How Physicists Cracked a Black Hole Paradox

A few years ago a team of chemists unboiled an egg. Boiling causes protein molecules in the egg to twist around one another, and a centrifuge can disentangle them to restore the original. The technique is of dubious utility in a kitchen, but it neatly demonstrates the reversibility of physics. Anything in the physical world can run both ways—it’s one of the deepest features of the laws of physics, reflecting elemental symmetries of space, time and causality. If you send all the parts of a system into reverse, what was done will be undone. The information required to wind back the clock is always preserved. Of course, undoing a process may be easy in simple systems but is less so in complex ones, which is why the egg unboiler was so nifty.

But there’s a troubling exception: black holes. If a massive enough star collapses under its own weight, its gravity intensifies without limit and locks matter in its grip. Jump into one, and there’s no going back. Merge two together, and you can’t split them apart. A black hole presents an almost completely featureless façade to the universe. Looking at it, you can’t tell what fell in. The black hole does not seem to preserve information. This irreversibility, first appreciated by physicist David Finkelstein in 1958, was the earliest inkling of the black hole information paradox—“paradox” because how could reversible laws have irreversible effects? The paradox signaled a deeper disease in physicists’ understanding of the world. Scientists have many reasons to seek a grand unified theory of nature, but the information paradox is their most specific motivation, and it has guided their way when they have little else to go on.

At last, more than 60 years after this puzzle began to appear, physicists are seeing hope for a solution. In the year leading up to the pandemic and through the months of lockdown, a coalition of theorists took huge strides to understand the paradox—the most progress in decades, some say. They bolstered the idea that black holes, despite appearances, are reversible, and they dissolved the official paradox. Physical theory is no longer at odds with itself. The work is contentious, though, and by its proponents’ own admission, it is at best a starting point for a full explanation of black holes.

Until recently, most of the “progress” physicists have made on this paradox over the decades has consisted of realizing the problem is even harder than they’d thought. Finkelstein’s original work left loopholes. For one, it was based on Einstein’s general theory of relativity, which physicists knew was not the full story, because it left out quantum effects. In the 1970s Stephen Hawking—in the work that made him a household name—took a first crack at including those effects. His calculations predicted that black holes slowly release energy. But this emission carries no information about whatever had fallen in, so it doesn’t help wind back the clock. If anything, the outgoing trickle of particles worsens the predicament. The black hole eventually empties itself of energy and evaporates away like a puddle on a summer’s day. All the matter it imprisoned is not freed but wiped out of existence. Hawking’s analysis elevated a general unease into a full-fledged crisis for physics.

In 1993 Hawking’s former graduate student Don N. Page, now at the University of Alberta, dug the hole even deeper. He showed that if a black hole is to disgorge its information, it can’t wait until its dying moments but has to begin roughly halfway through its lifetime. That’s significant because a middle-aged black hole will have shrunk only modestly from its original size and should still be governed by the ordinary laws of physics. So physicists can’t just pin the entire problem on unknown exotic physics; it signals an inconsistency within even the best-established of theories. In 2009 Samir D. Mathur of the Ohio State University further showed that slight tweaks to Hawking’s calculations won’t do. Something big is missing.

The key element in Page’s and Mathur’s analyses was quantum entanglement, a special kind of correlation that particles can have even when no force or other influence links them. Entanglement is mysterious in its own right, but physicists can set that aside and ask what it means for black holes. Most particles that fall into one are entangled with particles that remain outside, and these linkages must be maintained if the black hole is to preserve information. Yet the linkages can’t simply be transferred to the outgoing particles that Hawking postulated, at least not without causing other troubles, according to an influential study by Ahmed Almheiri of the Institute for Advanced Study in Princeton, N.J., and his colleagues in 2013.

So black holes may be reversible, but theorists’ confusion goes only one way. On the bright side, studying the paradox has spun off ideas about gravity, spacetime and the unification of physics. For one thing, black holes imply that space has a limited capacity to hold material—you can pack in stuff only so tightly before it implodes to form a black hole. Oddly, the storage capacity of space scales up with a region’s area rather than with its volume. Space looks three-dimensional but acts as if it were two-dimensional. It has an illusory quality that we are usually oblivious to but that becomes evident in a black hole.

That realization is the origin of what became known as the holographic principle, one of the most fascinating—and baffling—ideas in modern theoretical science. It says that at least one of the spatial dimensions we experience is not fundamental to nature but instead emerges from quantum dynamics. The best-developed version of the holographic principle is the so-called AdS/CFT (anti–de Sitter space/conformal field theory) duality. It conceives of the universe as a gigantic snow globe. In one version, a three-dimensional space called the bulk (AdS) is encased within a two-dimensional boundary (CFT). Bulk and boundary are mathematically equivalent (“dual”), although theorists often consider the boundary to be more fundamental and the bulk to emerge from it. Whatever happens in the bulk has a parallel in the shadow world of the boundary. If a planet orbits a star in the bulk, the shadows of the planet and star do a little dance on the boundary.

Scientists have refined this duality over the years. Today not only can physicists equate a 3-D space to a 2-D space, they can match specific parts of the 3-D space to specific parts of the 2-D one. They can also associate particular physical quantities on both sides. The most advanced version of this correspondence, developed by Netta Engelhardt of the Massachusetts Institute of Technology and Aron Wall of the University of Cambridge in 2014, relates the area of surfaces to the amount of quantum entanglement. These very different quantities are secretly the same, and this equivalence gives theorists a glimpse of the underlying unity of nature.

With all these ingredients in place, theorists were recently able to make a new assault on the black hole information paradox. In 2019 Almheiri, Engelhardt and their colleagues, and independently Geoff Penington of the University of California, Berkeley (who was using broadly similar methods), were able to show how information could escape from black holes in the way Page had prescribed. (Read more about this breakthrough in Almheiri’s article on page 34.) In so doing the researchers confirmed that black holes are reversible after all. Later the same year these and other authors, again working in two parallel teams, double-checked that the outgoing radiation bears the information that the black hole lets out. This time their calculations did not directly rely on the AdS/CFT duality. Instead they adopted essentially the same mathematical techniques as Hawking’s. If, as Page argued, the paradox lay in well-established theories, its resolution should not hinge on anything so fancy as AdS/CFT.

The teams confirmed that it doesn’t. A black hole builds up such a gargantuan amount of entanglement that the geometry of spacetime undergoes a dramatic transition. Spacetime inside and around the black hole takes on convoluted shapes, including wormholes that resemble the spacetime portals of science fiction. These wormholes connect the interior of the black hole to the outside world, although how they enable information to escape is still unclear. Bizarre though this geometric transition may sound, it fits perfectly well into existing physics. Whatever else you may say about black holes, they are no longer paradoxical—they don’t represent an internal inconsistency within current theories.

These calculations were daunting even by the standards of modern physics. Skeptics were impressed, although that didn’t stop them from poking holes in the argument. By the time the debate was in full swing, however, the pandemic hit, and science went into lockdown. In-person meetings resumed only at the end of 2021. Some physicists say that science by Zoom just isn’t the same and that proponents and skeptics have yet to really engage with one another. “Maybe this is partly a function of the pandemic, that there is more splintering of the field,” says Suvrat Raju of the Tata Institute of Fundamental Research in Bangalore.

In one especially sharp critique, Raju and his colleagues complained that the two teams’ setup is highly contrived. To a degree, the same can be said of most theoretical models, but this one makes idealizations that are not at all innocent, these authors say. For instance, it supposes that gravity not only weakens with distance but eventually shuts off altogether. That assumption fundamentally changes the nature of this force, so that the calculations, though technically correct, say little about gravity or black holes in the real world.

Mathur and others also argued that the new work implies a nonlocal effect—one that does not propagate through space but jumps from one place to another—to extract information from the black hole. That in itself is not surprising. Physicists broadly agree that black holes require nonlocal effects to make sense. But the specific type of nonlocality in the new analyses strikes some skeptics as implausible.

Both Raju and Mathur advocate alternative solutions to the information paradox. Raju suggested that information doesn’t have to get out of a black hole, because it is already out. Gravity has a long tail—the force acts over an unlimited range—that prevents information from ever being bottled up in the first place, he says. The gravitational, electromagnetic and other quantum fields outside the black hole retain an imprint of whatever falls in. “This region is rich in information,” Raju says. Mathur, for his part, argues that true black holes never actually form. As a star starts to collapse, it awakens the exotic physics of string theory, according to which all particles are vibration patterns in a more primitive type of matter. Stringy physics arrests the collapse, leaving a highly compact star, also known as a fuzzball. This little star does not wall itself off gravitationally, and information rides out on its light.

These ideas and their variants have critics, too. Indeed, Mathur and Raju disagree with each other’s approaches. So the nature of black holes is still up for grabs. And continuing the historical trend, theorists are doing better at finding new puzzles than at solving old ones. In recent years Leonard Susskind of Stanford has noted yet another paradox of black holes. Space inside them is so stretchy that their interior volume should grow forever. Such expansion, however, would violate the principle that any closed system will reach equilibrium. Some heretofore unsuspected physics must eventually intervene to stabilize the interior.

Susskind and others also find that black holes are frenetically chaotic systems, swirling and seething underneath their featureless façades. This aspect of black holes, at least, can be studied in computer simulations and laboratory experiments. Creating a real black hole is beyond them, but experimentalists are looking at the same chaotic dynamics in ions, condensates and other material systems. They run the system, then unwind it; bringing it back to its exact starting point requires exquisite precision, demonstrating how black holes can look irreversible even if, in principle, they are rewindable.

Meanwhile theorists think that what goes for black holes may go for the universe as a whole. Because our universe is expanding at an accelerating rate, it has a one-way surface much like that of a black hole’s event horizon, and physicists hope that insights about black holes will offer up secrets of the cosmos as well. (Read more about this idea in Edgar Shaghoulian’s article.)

Truth be told, physicists are happy black holes are proving so tough to figure out. If the problem is this hard, the solution has got to be profound.

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