Is It IMPOSSIBLE To Enter a Black Hole? (Patreon)

So you’ve decided to  jump into a black hole. Good news: as long as the black hole is big enough you can sail through the event horizon without harm and get to experience the interior of the black hole before you’re annihilated by the central singularity. Or so we once thought. These days, quite a few physicists believe that the only way to avoid horrible contradictions in fundamental physics generated by black holes is for all them to be surrounded by screens of extreme energy that prevent anything from ever entering the event horizon. Sounds outlandish? Welcome to black holes. So let’s find out why many of our most brilliant physicists take these black hole firewalls deadly seriously.

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Einstein’s general theory of relativity has been wildly successful at describing the behaviour of space and time and gravity and its crazy predictions have been verified over and over, from time dilation to  black holes to gravitational waves. And it all started with this one idea—what Einstein called his happiest thought—that there is a fundamental equivalence between the feeling of floating you have when falling and the same feeling of floating in the absence of gravitational fields. All of general relativity came from following this equivalence principle to its logical conclusions, plus the thing about the speed of light being constant for everyone. That’s why it makes physicists very sceptical when a new idea appears to violate this principle. But what if the alternative to violating equivalence is violating something that’s even more fundamental? 

In recent episodes, we saw how the prospect o f black holes either destroying or duplicating quantum information violates something called unitarity—as foundational to quantum mechanics as the equivalence principle is to general relativity. TLDW: if black holes both swallow quantum information and also radiate that information as Hawking radiation, then the same bit of quantum info is in two places at once and physics breaks. But if you don’t let quantum information fall into the black hole in the first place then you violate the equivalence principle, because this principle tells us that nothing special or weird should happen to anything falling through an event horizon—as long as that horizon is large enough so there’s no observable tidal force.

This catch-22—violate unitarity or equivalence—is the black hole information paradox. One way around this is to argue that apparent qubit duplication is fine as long as there’s no observer—no conceivable reference frame—that can access both versions of the information. This is black hole complementarity, and in our previous episode on the topic we followed the adventures of Alice and Bob as they attempted to outsmart reality and observe both the swallowed and the Hawking radiated qubit. But reality was too smart for them—it seemed impossible for one observer to ever see duplicate qubits. 

For a while, this black hole complementarity was thought to have solved the black hole information paradox, but it turns out it’s not as neat a solution as we had hoped. Not long after these early Alice and Bob expeditions were conceived, a new thought experiment appeared that may have found a way to outsmart reality after all. The thought experiment didn’t just reveal a way to detect quantum cloning, but also necessitated the appearance of a firewall—a screen of extreme energy that prevents anyone ever entering a black hole in the first place.

This proposal saves unitarity, but violates the equivalence principle so utterly that many physicists despise the idea. And yet some argue that the chain of logic behind the firewall is so robust that we need to seriously consider throwing equivalence out the window.

So how did we end up in this unfortunate state of contradictory affairs? Well, to understand that we need to go back to the black hole information paradox and understand it in terms of not just quantum information, but also quantum entanglement. Quantum entanglement is when a pair of quantum objects are correlated with each other in a sort of fuzzy way, such that the information about their individual states is undetermined—it’s in a superposition of multiple states at once. But this superposition of states is correlated between the entangled pair, such that the measurement of one defines the properties of the other. We have episodes on this crazy stuff if you want to dig into that weird hole. But for now just know that quantum entanglement is ubiquitous and the information about quantum systems is largely woven into webs of entanglement. That’s why entanglement is important for the information paradox.

So let’s look at entanglement in black holes. As a black hole grows, so does its entropy. This is the finding by Steven Hawking and Jacob Bekenstein that led to the black hole information paradox in the first place. Entropy is basically a measure of the information that’s hidden in a system that we can’t access. Black hole entropy grows because almost all the details about the stuff that fell in is lost to us. Most physicists think that this information has to be somehow encoded on the horizon and then must escape as Hawking radiation, because if it didn’t then it would blink out of existence when that same Hawking radiation causes the black hole to evaporate. 

The high entropy at the horizon means that the qubits on the horizon are all entangled with each other—the quantum information about their original pre-falling-in state is scrambled across the horizon. When the first particle of Hawking radiation leaks out it contains almost no information about the stuff that fell in because that information is spread across its entanglements with other horizon particles. 

But as more and more particles leave, we can start to see patterns. Information about the material that fell in could, in principle, be slowly reconstructed. That really only becomes possible when the particles of Hawking radiation are no longer exclusively entangled with the inaccessible horizon, but rather with other particles of Hawking radiation. There’s a very specific transition point when the qubits remaining on the horizon are mostly entangled with qubits in the expanding cloud of Hawking radiation—we would say that the entanglement between the black hole and the Hawking cloud is at its maximum, and it’s around half the mass of the black hole is evaporated, but in terms of time it’s about 90% of the way to complete evaporation. This moment is called the  Page time, after Don Page who figured out how the entanglement entropy of black hole horizons must first rise as information  and then shrink. After this time it becomes increasingly possible to find and decode pairs of entangled Hawking qubits.

So let’s consider a single qubit that’s still encoded on the horizon at around the Page time. It’s entangled with a distant particle of Hawking radiation. It now wants to join its quantum sibling and become Hawking radiation itself. 

A popular way to describe Hawking radiation is like this: in the vacuum of space, pairs of matter and antimatter particles are constantly appearing and vanishing. If this happens at an event horizon, one of these particles can be captured, leaving the other free to escape and effectively become Hawking radiation. A more precise way to describe this is in terms of quantum field theory—and we obviously have an episode on this. We can describe the vacuum of space as consisting of equal parts positive and negative frequency modes of the quantum fields in that space—equal and opposite vibrations in those  fields that cancel each other out perfectly. Black hole horizons perturb these modes, and the non-perfect cancelling leads to a non-perfect vacuum. The quantum fields end up in excited states, and this manifests as particles—of Hawking radiation. However you like to describe Hawking radiation, we have one thing being swallowed by the black hole and one escaping. 

And listen, because this is very important—these pairs of swallowed and radiated things have to be entangled with each other. In fact it’s been argued that the fabric of space is stitched together by the entanglement between these virtual particles or modes. The entanglement of adjacent fluctuations is fundamental. In fact, it seems that without this entanglement there is no space. That’s something we’ll come back to another time, but keep it in mind for now.

OK, so back to our qubit sitting at the horizon waiting to radiate away. It’s entangled with a distant qubit of Hawking radiation, but it also needs to be entangled with an adjacent qubit just below the horizon. Without the latter there is no partner particle or mode that it can sacrifice to the black hole in order to escape. So this qubit must be entangled twice—with both the Hawking cloud and the black hole interior. 

You might say it’s quite promiscuous in its entanglement. Naughty qubit—quantum mechanics has rules about these things. In fact, we know that entanglement has to be monogamous. Monogamy of entanglement says that if a pair of qubits are maximally entangled with each other then neither qubit can share any entanglement with a third qubit outside this pair. Monogamy of entanglement is closely related to the no-cloning theorem, and absolutely violates unitarity. 

If we want to avoid over-entangling our black hole it seems we need to break one of these entanglements. Because the entanglement over the Hawking radiation holds the information we want to preserve, it’s safer to break the entanglement between qubits above and below the horizon. Unfortunately there are dire consequences to doing that. It takes energy to break any entanglement. You can calculate the amount of energy required to break the links between the swallowed and radiated particles at the horizon. It’s a lot of energy. In fact in order for all Hawking radiation to break its entanglement connection with the black hole there would need to be a screen of energy just above the horizon so intense that nothing could ever cross that horizon without being completely thermalized. Severing entanglement requires a firewall.

Incidentally, the firewall solves the violations of unitarity in two ways: it breaks the entanglement between the Hawking radiation and the interior of the black hole, so monogamy of entanglement is saved. And it also stops anyone observing the interior of the black hole by turning them to plasma. That makes it extra impossible to even think about observing the same qubit both inside and outside the black hole. And this firewall wouldn’t be visible to a distant observer—the extreme gravitational redshift of the radiation emerging from a miniscule Planck length above the horizon would turn that radiation into faint Hawking radiation.

OK, so firewalls sound cool and useful even if they ruin our trip into the black hole. Unfortunately, the firewall hypothesis pretty thoroughly violates the sacred idea we started with: the equivalence principle. 

More formally, the equivalence principle states that there’s no experiment you can do on the local patch of spacetime to distinguish between this freefall or gravity-free floating, or between standing still against a gravitational field with a certain g-force versus acceleration absent gravity with the same g-force.

If Alice is in freefall towards an event horizon, the equivalence principle says that she should measure a quantum vacuum consistent with empty space and should see no local sign revealing the location of the event horizon. But the firewall is a hell of a sign. It reveals to Alice that the vacuum is massively altered by some apparently non-local influence.

The black hole firewall paradox is a refinement of the black hole information paradox. It’s also called the AMPS paradox after the physicists who first outlined it in 2012:  Ahmed Almheiri, Donald Marolf, Joseph Polchinski, and James Sully. Whether or not firewalls exist—and physicists are still divided on this—the main point of the AMPS paper was to show that the black hole information paradox is still a paradox. In particular, it’s not fully solved by black hole complementarity. As we saw in our episode on the topic, it’s possible to hedge around the problem of quantum cloning by noting that no possible observation can detect that cloning. 

But the firewall paradox grants a way to cheat. For example, Alice could descend very close to the event horizon to see if there’s a firewall. If there is then the equivalence principle is violated. That’s bad. If there isn’t, she has evidence that quantum entanglement must exist across the event horizon. She could then back out and see that quantum entanglement also exists between the horizon and the past Hawking radiation, revealing that monogamy of entanglement is violated and with it unitarity. Also bad. 

So the power of the firewall argument is that Alice can learn whether the exterior and interior of the black hole are entangled without having to enter the black hole. That seems to defeat the main value of black hole complementarity, even if this complementarity seems to be still needed for other things.

If firewalls do exist, then it’s not just that the black hole interior is inaccessible, it means the black hole interior may not exist. Breaking the entanglement between the vacuum modes across the horizon is the same thing as breaking the stitching of the fabric of space itself. In a regular black hole, that spatial fabric ends at the central singularity. If firewalls exist, then it’s like the singularity has expanded to the event horizon, and that there’s literally nothing—not even a vacuum—beneath.

So, what’s it all mean? This is not a solved problem. Some, including the AMPS four, argue that breaking the equivalence principle is less radical than breaking unitarity, and so favour the firewall. But breaking equivalence is radical enough, and many would prefer a solution which doesn’t violate either. For example we have Leonard Susskind and Raphael Bousso, who both point to other very general options. If we don’t want to break unitarity or the equivalence principle, we have to admit that the theories we use to describe the happenings above the event horizon are broken. For example, that the quantum field theory we’re using to describe these vacuum modes and Hawking radiation break down. But this is the same QFT that works perfectly well in situations that are no more extreme than the event horizon of a large black hole. 

There are some other pretty funky notions. For example Gary Horowitz and Juan Maldecena have a scheme to reframe quantum field theory with both forward and backward causal directions, which enables the information swallowed by the black hole to effectively teleport back out to the horizon qubit. This avoids the need to break entanglement and so ignite firewalls. Or maybe a full theory of quantum gravity will help us to avoid information-swallowing black holes after all. For example, fuzzballs of string theory propose that matter unravels into giant balls of elementary strings below the event horizon. These happen to offer a way to move quantum information from below the horizon back into the universe, avoiding the firewall. 

Long story short is that the black hole firewall paradox tells us that our current ways of thinking about black holes need to be cleaned up. Many believe that this little glitch in the consistency of our best theories of nature is the most promising path to a deeper theory that could unite quantum mechanics and general relativity. These ideas may even lead us to an idea we’ll explore soon—to an understanding of how space emerges from quantum entanglement, and how, if we unstitch that entanglement, we get firewalls at the end of space time.