Computer science shedding new light on black holes
When it comes to black holes, a change in perspective can make all the difference. Standing outside one of these massive objects in the universe, for instance, there’s only darkness—the black hole’s gravity is so strong that not even light escapes. But just inside the black hole, there may lie a blazing wall of fire, waiting to destroy whatever enters.
This firewall poses a problem, and not just for the poor soul entering the black hole. The existence of such a firewall would be a violation of a key principle in general relativity. However, some theorists pointed out that if it weren’t there, an equally important component of quantum mechanics would be violated. To resolve this paradox, it was clear that sacred beliefs must be sacrificed, one way or another.
Now a fresh take on the problem comes not from physics but from complexity theory, a branch of computer science that measures the difficulty of computations. Scott Aaronson, an associate professor of computer science and electrical engineering at the Massachusetts Institute of Technology, described the approach in an Oct. 11 briefing to science writers attending CASW’s New Horizons in Science program at MIT, part of the ScienceWriters2015 conference. According to the new perspective, the fate of the firewall hangs on the length of time required to execute a key computation.
Quantum constraints on black hole behavior
At the core of the firewall debate is the issue of information—specifically, what information is available and where. Physicists believe that information about the contents of a black hole radiates out from its surface in the form of Hawking radiation. This radiation continues for the lifespan of the black hole, until it has entirely radiated away.
To understand the how this leads to a problem, imagine an observer named Alice (the ill-fated participant in many quantum thought experiments), who stands outside a black hole. Alice collects all the particles coming out of her black hole and enters this information into a powerful quantum computer that processes it. If she waits long enough, she’ll begin to see that information that came out early in the black hole’s life is correlated with information coming out later. In fact, these particles that radiated out at different times are “entangled.” And in quantum mechanics, entanglement has many special properties.
One of those properties is quantum monogamy, the idea that a particle can only be maximally entangled with one other particle. But monogamy gets Alice in trouble. If Alice were to jump into her black hole, she’d see that the particles currently radiating out of it are entangled with the particles inside it. Yet this is a clear violation of monogamy: particles coming out of a black hole now can’t be entangled both with particles in the black hole and with particles that previously radiated from it.
Cleansing by firewall
This problem set the stage for a debate in black hole science, and for the eventual entrance of complexity theory into the brawl.
One solution, put forth by four theorists at the University of California at Santa Barbara (Ahmed Almheiri, Donald Marolf, Joseph Polchinski and James Sully, collectively referred to as AMPS) in 2012, has a particularly violent outcome. They claim that when Alice tries this experiment, her jump into the black hole does not go smoothly. Rather than pass through without incident, she encounters a burning firewall, created by the need to break the entanglement between outside and inside the black hole, and is immediately destroyed.
As is frequently the case in the labyrinth of theoretical physics, the solution is not without a paradox of its own. The presence of a firewall violates general relativity, which says (somewhat unintuitively) that Alice’s pass through the black hole boundary should be unremarkable. Thus physicists are still left with a forced choice. As Aaronson explained, “If you claim to understand what’s happening with black holes, you need to be able to explain what would happen if the AMPS experiment were carried out.”
In seeking an explanation, however, you are not limited to the tools physics has to offer.
An impossible thought experiment
That is exactly what Daniel Harlow of Princeton University, a physicist, and Patrick Hayden, a computer scientist at McGill University, realized. Rather than accept the premise of the thought experiment and try to find a solution, in a 2013 article they used complexity theory to ask if the experiment could even be done. Specifically, they focused on Alice’s quantum computer.
Information is radiating out of the black hole; however, there is no requirement that the information be packaged in a particularly accessible way. So while it is possible for Alice’s computer to measure the shared information between the earlier and later particles radiating from her black hole, it would actually take a mighty complicated computation to do it. It’s a problem more difficult than even unscrambling an egg. In fact, as Harlow and Hayden calculated using a finding from Aaronson’s Ph.D. thesis, it would take more time to complete the computation than the lifespan of the black hole itself.
Alice couldn’t measure one form of entanglement and then jump into the black hole to measure the other. The black hole would evaporate as she waited for her quantum computer to output its results. No need for a firewall—computational complexity prevents the situation requiring it from occurring.
While this may be the first time black hole science has felt the touch of complexity theory, the theory’s reach has already extended into other fields. In biology, the complexity viewpoint is being applied to protein folding. In the field of statistical physics, it’s used to characterize the annealing process. Complexity theory can even be helpful to economics, helping explain why markets can’t find equilibrium states.
When Aaronson was asked to talk about computational complexity at a meeting on the firewall paradox, he hadn’t actually done any work on the firewall problem himself. In an interview after the Oct. 11 presentation, he recalled that he thought, “Why are they inviting me? But it sounded interesting.” He was impressed by the Harlow and Hayden paper. “It’s one of the more striking papers I’ve seen in my career,” he said. And more than that, in preparing for the meeting, Aaronson was able to expand on their findings, further supporting how difficult the computation would be. It became clear that a collaboration between these fields could be a fruitful one.
Though not a physicist himself, Aaronson will continue to spend some of his time on the black hole problem in collaboration with physicists. But mostly he intends to retain his position as an outsider.
“I like to do more down-to-earth things,” he says, “like quantum computing.”