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“PARADOXES are good in physics,” reflects . “They help to point the way towards important discoveries.” Quantum mechanics and Einstein’s theories of relativity offer plenty to choose from. There’s the cat that can be dead and alive at the same time. Or the Back to the Future-style time traveller who kills his own grandfather, rendering his own birth impossible. Or the twins who disagree on their age after one returns from a near light-speed trip to a neighbouring star. Each perplexing scenario forces us to examine the fine print of the problem, thereby advancing our understanding of the theory behind it. A case in point is Einstein, whose own theories came from trying to resolve the paradoxes of his time.

Now Preskill, a theoretical physicist at the California Institute of Technology in Pasadena, is scratching his head over the latest one to surface. Nicknamed the black hole firewall paradox, it comes about when you consider what happens to someone falling into a black hole.

With the nearest black hole more than 1000 light years away, the question is very much a theoretical one. Yet just by studying such a possibility, physicists are hoping to make a breakthrough in their efforts to combine general relativity and quantum mechanics into a theory of quantum gravity – one of the most intractable problems in physics today.

Black holes have long been fertile breeding grounds for paradoxes. Back in 1974, Stephen Hawking, along with Jacob Bekenstein of the Hebrew University in Jerusalem, Israel, famously showed that black holes are not entirely black. Instead, they radiate energy known as Hawking radiation comprising photons and other quantum particles – an agonisingly slow process that eventually causes the black hole to evaporate completely.

Hawking spotted a problem with this picture. The radiation seemed so random that he surmised it couldn’t carry any information about the stuff that had fallen in. So as the black hole evaporates, the information it holds must eventually disappear. Yet this is in direct conflict with a central tenet of quantum physics, which says that information cannot be destroyed. The black hole information paradox was born.

Over the decades, physicists have struggled with this paradox. Hawking thought that black holes destroyed information and the answer was to question quantum mechanics. Others disagreed. After all, Hawking’s idea came from his efforts to meld general relativity and quantum mechanics – a mathematical feat so elusive that he was forced to make approximations. Preskill even made a bet with Hawking that black holes don’t destroy information.

Several arguments suggest that Hawking was wrong. One of the most compelling comes from thinking about what happens as the evaporating black hole gets smaller and smaller. If information can’t escape or be destroyed, then more and more has to be stored in an ever-shrinking volume. But if this is the case, quantum theory says the probability for making a tiny black hole increases from virtually nothing to almost infinity wherever matter collides against matter. “You should have seen it at the Large Hadron Collider, you should have seen it at Fermilab, you should have seen it in tiny room-sized particle accelerators from the 1930s,” says , a theorist at the University of California in Santa Barbara (UCSB). “You should see it when you go and jump up and down on the grass.”

Obviously that hasn’t happened. The other possibility – that matter and the information it carries can leak out from a black hole – is unlikely. Any material that falls in would need to travel faster than light to escape the black hole’s fearsome gravity.

Perhaps, instead, the answer lies with the Hawking radiation itself. Maybe it isn’t so featureless. “A common reaction was that Hawking had simply been careless,” says , also at UCSB. “It wasn’t that information was lost, it was that he hadn’t kept track of it enough.”

Yet all early efforts to do away with the paradox proved unsuccessful. “Hawking had identified a really deep problem,” says Polchinski.

As it happened, Hawking changed his mind in 2004, partly due to work by an Argentinian physicist called Juan Maldacena (see “Hawking’s change of heart“). Black holes don’t destroy information after all, he conceded. He honoured the bet he made with Preskill and presented him with an encyclopaedia of baseball, which , because it was heavy and it took effort to get information out of it.

Into the abyss

Attention soon shifted to wondering how information could get out of a black hole. This isn’t an easy question to answer. And it is by exploring these issues that the new black hole firewall paradox has come into sharp focus.

A firewall is the catchy new term for something physicists have long suspected might happen if information escapes from a black hole. To understand the argument, we need a simplified picture of Hawking radiation. The vacuum of space-time is constantly producing pairs of virtual particles, which pop into existence and just as quickly disappear. This picture changes near the black hole’s event horizon, considered the point of no return for anything falling in. Occasionally one of the pair is sucked into the black hole while the other escapes. It is a rare particle that flees a black hole, but it is these that constitute Hawking radiation.

Now if Hawking radiation is carrying out quantum information, then that creates a problem. One of Hawking’s great insights was to show how quantum theory, general relativity and thermodynamics are all linked at a black hole. This means that the paired particles just inside the event horizon would become immensely energetic as information is transferred to their partners outside, creating a wall of fire hot enough to burn up anything, or anyone, falling into the black hole.

This dramatically contradicts anything general relativity tells us about black holes. In fact, such firewalls seemed so preposterous that physicists started looking for ways to transfer information out of the black hole without such transgressions.

One possibility has been put forward by , also at UCSB. Building on work done by of Ohio State University, Giddings developed a . The work showed that if quantum theory breaks down in the vicinity of the event horizon, then it is possible to transfer information from within the black hole to distant outside regions, and thus avoid creating a firewall.

The trouble is, for it to work, Giddings had to relax the law that forbids faster-than-light information transfer. Another problem was that he couldn’t say exactly where in space-time quantum theory should break down. Still, it was a tantalising idea.

Enter Polchinski and his students Ahmed Almheiri and James Sully. They reckoned they could crack the problem by combining Giddings’s model with earlier work carried out by Leonard Susskind at Stanford University in California.

That meant reconciling the model with three postulates put forward by Susskind, which many physicists hold dear. One is, of course, that information is not lost as a black hole evaporates. The others relate to thought experiments using two observers called Alice and Bob who are approaching a black hole. Intrepid Alice crosses the black hole event horizon. Cautious Bob stays outside.

According to the second postulate, Bob sees nothing unusual as he sits outside the black hole. The third postulate says that Alice also sees nothing amiss as she crosses the event horizon. That’s because the event horizon is not a physical boundary, it is just an ordinary patch of vacuum in an ordinary patch of space-time that curves gently.

Polchinski and his colleagues failed in their attempt to reconcile all three – if information wasn’t lost then the firewall still existed and Alice ended up burning to a crisp. But that didn’t deter them. “You first try to do something, and if you fail to do it, you try to prove that it is impossible,” says Polchinski.

Their colleague Marolf joined them in this new effort and their work led to a paper, published last July, showing that the postulates cannot all be true simultaneously (). It caused a storm of controversy; there are already more than 40 papers discussing the work, including one that says the answer is to ignore gravity.

If Hawking radiation does carry quantum information out of the black hole, as many think it does, then quantum mechanics has a few things to say about it. Let’s say particle A of Hawking radiation comes out early in the life of the hole. Quantum theory says that particle A shares a spooky connection, or is entangled, with another Hawking radiation particle that emerges later in the life of the black hole.

Now, think about particle B, which exists much later than A. Particle B is one of a pair of particles, B and C, produced at the horizon, and C has fallen into the black hole. Space-time at the horizon is assumed to be nothing special, just gentle gravity and low curvature. This demands that the virtual particles produced at the horizon be entangled with each other. So B must be entangled with C. But since early and late Hawking radiation must be entangled, B is also entangled with A.

Unfortunately this violates another cherished principle of quantum mechanics known as the monogamy of entanglement. Simply speaking, it says that particle B can be entangled with A or C, but not both.

So the conundrum has come full circle. If we want to get information out of a black hole, A must be entangled with B. If we want the vacuum of space-time to be ordinary at the event horizon – which is what allows Alice to slip into the black hole without bursting into flames – then B must be entangled with C. Something has to give. Is it going to be quantum mechanics or general relativity?

Take quantum mechanics and its prediction that information is conserved. Could this be wrong? Polchinski doesn’t think that is possible because of Maldacena’s work, which is one of the strongest mathematical statements in favour of leaving quantum mechanics as it is. What’s more, quantum mechanics is a theory that has been extremely well tested, and even tiny changes put it at odds with experimental results.

The other option is to call into question the state of the vacuum at the horizon. Messing with monogamy could be avoided if particles B and C on either side of the horizon aren’t entangled. But destroying this entanglement leaves the black hole’s event horizon in an agitated thermal state and re-instates the firewall. Instead of floating across the event horizon without drama, Alice would face instant incineration by temperatures as high as 10³² kelvin.

This has dismayed Marolf. General relativity says crossing a black hole’s event horizon should be uneventful. “A firewall would be a strong violation of general relativity,” he says. “In that struggle between general relativity and quantum mechanics, general relativity loses badly. I feel bad about that, because I think of myself as a relativist by training.”

“In the struggle between general relativity and quantum mechanics, relativity loses badly”

Fresh thinking

He’s not alone in finding it unpalatable. “You are sailing along fairly fine in this very smooth space-time, and all of a sudden, bam! you hit this firewall and just burn up,” says Preskill. “It’s pretty crazy.”

“You’re sailing along through space-time and then, bam! you hit this firewall and burn up”

Nonetheless, the firewall is the best explanation if black holes transfer information into the Hawking radiation. Susskind remains sceptical of firewalls, but he has argued that , which in traditional black hole physics lies at the centre of the black hole, to the horizon.

Even if firewalls do form, Susskind differs on when they might form. For instance, for a black hole with the radius of a proton, Polchinski, Marolf and colleagues say that firewalls would form 10^-20 seconds after the formation of the black hole, while in Susskind’s view it would take as long as the age of the universe.

Regardless of when firewalls form, if they do, then space-time as we know it may terminate at the horizon. “If the entire black hole horizon becomes this firewall that cuts off the interior, maybe the interior just doesn’t exist,” says Marolf.

The paradox would also be resolved if there is something special about space-time near a black hole, so that information can be transferred faster than the speed of light. Maybe Giddings and Mathur were on to something, although that would be another blow to relativity.

The upshot of all this is that nearly 40 years after Hawking proposed the black hole information paradox, the problem hasn’t gone away. It has just made physicists look deeper at their theories. “I am as confused as I was 20 years ago,” says Polchinski.

Preskill says this isn’t a bad thing. “There is always a fourth possibility: none of the above, something we haven’t thought of. Any way it shakes down, it’s going to be interesting,” he says. “All the options are crazy, that is what’s so wonderful about the situation.”