In chatting with colleagues after a talk this week, Joe Polchinski said he’d love to fall into a black hole. Most theoretical physicists would. It’s not because they have some peculiar death wish or because science funding prospects are so dark these days. They are just insanely curious about what would happen. Black holes are where the known laws of physics come into their most direct conflict. The worst trouble is the black hole information paradox that Stephen Hawking loosed upon the world in 1976. Polchinski and his colleagues have shown that the predicament is even worse than physicists used to think.
I first heard about their brainstorm while visiting the Kavli Institute for Theoretical Physics in Santa Barbara this spring, and the team—Polchinski and fellow Santa Barbarans Don Marolf, Ahmed Almheiri, and James Sully—wrote it up over the summer. Polchinski blogged about it a few months ago, and another theorist who helped to usher in the idea, John Preskill, did so last week. Polchinski’s talk to the New York University physics department drew a standing-room-only crowd, not a single person snuck out early, and he was still fending questions an hour after it ended.
Almost as much has been written about Hawking’s original paradox (including by me) as about the fiscal cliff, so I’ll jump straight to the new version. Step #1 of the argument is what Polchinski and his co-authors call the “no-drama” principle. According to current theories of physics, a black hole is mostly just empty space. Its perimeter or “event horizon” is not a material surface, but just a hypothetical location that marks the point of no return. Once inside, you are gripped too tightly by gravity ever to get back out. By then, falling at nearly the speed of light, you have a few seconds to look around before you reach the very center and get crushed into oblivion. But nothing noticeable should happen at the moment of crossing. One of Einstein’s great insights was that observers who are freely falling—whether into a black hole or toward the ground—don’t feel the force of gravity, since everything around them is falling, too. As they say, it’s not the fall that kills you; it’s the sudden stop at the end.
An outside observer knows you’re doomed, but likewise doesn’t think anything untoward happens upon passing through the event horizon. Indeed, this observer never sees anything actually cross over. Because of a kind of gravitational mirage, things seem to slow down and freeze in time. All the stuff piling up at the horizon forms a ghostly membrane, which obeys the usual laws of physics and has conventional properties such as viscosity and electrical conductivity.
Step #2 is to relate these two viewpoints. To the infalling observer, space looks like a vacuum, and in quantum theory, a vacuum is a very special state of affairs. It is a region of space that is empty of particles. It is not a region that is empty of everything. There’s no getting rid of the electromagnetic field and other fields. (If you could, the region would not merely be empty, but nonexistent.) A particle is nothing more or less than a vibration one of these fields, and what makes a vacuum a vacuum is that all the possible vibrations cancel one another precisely, leaving the fields becalmed. To maintain this finely balanced condition, the vibrations must be thoroughly quantum-entangled with one another.
To the outgoing observer, the horizon (or membrane) cleaves space in two, and the vibrations no longer appear to cancel out. It looks like there are particles flying off in every direction. This is perfectly compatible with the infalling observer’s viewpoint, since the fields are what is fundamental and the presence of particles is a matter of perspective. To put it differently, emptiness is a holistic property in quantum physics—true for a region of space in its entirety, but not for individual subregions.
For consistency between the two viewpoints, the outside observer infers that each particle he or she sees has a doppelgänger inside the horizon. The two are quantum-entangled, like those particles in laboratory experiments you read about. (Watch this lighthearted video that my colleagues made earlier this year to explain entanglement.) Individually, both particles behave completely randomly, but together they form a matched pair. See the diagram at left: the infalling observer sees vacuum state a, the outside observer sees entangled particles b and b′. Particle b is part of what physicists call the Hawking radiation.
Step #3 is to consider the long-term fate of the hole. Like everything else in this world, black holes must decay—quantum mechanics mandates it. In the process, a hole must gradually release everything that fell in. If Joe Polchinski jumps into a black hole, he will get scrambled with all the other theorists who have done the same, and the morbid gruel will emerge particle by particle in the Hawking radiation. Though mangled beyond recognition, each martyr to the cause of knowledge can still be separated out and pieced back together. To enable this reconstruction, the particles of the Hawking radiation must be thoroughly entangled with one another.
So, by step #2, each particle flying away from the hole must be thoroughly entangled with its doppelgänger inside the hole. By step #3, the particle must also be thoroughly entangled with other particles that are flying away from the hole. These two conclusions clash, because quantum mechanics says that particles are monogamous. They can’t be thoroughly entangled with more than one other partner at a time. They can be partially entangled, but that is not enough to ensure consistency between the observers’ view or to reconstruct the infalling physicists.
This formulation of the black-hole paradox vindicates Hawking’s original argument. For years physicists hoped that the devil lay in the details—that more precise calculations would reveal an escape route—only to be serially disappointed. Now they have officially given up hope. One of the basic premises must be wrong—which is to say, something deep about modern physics must be wrong. “You need huge changes, not just quantum-gravitational corrections, to invalidate Hawking’s argument,” Polchinski told the assembled multitudes at NYU.
More surprisingly, Polchinski and his co-authors have shown that a popular approach known as black-hole complementarity, championed by Leonard Susskind of Stanford University, isn’t up to the task, either. Susskind reasoned that, although infalling and outside observers might see different and mutually incompatible events, no single observer can be both infalling and outside, so no single observer is ever faced with a direct contradiction. In that case, the paradox is only ever conceptual—suggesting it is somehow illusory, the product of thinking about the situation in the wrong way. But Polchinski and colleagues showed that a single observer can catch a particle in the act of polygamy by first lingering outside the hole and then jumping in.
The least radical conclusion is that the no-drama principle is false. Someone falling into a black hole doesn’t pass uneventfully through the horizon, but hits a wall of fire and is instantly incinerated. “I think it’s crazy,” Polchinski admitted. But in order for a black hole to decay and its contents to spill out, as quantum mechanics demands, the infalling observer can’t see just a vacuum. The firewall idea strikes me as similar to past speculation that black holes are somehow material objects—so-called black stars or dark matter stars—rather than merely blank space.
“I spent 20 years confused by this,” Polchinski said, “and now I’m as confused as ever.” It would be nice to answer the question, if only so that no one ever has to undertake the journey to answer the question.
Diagrams courtesy of Joseph Polchinski