Akers had already convinced himself that the conversion program should be written in the language of quantum error correction, as Harlow had already worked out for empty space. The semiclassical interior would be the message, and the quantum exterior would be the transmission. And given that the interior seemed to grow inside a shrinking horizon, they were just going to have to invent an error-correcting code that could cram an SOS into a single S.
Akers faced skepticism from his colleagues. The way in which the encoding would have to delete information inside the black hole violated the quantum mechanical prohibition against information loss. If the interior astronaut burned her mission log, she might not be able to reconstruct a replica from the ashes.
“If you’re modifying quantum mechanics, people will think you’re crazy, and usually they’ll be right,” Harlow said. “I was hesitant.”
Later that year, an MIT graduate student (now at Stanford) named Shreya Vardhan joined the crew. She did some concrete entropy calculations that finally convinced everyone that lightly breaking quantum mechanics inside was the only way to completely save it outside.
“Shreya and Chris in particular were pushing that in different ways,” Harlow said. “Shreya broke down the last barrier for me, and I realized that this really does make sense.”
Akers had been working with Penington, so he got involved too. The effort took a few years of on-and-off work. And just as they sat down to write up their results, three-fifths of the team simultaneously came down with Covid-19. But last July they finally posted a preprint detailing their theory of how the black hole interior could be encoded in its exterior with the world’s weirdest error-correcting code.
Here’s how it works. A self-sacrificing astronaut inside the black hole records the configuration of all the photons, electrons and other particles surrounding her and the black hole — a file of quantum data made up of a bunch of qubits capturing her semiclassical experience. Her goal is to understand the quantum perspective of her partner outside at that moment. The group developed a two-step algorithm that one could imagine running on a quantum computer for converting that interior snapshot.
First, the program scrambles the semiclassical qubits almost beyond recognition using one of the most random transformations in mathematics.
Then comes the secret sauce. The second step involves postselection, a strange operation more commonly used by information theorists than physicists. Postselection lets an experimenter rig a random process to get a desired outcome. Say you want to flip a coin and get 10 heads in a row. You can do it, provided you have the patience to start over every time it comes up tails. Similarly, the encoding program begins measuring the semiclassical qubits but reboots every time it gets a 1. Eventually, when it has measured most of the scrambled qubits and successfully gotten a string of zeros, it throws those qubits away. The few remaining, unmeasured qubits represent the pixels of the quantum image of the black hole as viewed from the exterior. Thus, the code squeezes a large semiclassical RAW file into a compact quantum JPEG.
It’s “a lossy way to compress a lot of semiclassical information into a finite quantum space,” Hartman of Cornell said.
But there’s a big catch. How could such a program delete so much semiclassical information without erasing any essential details? The procedure implies that semiclassical physics is full of fluff — configurations of particles that the interior astronaut might observe that aren’t actually real. But semiclassical physics has been rigorously tested in particle colliders on Earth, and experimenters have seen no signs of such mirages.
“How many states are reliably encoded? And how well can the semiclassical theory do?” Hartman said. “Given that it has to be lossy, it’s not obvious that it can do anything at all.”
To explain how a flawed theory could perform so well, the team turned to the odd observation that Hayden and Harlow had made in 2013, that decoding the radiation for the AMPS experiment would take so many steps as to be effectively impossible. Perhaps complexity could be papering over cracks in semiclassical physics. The encoding wasn’t deleting configurations willy-nilly. It erased only certain arrangements of particles that were complex in the sense that they would take so long to come about that the interior astronaut could never expect to witness them.
Making the case that the code left simple states essentially untouched made up the bulk of the work. The group argued that for any version of their two-step process, creating a complex semiclassical configuration with no counterpart from the outside perspective would essentially take an eternity — something like 10,000 times the current age of the universe just for a 50-qubit, subatomic speck of a black hole. And for a real black hole, such as M87 with its 1070-odd qubits, an experiment that broke semiclassical physics would take exponentially longer than that.
The team proposes that black holes highlight a new breakdown in the established framework of physics. Much as Einstein once predicted that Newton’s notion of rigid distances would fail at sufficiently high speeds, they predict that semiclassical physics fails for extremely complex experiments involving unthinkable numbers of steps and incomprehensible lengths of time.
Firewalls, the group believes, would be a manifestation of such unthinkable complexity. A real black hole like the one in M87 has only been around for billions of years — not nearly long enough for the semiclassical interior to break down in a firewall. But if one were able to do improbably complicated experiments, or if a black hole lived for an extremely long time, all semiclassical bets would be off.
“There’s a complexity frontier,” Harlow said. “When you start doing exponential things, then [physics] really starts being different.”
Saved by the Curse of Complexity
Once the physicists had convinced themselves that the code’s lossiness wouldn’t lead to noticeable cracks in semiclassical physics inside the black hole, the team investigated the consequences. They found that the apparent bug turned out to be the ultimate feature.
“It seems bad. It seems like you’re going to lose information because you’re deleting a lot of the states,” Akers said. But “it turns out it’s everything you ever wanted.”
In particular, it goes beyond the 2019 work in addressing how information gets out of the black hole. Or rather, it suggests that the qubits aren’t exactly inside to begin with.
The secret lies in the funky second step of the conversion, postselection. Postselection involves the same mathematical ingredients, namely the measurement of entangled partners, as a textbook quantum process that teleports information from one location to another. So, while the conversion process is not a physical event that plays out in time, it accounts for how information appears to switch from the interior to the exterior.
Essentially, if the interior astronaut converts a snapshot taken late in the black hole’s life, she’ll learn that the information that appears to reside in particles around her — or even in her own body — is from the external perspective actually floating in the Hawking radiation outside. As time goes on, the conversion process will reveal more and more of her world to be unreal. The instant before the black hole disappears, despite the astronaut’s impression to the contrary, her information will exist almost entirely outside, scrambled up in the radiation. By tracing this process, snapshot by snapshot, the group was able to derive Engelhardt’s entropy formula that had found information in the radiation in 2019. It too is a byproduct of the conversion’s lossiness.
In short, the conversion explains how an astronaut could unknowingly experience an interior that grows more and more detached from the reality outside as it matures. Hawking’s mistake, they argue, was to put himself fully in the boots of the interior astronaut and assume that semiclassical physics worked perfectly well both inside and outside the black hole.
He didn’t realize, as Harlow and company now believe, that semiclassical physics fails to accurately capture phenomena and experiments that require exponential complexity. Decoding the scrambled information in the radiation would take an exponentially long time, for instance, which is why his semiclassical analysis erroneously predicts the radiation to be featureless. The features are there; it would just take many, many times the age of the universe to uncover them.
In addition, there’s a reason why the interior’s information capacity appears to grow while the size of the black hole’s surface shrinks: The semiclassical calculation mistakenly includes a huge number of complex states that don’t have quantum counterparts outside. If physicists take into account the ways that complexity can mess with semiclassical physics, the clash between the space-time picture inside and the quantum picture outside evaporates.
“We now see a consistent way through the paradox,” Harlow said.
Black Hole Confusion
For all Harlow’s confidence, however, others in the black hole community have plenty of questions.
The major limitation is that the theories the code connects are extremely simple. The quantum mechanical description has a collection of qubits that radiates information. The semiclassical description has an interior cleaved from an exterior by an event horizon. And that’s it. There’s no gravity, and no sense of space-time. The code has the core features of the paradox, but it lacks many details that would be necessary to argue that real black holes operate in this fashion.
“The hope as always is you have a toy model that you’ve extracted all of the important physics and discarded all of the unimportant physics,” Maloney said. “There are pretty good reasons to think that’s true here, but nevertheless it’s important to be cautious.”
Plenty of alternative solutions exist, and real gravity could still resolve the paradox in one of those ways. Mathur of Ohio State, for instance, leads a research program studying one such option. While analyzing what would happen to a collapsing star in string theory, he and his collaborators found that strings may halt the collapse. They form a writhing mass, a “fuzzball,” whose intricate wriggling would stop an event horizon — and a paradox — from forming. Mathur raises various objections to the new solution and generally believes the lossy code to be an overly complicated proposal. “The information paradox was solved long ago,” he said. (By fuzzballs.)
Meanwhile Marolf, who worked with Engelhardt to spot the information in the radiation in 2019, suspects that their solution may be overly conservative. “My concern is that it’s almost too easy,” he said.
He chokes on the lossiness, which means that the code in its current form gives unique answers only to the interior astronaut. If an exterior astronaut takes a picture and wants to know what it says about the inside, he’ll have to guess at the semiclassical pixels the code erases. Even though those states are in some sense illusory, they’re essential for understanding the human experience inside. For some guesses, he might find a calm interior. In others, a raging firewall. No matter how refined the quantum theory is outside, it will never be able to say for sure what he’d find if he jumped in.
“It disturbs me a little bit,” Marolf said. “I would have thought that a theory which is fundamental should predict everything — including what we experience as reality.”
Lossiness on the Rise
Some skeptics of the initial proposal have since come around to the idea, including Isaac Kim, a computer scientist at the University of California, Davis, and John Preskill, a quantum physicist at the California Institute of Technology and one of the luminaries in attendance at the 2013 firewall showdown.
“We heard through the grapevine that this work was coming,” Kim said. “It sounded like something has to go wrong.”
Kim was unnerved by the use of postselection. Past applications of postselection had included blueprints for time machines and unreasonably powerful quantum computers, so its appearance leapt out as a red flag. He suspected that details missing from the initial code, such as how it works for an astronaut who measures radiation outside and then falls in, might combine with the postselection to muck up even the external perspective and delete information there.
Then in December, Kim and Preskill upgraded the code and found that the black hole safely continued to radiate information in the external picture. They also found that postselection did not serve as a loophole for the black hole to perform absurdly powerful computations — or launch astronauts back to the future.
“Remarkably within this model, even though you allow postselection, that doesn’t happen,” he said. “That’s what convinced me that something correct is going on here.”
DeWolfe and his collaborator Kenneth Higginbotham further generalized the lossy code in April. They also concluded that it could withstand infalling astronauts.
Other researchers have spent the last few months checking whether their favorite theories of gravity are hiding lossiness. In October, Arjun Kar of the University of British Columbia ported Harlow and colleagues’ lossy code into a well-known theory of 2D gravity and found that it held. “They really seem to have hit on something interesting about quantum error correction,” he said.
Continuing along this path — searching for lossiness in more theories of gravity — is the main way physicists hope to build or destroy confidence that real gravity actually works like this. Few dream of probing the code with an experiment.
“It’s not clear how we would ever test this account,” Aaronson said, “except for trying to further build a quantum theory of gravity on top of it and seeing whether that theory is successful.”
Harlow, however, is a dreamer. “I don’t think it’s impossible. It’s just hard,” he said, laying out the following thought experiment.
You put a tiny black hole in a box and capture every photon of Hawking radiation coming out of it, storing all that information in a quantum computer. Because that information would appear to exist inside the black hole from the point of view of an interior particle, manipulating the radiation could instantly affect the particle — a true action at a distance spooky enough to haunt any physicist. “There shouldn’t be anything I can do to the radiation that changes anything in the interior,” Harlow said. “That’s a breakdown that came because you crossed the complexity frontier.”
But even to fantasize about such an experiment, Harlow has to switch over to an eternal universe to give himself enough time, as activity in our expanding cosmos would peter out trillions of times over before one could hope to manipulate the radiation of even the tiniest of black holes. (Additionally, Susskind and others working on a related angle of the black hole puzzle have recently found overlapping ideas relating complexity and unfathomably long periods of time.)
Nevertheless, Harlow is undeterred by minor details such as the heat death of the universe. If impossible thought experiments involving trains traveling at nearly light speed were good enough for Einstein, he believes, they’re good enough for him.
“We still don’t have the trains, but [relativity] has consequences for various other things that we tested,” he said.
Harlow is the latest in a long line of black hole physicists with a relationship to physical evidence that casual observers might find surprising. After all, no one has ever seen one photon of Hawking radiation, and no one ever will. It’s far too weak, even if you parked the James Webb Space Telescope in orbit around a real black hole.
But that hasn’t stopped multiple generations of physicists, from Stephen Hawking and Leonard Susskind to Netta Engelhardt, Chris Akers and dozens more, from spiritedly debating how to handle the bundle of conflicts that come tumbling out of the black hole along with the theoretical bath of photons.
Even as they build and fortify their cases, they acknowledge that the only conclusive way to see whether black holes represent the ultimate cosmic prison or a fiery death sentence is to embark on the original unthinkable thought experiment.
“If there are two people who care about nothing more than resolving their disagreement, all they can do is jump in,” Penington said. “Either they both get vaporized instantly and they never resolve it anyway, or they make it inside and one of them goes, ‘Oh, fair enough, I was wrong.’”
Editor’s note: A number of the scientists featured in this article, including Daniel Harlow and Chris Akers, have received funding from the Simons Foundation, which also funds this editorially independent magazine. Simons Foundation funding decisions have no influence on our coverage. More details are available here.
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