, boot up your black hole

Don't ask me why, but I just remembered this article about the work of Leonard Susskind. Decided to blog it in case I wish to locate it again.
The last line is pretty zany:

So the idea of a black hole computer remains controversial

but the rest of the article is simply fascinating.

Stephen Hawking of the University of Cambridge showed theoretically that black holes are not truly black, but emit radiation. In fact they evaporate very slowly, disappearing over many billions of years. This "Hawking radiation" comes from quantum phenomena taking place just outside the event horizon, the gravitational point of no return. But, Hawking asked, if a black hole eventually disappears, what happens to all the stuff inside? It can either leak back into the universe along with the radiation, which would seem to require travelling faster than light to escape the black hole's gravitational death grip, or it can simply blink out of existence.

Trouble is, the laws of physics don't allow either possibility. "We've been forced into a profound paradox that comes from the fact that every conceivable outcome we can imagine from black hole evaporation contradicts some important aspect of physics," says Steve Giddings, a theorist at the University of California, Santa Barbara.

Researchers call this the black hole information paradox. It comes about because losing information about the quantum state of an object falling into a black hole is prohibited, yet any scenario that allows information to escape also seems in violation. Physicists often talk about information rather than matter because information is thought to be more fundamental.

In quantum mechanics, the information that describes the state of a particle can't slip through the cracks of the equations. If it could, it would be a mathematical nightmare. The Schrödinger equation, which describes the evolution of a quantum system in time, would be meaningless because any semblance of continuity from past to future would be shattered and predictions rendered absurd. "All of physics as we know it is conditioned on the fact that information is conserved, even if it's badly scrambled," Susskind says.

Something about the power of abstract mathematical models

In 1997, Maldacena developed a type of string theory in a universe with five large dimensions of space and a contorted space-time geometry. He showed that this theory, which includes gravity, is equivalent to an ordinary quantum field theory, without gravity, living on the four-dimensional boundary of that universe. Everything happening on the boundary is equivalent to everything happening inside: ordinary particles interacting on the surface correspond precisely to strings interacting on the interior.

This is remarkable because the two worlds look so different, yet their information content is identical. The higher-dimensional strings can be thought of as a "holographic" projection of the quantum particles on the surface, similar to the way a laser creates a 3D hologram from the information contained on a 2D surface. Even though Maldacena's universe was very different from ours, the elegance of the theory suggested that our universe might be something of a grand illusion - an enormous cosmic hologram....

The holographic idea had been proposed previously by Susskind, one of the inventors of string theory, and by Gerard't Hooft of the University of Utrecht in the Netherlands. Each had used the fact that the entropy of a black hole, a measure of its information content, was proportional to its surface area rather than its volume. But Maldacena showed explicitly how a holographic universe could work and, crucially, why information could not be lost in a black hole.

According to his theory, a black hole, like everything else, has an alter ego living on the boundary of the universe. Black hole evaporation, it turns out, corresponds to quantum particles interacting on this boundary. Since no information loss can occur in a swarm of ordinary quantum particles, there can be no mysterious information loss in a black hole either. "The boundary theory respects the rules of quantum mechanics," says Maldacena. "It keeps track of all the information."

And what this means to a mahout and elephant who happen to fall into a black hole

Let's say Alice is watching a black hole from a safe distance, and she sees an elephant foolishly headed straight into gravity's grip. As she continues to watch, she will see it get closer and closer to the event horizon, slowing down because of the time-stretching effects of gravity in general relativity. However, she will never see it cross the horizon. Instead she sees it stop just short, where sadly Dumbo is thermalised by Hawking radiation and reduced to a pile of ashes streaming back out. From Alice's point of view, the elephant's information is contained in those ashes...

There is a twist to the story. Little did Alice realise that her friend Bob was riding on the elephant's back as it plunged toward the black hole. When Bob crosses the event horizon, though, he doesn't even notice, thanks to relativity. The horizon is not a brick wall in space. It is simply the point beyond which an observer outside the black hole can't see light escaping. To Bob, who is in free fall, it looks like any other place in the universe; even the pull of gravity won't be noticeable for perhaps millions of years. Eventually as he nears the singularity, where the curvature of space-time runs amok, gravity will overpower Bob, and he and his elephant will be torn apart. Until then, he too sees information conserved.

Susskind argues that both stories are right, which takes relativity to a new level

The elephant is both inside and outside the black hole; the answer depends on who you ask. "What we've discovered is that you cannot speak of what is behind the horizon and what is in front of the horizon," Susskind says. "Quantum mechanics always involves replacing 'and' with 'or'. Light is waves or light is particles, depending on the experiment you do. An electron has a position or it has a momentum, depending on what you measure. The same is happening with black holes. Either we describe the stuff that fell into the horizon in terms of things behind the horizon, or we describe it in terms of the Hawking radiation that comes out."

Wait a minute, you might think. Maybe there are two copies of the information. Maybe when the elephant hits the horizon, a copy is made, and one version comes out as radiation while the other travels into the black hole. However, a fundamental law called the no-cloning theorem precludes that possibility. If you could duplicate information, you could circumvent the uncertainty principle, something nature forbids. As Susskind puts it, "There cannot be a quantum Xerox machine." So the same elephant must be in two places at once: alive inside the horizon and dead in a heap of radiating ashes outside.

What's more, this new type of "non-locality" is not just for black holes. It occurs anywhere a boundary separates regions of the universe that can't communicate with each other. Such horizons are more common than you might think. Anything that accelerates - the Earth, the solar system, the Milky Way - creates a horizon. Even if you're out running, there are regions of space-time from which light would never reach you if you kept speeding up. Those inaccessible regions are beyond your horizon.