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The Black Hole Information Paradox Comes to an End

In a series of breakthrough studies and research papers, theoretical physicists have come tantalizingly close to breaking down the black hole information paradox that has delighted and bedeviled them for nearly 50 years. Information, they now say with confidence, does escape a black hole. If you jump into one, you will not be gone for good. Particle by particle, the information needed to reconstitute your body will reemerge. Most physicists have long assumed it would; that was the upshot of string theory, their leading candidate for a unified theory of nature. But the new calculations, though inspired by string theory, stand on their own, with nary a string in sight. Information gets out through the workings of gravity itself — just ordinary gravity with a single layer of quantum effects.

This is a peculiar role reversal for gravity. According to Einstein’s general theory of relativity, the gravity of a black hole is so intense that nothing can escape it. The more sophisticated understanding of black holes developed by Stephen Hawking and his colleagues in the 1970s did not question this principle. Hawking and others sought to describe matter in and around black holes using quantum theory, but they continued to describe gravity using Einstein’s classical theory — a hybrid approach that physicists call “semiclassical.” Although the approach predicted new effects at the perimeter of the hole, the interior remained strictly sealed off. Physicists figured that Hawking had nailed the semiclassical calculation. Any further progress would have to treat gravity, too, as quantum.

That is what the authors of the new studies dispute. They have found additional semiclassical effects — new gravitational configurations that Einstein’s theory permits, but that Hawking did not include. Muted at first, these effects come to dominate when the black hole gets to be extremely old. The hole transforms from a hermit kingdom to a vigorously open system. Not only does information spill out, anything new that falls in is regurgitated almost immediately. The revised semiclassical theory has yet to explain how exactly the information gets out, but such has been the pace of discovery in the past two years that theorists already have hints of the escape mechanism.

“That is the most exciting thing that has happened in this subject, I think, since Hawking,” said one of the co-authors, Donald Marolf of the University of California, Santa Barbara.

“It’s a landmark calculation,” said Eva Silverstein of Stanford University, a leading theoretical physicist who was not directly involved.

You might expect the authors to celebrate, but they say they also feel let down. Had the calculation involved deep features of quantum gravity rather than a light dusting, it might have been even harder to pull off, but once that was accomplished, it would have illuminated those depths. So they worry they may have solved this one problem without achieving the broader closure they sought. “The hope was, if we could answer this question — if we could see the information coming out — in order to do that we would have had to learn about the microscopic theory,” said Geoff Penington of the University of California, Berkeley, alluding to a fully quantum theory of gravity.

What it all means is being intensely debated in Zoom calls and webinars. The work is highly mathematical and has a Rube Goldberg quality to it, stringing together one calculational trick after another in a way that is hard to interpret. Wormholes, the holographic principle, emergent space-time, quantum entanglement, quantum computers: Nearly every concept in fundamental physics these days makes an appearance, making the subject both captivating and confounding.

And not everyone is convinced. Some still think that Hawking got it right and that string theory or other novel physics has to come into play if information is to escape. “I’m very resistant to people who come in and say, ‘I’ve got a solution in just quantum mechanics and gravity,’” said Nick Warner of the University of Southern California. “Because it’s taken us around in circles before.”

But almost everyone appears to agree on one thing. In some way or other, space-time itself seems to fall apart at a black hole, implying that space-time is not the root level of reality, but an emergent structure from something deeper. Although Einstein conceived of gravity as the geometry of space-time, his theory also entails the dissolution of space-time, which is ultimately why information can escape its gravitational prison.

The Curve Becomes the Key

In 1992, Don Page and his family spent their Christmas vacation house-sitting in Pasadena, enjoying the swimming pool and watching the Rose Parade. Page, a physicist at the University of Alberta in Canada, also used the break to think about how paradoxical black holes really are. His first studies of black holes, when he was a graduate student in the ’70s, were key to his adviser Stephen Hawking’s realization that black holes emit radiation — the result of random quantum processes at the edge of the hole. Put simply, a black hole rots from the outside in.

The particles it sheds appear to carry no information about the interior contents. If a 100-kilogram astronaut falls in, the hole grows in mass by 100 kilograms. Yet when the hole emits the equivalent of 100 kilograms in radiation, that radiation is completely unstructured. Nothing about the radiation reveals whether it came from an astronaut or a lump of lead.

That’s a problem because, at some point, the black hole emits its last ounce and ceases to be. All that’s left is a big amorphous cloud of particles zipping here and there at random. It would be impossible to recover whatever fell in. That makes black hole formation and evaporation an irreversible process, which appears to defy the laws of quantum mechanics.

Hawking and most other theorists at the time accepted that conclusion — if irreversibility flouted the laws of physics as they were then understood, so much the worse for those laws. But Page was perturbed, because irreversibility would violate the fundamental symmetry of time. In 1980 he broke with his former adviser and argued that black holes must release or at least preserve information. That caused a schism among physicists. “Most general relativists I talked to agreed with Hawking,” said Page. “But particle physicists tended to agree with me.”

On his Pasadena vacation, Page realized that both groups had missed an important point. The puzzle wasn’t just what happens at the end of the black hole’s life, but also what leads up to it.

He considered an aspect of the process that had been relatively neglected: quantum entanglement. The emitted radiation maintains a quantum mechanical link to its place of origin. If you measure either the radiation or the black hole on its own, it looks random, but if you consider them jointly, they exhibit a pattern. It’s like encrypting your data with a password. The data without the password is gibberish. The password, if you have chosen a good one, is meaningless too. But together they unlock the information. Maybe, thought Page, information can come out of the black hole in a similarly encrypted form.

Page calculated what that would mean for the total amount of entanglement between the black hole and the radiation, a quantity known as the entanglement entropy. At the start of the whole process, the entanglement entropy is zero, since the black hole has not yet emitted any radiation to be entangled with. At the end of the process, if information is preserved, the entanglement entropy should be zero again, since there is no longer a black hole. “I got curious how the radiation entropy would change in between,” Page said.

Initially, as radiation trickles out, the entanglement entropy grows. Page reasoned that this trend has to reverse. The entropy has to stop rising and start dropping if it is to hit zero by the endpoint. Over time, the entanglement entropy should follow a curve shaped like an inverted V.

Page calculated that this reversal would have to occur roughly halfway through the process, at a moment now known as the Page time. This is much earlier than physicists assumed. The black hole is still enormous at that point — certainly nowhere near the subatomic size at which any putative exotic effects would show up. The known laws of physics should still apply. And there is nothing in those laws to bend the curve down.

With that, the problem got much more acute. Physicists had always figured that a quantum theory of gravity came into play only in situations so extreme that they sound silly, such as a star collapsing to the radius of a proton. Now Page was telling them that quantum gravity mattered under conditions that, in some cases, are comparable to those in your kitchen.

Page’s analysis justified calling the black hole information problem a paradox as opposed to merely a puzzle. It exposed a conflict within the semiclassical approximation. “The Page-time paradox seems to point to a breakdown of low-energy physics in a place where it has no business breaking down, because the energies are still low,” said David Wallace, a philosopher of physics at the University of Pittsburgh.

On the bright side, Page’s clarification of the problem paved the way to a solution. He established that, if entanglement entropy follows the Page curve, then information gets out of the black hole. In doing so, he transformed a debate into a calculation. “Physicists are not always so good at words,” said Andrew Strominger of Harvard University. “We do best with sharp equations.”

Now physicists just had to calculate the entanglement entropy. If they could pull it off, they’d get a straight answer. Does the entanglement entropy follow an inverted V or not? If it does, the black hole preserves information, which means particle physicists were right. If it doesn’t, the black hole destroys or bottles up information, and general relativists can help themselves to the first doughnut at faculty meetings.

Yet even though Page spelled out what physicists had to do, it took theorists nearly three decades to figure out how.

The Inside-Out Black Hole

Over the past two years, physicists have shown that the entanglement entropy of black holes really does follow the Page curve, indicating that information gets out. They did the analysis in stages. First, they showed how it would work using insights from string theory. Then, in papers published last fall, researchers cut the tether to string theory altogether.

Read more here.

1 comment

  1. The black hole is my ex-husband. It's just a bottomless abyss, which no matter how much you fill, but it will never be filled. I filed for divorce and he went to hell. Finally, my life will be easier.
    And the article is interesting, thanks.


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