Alice and Bob Meet the Wall of Fire

How a new black hole paradox has set the physics world ablaze.

Illustration by NASA/JPL-Caltech

An illustration of a galaxy with a supermassive black hole shooting out jets of radio waves. 

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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.

Joseph Polchinski, a string theorist at the University of California, Santa Barbara, is the “P” in the “AMPS” team that presented a new hypothesis about black hole firewalls.

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.

Illustration courtesy of John Preskill

With quantum correlations, Bob can be highly entangled with Alice or with Carrie, but not both.

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 asecond 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.

Illustration courtesy of Joseph Polchinski

The entanglement of particles in the No Drama scenario: Bob, outside the event horizon (dotted lines), is entangled with Alice just inside the event horizon, at point (b). Over time Alice (b’) drifts toward the singularity (squiggly line) while Bob (b”) remains outside the black hole.

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.

Illustration courtesy of Joseph Polchinski

The Hawking radiation is the result of virtual particle pairs popping into existence near the event horizon, with one partner falling in and the other escaping. The black hole’s mass decreases as a result and is emitted as radiation.

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.

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  • This is just a fantastic piece, taking on ridiculously abstract/far-from-experience ideas and making them come to life.

    I have just one quibble. You follow just about everyone in saying that Einstein “ridiculed” entanglement as “spooky action at a distance.” In my ever humble opinion, that is a now distressingly standard mischaracterization of what Einstein was saying.

    The original of that phrase comes from a letter to Max Born in the forties. Here’s the passage:

    “I cannot make a case for my attitude in physics which you would consider at all reasonable. I admit, of course, that there is a considerable amount of validity in the statistical approach which you were the first to recognise clearly as necessary given the framework of the existing formalism. I cannot seriously believe in it because the theory cannot be reconciled with the idea that physics should represent a reality in time and space, free from spooky actions at a distance. I am, however, not yet firmly convinced it can really be achieved with a continuous field theory, although I have discovered a possible way of doing this which so far seems quite reasonable…But I am quite convinced that someone will eventually come up with a theory whose objects, connected by laws, are not probabilities but considered facts, as used to be taken for granted until quite recently. I cannot however, base this conviction on logical reasons, but can only produce my little finger as witness, that is I offer no authority which would be able to command any kind of respect outside of my own hand.” (Einstein to Born, 2 Mar. 1947.)

    Born comments: “I too had considered this postulate [that physics should represent a reality in time and space] to be one which could claim absolute validity. But the realities of physical experience had taught me that this postulate is not an a priori principle but a time-dependent rule which must be, and can be, replaced by a more general one.”

    Born’s remark could be a motto for this entire piece. But while Einstein was a master of the pungent phrase, he’s not ridiculing anything here, except, perhaps, his own mulishness in the face of all the power of the new formulation. One thing to remember is that he used the spooky thing in the context of an informal letter to one of his oldest friends and someone who had been over the years as sympatico a physical thinker as any in Einstein’s circle. It’s easy, I think — and lord knows lots of folks have done so — to pick on this phrase and God’s dice and some others and paint Einstein as reflexively dismissive of quantum mechanics. But he wasn’t — and he even (perhaps ruefully, though I don’t really think so) knew just how much he’d contributed both to the specific underpinnings of quantum theory and to interpretations he came to dislike. (For example, in a much earlier letter to Born he wrote “That business about causality causes me a lot of trouble too” as he came to realize that there seeme to be a “statistical residue” in any account of “the quantum absorption and emission of light…” — this in 1920, years before quantum mechanics reared its head.)

    I do feel like I’m becoming the guy who keeps shouting “but “data” is plural!” — but still, I don’t think it’s accurate to characterize Einstein’s reaction to QM in general or entanglement in particular as scornful or ridiculing. It perplexed him, worried at him, and troubled him precisely because he took it so seriously. I do know that we’re probably stuck with the image of the old Einstein as this almost comically shouting against the indignities of QM — but it don’t seem right to me.

    [Exhales] There, I feel better.

  • By far the best popular account of the topic. Nevertheless I have the following two simple comments.

    1) In the second paragraph from the beginning – credit for the phrase “No Drama” should go to Joe Polchinski.

    2) Last line of the third paragraph,”… at least one of three cherished notions in theoretical physics must be wrong”- to improve the readability, mention what are those three principles of physics. I know you have done a good job of explaining them in the next section/paragraph.

  • Yes, very interesting and, to my mind as merely a retired information systems analyst, very curious, indeed. I have great difficulty grasping physicists’ conception of information as it’s purported to apply to the universe. So, let me ask: is information maintained by particle collider experiments? It seems to me that no information pertaining to the configuration of the disintegrated matter can persist…

    Conceptually, it seems to me that the physical conditions approaching the event horizon of a black hole become nearly identical to those produced by particle accelerators. Poor Alice would be accelerated to nearly the speed of light. Since this conflicts with the rules governing mass and velocity, as I understand, I suggest that poor Mary’s atoms begin to heat up and vibrate to the point that they disintegrate into more fundamental particles. They in turn would eventually forcibly collide, disintegrating completely, similarly to particle collider experiments.

    What happens to the mass-energy of particles collided at the energies of, for example, the LHC? It seems to me that, within the conditions of the LHC, the tiny amounts of liberated mass-energy must dissipate into space along with the particle residue that it once bound together in a persistent configuration within locally halted spacetime.

    Considering the matter disintegrated as it approaches the event horizon of a black hole, its much larger quantities of now liberated mass-energy is not free to dissipate into space: it must be drawn into the event horizon, retained there, redirected to the focal point of its gravitational energy, the dimensionless singularity. Meanwhile, extremely hot, high velocity residual particle energy may be captured (perhaps in a ‘firewall’) in a magnetic field of its own creation, directed to the black hole’s polar jets, where is is expelled as high energy fundamental particles.

    In this process, there is no dimensional matter retained within any dimensional singularity, but the gravitational energy retained within the event horizon – directed to a singular focal point, or abstract singularity. This scenario avoids the problem of retaining dimensional material within a dimensionless singularity, while conceptually accounting for the hot accretion disk and relativistic polar jets of active black holes. I can’t account for any information, since material energy is physically separated from its binding mass-energy, never again to be reunited, at least within this universe…

    BTW, I came up with this idea based on a quip I heard from, I think it was Kip Thorne, that black holes don’t contain any matter…

  • Contrary to what the article states, Isn’t Complementarity a principal developed by Niels Bohr in 1927, *not* specifically to reconcile the viewpoints of observers on two sides of an event horizon?

  • So, I have been reading and trying to find out, why does the anti-particle of the PP have to be the one sucked into the black hole?

    Isn’t it as statistically like for a “real” particle to fall in?

  • I’m not a physicist, but I’ve always had one question about Alice and Bob. As Alice falls into the black hole, she accelerates, leading to time and space dilation. If she is shooting a photon back at Bob every second, he sees increasingly red-shifted photons at increasing intervals, but I was under the impression that the stream would never actually halt; the math was such that from Bob’s point of view Alice would never pass the event horizon. This would mean that, from Bob’s point of view, the event horizon would be surrounded by thin skin of flattened objects (which seems to me to be very similar to the wall of fire). Various quantum events, such as (but not limited to) pair formation, would occur within the skin, allowing some particles to escape, potentially carrying information about the composition of the skin (i.e. about items that fell into the back hole at arbitrary points in the past).

    I do recall that a black hole’s angular momentum has some sort of effect on the event horizon, so perhaps Bob does eventually see Alice pass the event horizon, but even recent explanations of dilation effects near black holes (such as in Susskind’s “The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics”) seem to agree with what I’ve said above.

  • Sam: Bob does not see Alice forever descending, even though time dilation from special relativity would predict that. What happens is that the event horizon expands outwards as Alice descends, essentially reaching out and grabbing her! This is because she has mass/energy too and also warps space-time. If this didn’t happen, it would be impossible to make black holes in the first place.

  • Dear readers: In an article I had published in Z.f. Naturforschung Physical Sciences 56a, 889 (2001), entitled “gamma ray bursters and Lorentzian Relativity”, I showed the following: 1.Cutting off the zero point vacuum energy at the Planck energy creates a distinguished refeference system at rest with this zero point energy, which without such a cut-off is Lorentz invariant up to the Planck energy. 2. The same must be true for the general theory of relativity, wich remains valid up to this energy. And as long as the astronomical objects, called black holes, move against this distinguished reference system with non-relativistic velocities, general relativity for particle energies small compared to the Planck energy, remains a good approximation. 3. According to the pre-Einstein theory of relativity by Lorentz and Poincare, objects for energies below the critical Planck energy are held together by electrostatic forces (or forces acting like them) in a stable equilibrium, as solution of a elliptic partial differential equation derived from Maxwell’s equation. 4.In reaching and passing the velocity of light, the elliptic equation goes over into an hyperbolic equation, similar as in the transition from subsonic to supersonic fluid mechanics. 6. While no particle accelerator can reach the Planck energy, a particle falling into a black hole can reach this energy in approaching the event horizon (Schwarzschild radius). 7. According to Schwarzschild’s interior solution, the event horizon first appears as a point in the center of a spherical mass in the course of its gravitational collapse. Thereafter the event horizon moves as a spherical surface radially outwards. In reaching the event horizon and the Planck energy, the particles disintegrate into leptons and photons, transforming the entire mass into a burst of radiation. This will result in a gamma ray burst with an energy equal to mc^2, where m is the order of a solar mass. And this is the firewall avoiding the problem of information loss and violation of unitarity.

  • Dear Ms. Ouellette:
    your article regarding the black hole firewall controversy is without any doubt the best I have seen. You and your readers may perhaps be interested to read my comments about the same on Professor Preskill’s quantumfrontiers blog. dated Dec. 3, 2012. Some readers incorrectly think that the firewall is Hawking radiation, which has never been observed, and which is very different from the gamma ray bursters (which are frequently seen). The important point is that the zero point energy of the vacuum cannot be ignored. It has a w^3 frequency spectrum solely obtained with quantum mechanics. This spectrum is frictionless and the only one invariant under a Lorentz transformation.One can therefore say it is the zero point vacuum energy which generates the Minkowski space-time of special relativity. But if it is cut off at the Planck length it creates a preferred reference system in which this energy is at rest. In the context of quantum gravity (not the daily life or the LHC) it makes a difference what the velocity against this absolute reference system is. Because the Planck energy is so high the special and general theory of relativity remain extremely good approximations, but not in approaching the event horizon where in the preferred reference system the velocity of light and the Planck energy is reached.

  • Just a note. There are two quite different concepts of complementarity here; which I will call Bohr complementarity and Susskind complementarity. There are some parallels between them … they were both developed in an attempt to avoid paradoxes, and in both of them,there are two complementarity points of view, which you cannot consider simultaneously. However, Susskind complementarity is not a special case of Bohr complementarity.

  • If the quantum mechanical multiverse depends on unitarity, then does this suggest that black holes are locations where the multiverse is combined into one single universe?

  • I dont think singularity is the key, rather the horizon. Imagine you accelerate constantly and the horizon comes to exist instantaneously. The question is the information behind the horizon can ever be retrieved in the accelerated frame? How can we preserve information in this case?

  • Peter S. Susskind himself refers to it as “Black Hole Complimentarity” and it is as you say something completely different from earlier complimentarities :-)

  • Hmmmm… Should Alice be consumed by a firewall, then based on the state of quantum entanglement should not Bob also have the same state. Therefore though the information is not lost, neither can Bob recover the information.

    Does Bob on the other hand disentangle from Alice when she is engulfed within the firewall and acquires a new non-entangled, Aliceless state. Does that lead to the next level of QM where Bob is a particle without entanglement within the quantum universe? QM with entangles particle pairs and non-entangled particles. >

  • It seems to this non-physicist that information can indeed be lost in a BH. Bob is free to compare his information with Alice’s after she falls through the event horizon, but only until she meets the singularity, which she cannot avoid doing. That is an event with a probability of one, preserving unitarity. Did I miss something?

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