# Alice and Bob Meet the Wall of Fire

## Introduction

Alice and Bob, beloved characters of various thought experiments in quantum mechanics, are at a crossroads. The adventurous, rather reckless Alice jumps into a very large black hole, leaving a presumably forlorn Bob outside the event horizon — a black hole’s point of no return, beyond which nothing, not even light, can escape.

Conventionally, physicists have assumed that if the black hole is large enough, Alice won’t notice anything unusual as she crosses the horizon. In this scenario, colorfully dubbed “No Drama,” the gravitational forces won’t become extreme until she approaches a point inside the black hole called the singularity. There, the gravitational pull will be so much stronger on her feet than on her head that Alice will be “spaghettified.”

Now a new hypothesis is giving poor Alice even more drama than she bargained for. If this alternative is correct, as the unsuspecting Alice crosses the event horizon, she will encounter a massive wall of fire that will incinerate her on the spot. As unfair as this seems for Alice, the scenario would also mean that at least one of three cherished notions in theoretical physics must be wrong.

When Alice’s fiery fate was proposed this summer, it set off heated debates among physicists, many of whom were highly skeptical. “My initial reaction was, ‘You’ve got to be kidding,’” admitted Raphael Bousso, a physicist at the University of California, Berkeley. He thought a forceful counterargument would quickly emerge and put the matter to rest. Instead, after a flurry of papers debating the subject, he and his colleagues realized that this had the makings of a mighty fine paradox.

## The ‘Menu From Hell’

Paradoxes in physics have a way of clarifying key issues. At the heart of this particular puzzle lies a conflict between three fundamental postulates beloved by many physicists. The first, based on the equivalence principle of general relativity, leads to the No Drama scenario: Because Alice is in free fall as she crosses the horizon, and there is no difference between free fall and inertial motion, she shouldn’t feel extreme effects of gravity. The second postulate is unitarity, the assumption, in keeping with a fundamental tenet of quantum mechanics, that information that falls into a black hole is not irretrievably lost. Lastly, there is what might be best described as “normality,” namely, that physics works as expected far away from a black hole even if it breaks down at some point within the black hole — either at the singularity or at the event horizon.

Together, these concepts make up what Bousso ruefully calls “the menu from hell.” To resolve the paradox, one of the three must be sacrificed, and nobody can agree on which one should get the ax.

Physicists don’t lightly abandon time-honored postulates. That’s why so many find the notion of a wall of fire downright noxious. “It is odious,” John Preskill of the California Institute of Technology declared earlier this month at an informal workshop organized by Stanford University’s Leonard Susskind. For two days, 50 or so physicists engaged in a spirited brainstorming session, tossing out all manner of crazy ideas to try to resolve the paradox, punctuated by the rapid-fire *tap-tap-tap* of equations being scrawled on a blackboard. But despite the collective angst, even the firewall’s fiercest detractors have yet to find a satisfactory solution to the conundrum.

According to Joseph Polchinski, a string theorist at the University of California, Santa Barbara, the simplest solution is that the equivalence principle breaks down at the event horizon, thereby giving rise to a firewall. Polchinski is a co-author of the paper that started it all, along with Ahmed Almheiri, Donald Marolf and James Sully — a group often referred to as “AMPS.” Even Polchinski thinks the idea is a little crazy. It’s a testament to the knottiness of the problem that a firewall is the least radical potential solution.

If there is an error in the firewall argument, the mistake is not obvious. That’s the hallmark of a good scientific paradox. And it comes at a time when theorists are hungry for a new challenge: The Large Hadron Collider has failed to turn up any data hinting at exotic physics beyond the Standard Model. “In the absence of data, theorists thrive on paradox,” Polchinski quipped.

If AMPS is wrong, according to Susskind, it is wrong in a really interesting way that will push physics forward, hopefully toward a robust theory of quantum gravity. Black holes are interesting to physicists, after all, because both general relativity and quantum mechanics can apply, unlike in the rest of the universe, where objects are governed by quantum mechanics at the subatomic scale and by general relativity on the macroscale. The two “rule books” work well enough in their respective regimes, but physicists would love to combine them to shed light on anomalies like black holes and, by extension, the origins of the universe.

## An Entangled Paradox

The issues are complicated and subtle — if they were simple, there would be no paradox — but a large part of the AMPS argument hinges on the notion of monogamous quantum entanglement: You can only have one kind of entanglement at a time. AMPS argues that two different kinds of entanglement are needed in order for all three postulates on the “menu from hell” to be true. Since the rules of quantum mechanics don’t allow you to have both entanglements, one of the three postulates must be sacrificed.

Entanglement — which Albert Einstein ridiculed as “spooky action at a distance” — is a well-known feature of quantum mechanics (in the thought experiment, Alice and Bob represent an entangled particle pair). When subatomic particles collide, they can become invisibly connected, though they may be physically separated. Even at a distance, they are inextricably interlinked and act like a single object. So knowledge about one partner can instantly reveal knowledge about the other. The catch is that you can only have one entanglement at a time.

Under classical physics, as Preskill explained on Caltech’s Quantum Frontiers blog, Alice and Bob can both have copies of the same newspaper, which gives them access to the same information. Sharing this bond of sorts makes them “strongly correlated.” A third person, “Carrie,” can also buy a copy of that newspaper, which gives her equal access to the information it contains, thereby forging a correlation with Bob without weakening his correlation with Alice. In fact, any number of people can buy a copy of that same newspaper and become strongly correlated with one another.

But with quantum correlations, that is not the case. For Bob and Alice to be maximally entangled, their respective newspapers must have the same orientation, whether right side up, upside down or sideways. So long as the orientation is the same, Alice and Bob will have access to the same information. “Because there is just one way to read a classical newspaper and lots of ways to read a quantum newspaper, the quantum correlations are stronger than the classical ones,” Preskill said. That makes it impossible for Bob to become as strongly entangled with Carrie as he is with Alice without sacrificing some of his entanglement with Alice.

This is problematic because there is more than one kind of entanglement associated with a black hole, and under the AMPS hypothesis, the two come into conflict. There is an entanglement between Alice, the in-falling observer, and Bob, the outside observer, which is needed to preserve No Drama. But there is also a second entanglement that emerged from another famous paradox in physics, one related to the question of whether information is lost in a black hole. In the 1970s, Stephen Hawking realized that black holes aren’t completely black. While nothing might seem amiss to Alice as she crosses the event horizon, from Bob’s perspective, the horizon would appear to be glowing like a lump of coal — a phenomenon now known as Hawking radiation.

This radiation results from virtual particle pairs popping out of the quantum vacuum near a black hole. Normally they would collide and annihilate into energy, but sometimes one of the pair is sucked into the black hole while the other escapes to the outside world. The mass of the black hole, which must decrease slightly to counter this effect and ensure that energy is still conserved, gradually winks out of existence. How fast it evaporates depends on the black hole’s size: The bigger it is, the more slowly it evaporates.

Hawking assumed that once the radiation evaporated altogether, any information about the black hole’s contents contained in that radiation would be lost. “Not only does God play dice, but he sometimes confuses us by throwing them where they can’t be seen,” he famously declared. He and the Caltech physicist Kip Thorne even made a bet with a dubious Preskill in the 1990s about about whether or not information is lost in a black hole. Preskill insisted that information must be conserved; Hawking and Thorne believed that information would be lost. Physicists eventually realized that it is possible to preserve the information at a cost: As the black hole evaporates, the Hawking radiation must become increasingly entangled with the area outside the event horizon. So when Bob observes that radiation, he can extract the information.

But what happens if Bob were to compare his information with Alice’s after she has passed beyond the event horizon? “That would be disastrous,” Bousso explained, “because Bob, the outside observer, is seeing the same information in the Hawking radiation, and if they could talk about it, that would be quantum Xeroxing, which is strictly forbidden in quantum mechanics.”

Physicists, led by Susskind, declared that the discrepancy between these two viewpoints of the black hole is fine so long as it is impossible for Alice and Bob to share their respective information. This concept, called complementarity, simply holds that there is no direct contradiction because no single observer can ever be both inside and outside the event horizon. If Alice crosses the event horizon, sees a star inside that radius and wants to tell Bob about it, general relativity has ways of preventing her from doing so.

Susskind’s argument that information could be recovered without resorting to quantum Xeroxing proved convincing enough that Hawking conceded his bet with Preskill in 2004, presenting the latter with a baseball encyclopedia from which, he said, “information can be retrieved at will.” But perhaps Thorne, who refused to concede, was right to be stubborn.

Bousso thought complementarity would come to the rescue yet again to resolve the firewall paradox. He soon realized that it was insufficient. Complementarity is a theoretical concept developed to address a specific problem, namely, reconciling the two viewpoints of observers inside and outside the event horizon. But the firewall is just the tiniest bit outside the event horizon, giving Alice and Bob the same viewpoint, so complementarity won’t resolve the paradox.

## Toward Quantum Gravity

If they wish to get rid of the firewall and preserve No Drama, physicists need to find a new theoretical insight tailored to this unique situation or concede that perhaps Hawking was right all along, and information is indeed lost, meaning Preskill might have to return his encyclopedia. So it was surprising to find Preskill suggesting that his colleagues at the Stanford workshop at least reconsider the possibility of information loss. Although we don’t know how to make sense of quantum mechanics without unitarity, “that doesn’t mean it can’t be done,” he said. “Look in the mirror and ask yourself: Would I bet my life on unitarity?”

Polchinski argues persuasively that you need Alice and Bob to be entangled to preserve No Drama, and you need the Hawking radiation to be entangled with the area outside the event horizon to conserve quantum information. But you can’t have both. If you sacrifice the entanglement of the Hawking radiation with the area outside the event horizon, you lose information. If you sacrifice the entanglement of Alice and Bob, you get a firewall.

“Quantum mechanics doesn’t allow both to be there,” Polchinski said. “If you lose the entanglement between the in-falling (Alice) and the outgoing (Bob) observers, it means you’ve put some kind of sharp kink into the quantum state right at the horizon. You’ve broken a bond, in some sense, and that broken bond requires energy. This tells us the firewall has to be there.”

That consequence arises from the fact that entanglement between the area outside the event horizon and the Hawking radiation must increase as the black hole evaporates. When roughly half the mass has radiated away, the black hole is maximally entangled and essentially experiences a mid-life crisis. Preskill explained: “It’s as if the singularity, which we expected to find deep inside the black hole, has crept right up to the event horizon when the black hole is old.” And the result of this collision between the singularity and the event horizon is the dreaded firewall.

The mental image of a singularity migrating from deep within a black hole to the event horizon provoked at least one exasperated outburst during the Stanford workshop, a reaction Bousso finds understandable. “We should be upset,” he said. “This is a terrible blow to general relativity.”

Yet for all his skepticism about firewalls, he is thrilled to be part of the debate. “This is probably the most exciting thing that’s happened to me since I entered physics,” he said. “It’s certainly the nicest paradox that’s come my way, and I’m excited to be working on it.”

Alice’s death by firewall seems destined to join the ranks of classic thought experiments in physics. The more physicists learn about quantum gravity, the more different it appears to be from our current picture of how the universe works, forcing them to sacrifice one cherished belief after another on the altar of scientific progress. Now they must choose to sacrifice either unitarity or No Drama, or undertake a radical modification of quantum field theory. Or maybe it’s all just a horrible mistake. Any way you slice it, physicists are bound to learn something new.

*This article was reprinted on ScientificAmerican.com.*