Black Hole Information Paradox (Script) (Patreon)

Stephen Hawking found a way to vanquish the black hole with his eponymous radiation. But that same radiation threatens the very foundations of quantum mechanics. It may be very well be the loose thread that leads to a theory of everything.

Black holes are engines of destruction that remove from our universe anything that crosses their event horizon. But matter and energy aren’t erased from existence – they add to the mass of the black hole. And we now know that this mass can escape. It gradually leaks away through Hawking radiation over unthinkably long timescales, but in a way, that same Hawking radiation may be more destructive than the black hole itself. It may destroy information. The apparent destruction of quantum information by Hawking radiation defies our current understanding of quantum mechanics,. This is the black hole information paradox. It’s one of the biggest unsolved problems in physics. And the quest for its solution may have completely overturned our understanding of the fundamental nature of the universe. IT may have revealed that the universe is a hologram. 

But I’m getting ahead of myself. First a quick recap. 

In recent episodes we’ve explored some critical facts about the universe and about black holes. First we looked at the law of conservation of quantum information. We saw that the very foundations of quantum mechanics demand that quantum information be preserved forever. With perfect knowledge of the current universe, it should be possible to perfectly trace the universe backwards and forwards in time. The second idea was the no-hair theorem. It states that black holes can only exhibit three properties: mass, electric charge, and angular momentum. The inescapable event horizon shields the outside universe from other influence. 

At first glance, the no-hair theorem seems to contradict the conservation of information. If we see a black hole, how can we possibly figure out what particles went in to form it? Actually, by itself the no-hair theorem isn’t really a problem because even though the black hole swallows information, that information persists inside the black hole. There’s nothing about the law of conservation of information that requires information to remain within our accessible part of the universe – just that it continue to exist somewhere.

But this is where Hawking radiation comes in. Hawking radiation is like a cosmic whiteboard eraser. It causes black holes to evaporate into a perfectly random buzz of radiation that contains none of the information about the original contents of the black hole. We went over this in detail previously, but TLDR the gravitational field of a black hole is expected to distort the surrounding quantum fields. That distortion looks like particles flowing away from the black hole. And the energy to create those particles must come from the mass of the black hole itself.

What type of particles? According to Hawking’s calculation, those particles should come out with energies that follow the black body spectrum. In other words, Hawking radiation should look exactly like the thermal radiation of heat! Black holes should radiate as though they have a temperature that is inversely proportional to their mass. And the mass of the black hole should be the ONLY thing that determines the nature of the radiation. 

The key here is that Hawking radiation doesn’t depend at all on what the black hole is made of. The black hole radiates particles - mostly photons - that contain no information. Eventually the black hole must completely evaporate into those particles, leaving no clue as to what fell into it in the first place. THAT’S the information paradox. Through his radiation, Stephen Hawking found a way to erase quantum information. Which is in severe violation of one of the foundational tenets of quantum theory.

And when Hawking first pointed out the paradox in the mid-70s, physicists were skeptical that there was a real problem. After all, without a theory of quantum gravity he had to hack both general relativity and quantum field theory to do his calculation. To quote theoretical physicist, John Preskill: “I was inclined to dismiss Hawking’s proposal as an unwarranted extrapolation from an untrustworthy approximation.” But over time, the importance of the contradiction became clear. Preskill went on to to say: “I have come to believe more and more (only 15 years behind Hawking) that the accepted principles lead to a truly paradoxical conclusion.”

So it turns out that if we assume that both general relativity and quantum theory are correct as we currently understand them, then Hawking radiation must exist and it must erase quantum information. But there’s no such thing as a true paradox: a deeper understanding of general relativity or of quantum theory must resolve this. The search for the resolution to this paradox has led to some incredible new physics and some pretty astounding ideas.

One of the early solutions is the most outlandish, but was strongly supported by Hawkings. Under a slight modification of general relativity called Einstein–Cartan theory, it’s predicted that the formation of a rotating black hole gives birth to an entire new universe, accessible by a wormhole. That’s cool. So what if all of the information lost into the black hole ends up in the new universe? It would be forever inaccessible to us, but would still exist. This solution to the paradox has been attributed to Freeman Dyson, but was championed by Hawking for many years.

The competing idea is that the information of everything that falls into the black hole becomes imprinted on the Hawking radiation itself. So it stays in this universe; no new universes required. A motivation for this idea is the fact that, from the point of view of an outside observer, nothing ever actually crosses the event horizon. For the outside universe, everything that ever fell into a black hole remains frozen in time and smeared flat over that horizon. It’s essentially invisible, but in principle the information is still there. 

In 1997 the debate between these ideas became a bet. On one side, John Preskill bet that information somehow leaked back out into the universe, on the other side Stephen Hawking and Kip Thorne bet that it was forever lost from our universe. And the stakes? An encyclopedia of the winner’s choice, "from which information can be retrieved at will".

To resolve the bet, physicists had to figure out how quantum information could be transferred to Hawking radiation. But there are two gigantic problems with this idea: One: there’s no known mechanism for that infalling stuff to leave enough of an information imprint to affect Hawking radiation; and two, if it did, it would break quantum mechanics as surely as the old information paradox. Let’s start with the second point.

It turns out that transferring quantum information to Hawking radiation may still violate the law of conservation of information, just as much as you would be deleting it. From the point of view of an observer falling into a black hole, they aren’t frozen at the horizon. They fall straight though, carrying their information with them. That means their information would radiate back out into the universe AND be absorbed into the black hole. The information would be duplicated, violating the conservation of information. Specifically it violates the quantum no-cloning theorem.

Physicist Leonard Susskind has argued that there is no violation. The two copies of the information are completely disconnected; no observer can ever see both. In fact, because the interior of the black hole doesn’t even exist on the same timeline as the external universe, it’s arguable that these copies don’t even exist at the same time. This idea is known as black hole complementarity. You might remember that there are certain pairs of quantum observable – complementary observables like position and momentum – that can’t both be perfectly measured at the same time. Susskind argues that the interior and exterior of a black hole is not simultaneously knowable in exactly the same way.

OK, so we can argue our way around the no-cloning theorem with black hole complementarity, but there was still no known mechanism for this to happen. The solution began with physicist Gerard t’ Hooft. He did a more careful calculation of the effect of infalling material and found that it doesn’t exactly freeze above a completely static horizon; rather it distorts the event horizon, creating a sort of lump at the point of crossing. Those distortions should contain all of the information about the infalling material. And in principle those distortions could potentially influence outgoing Hawking radiation, allowing them to carry away their information.

This idea seems straightforward, but it has stunning implications. T’ Hooft realised that the 3-dimensional gravitational and quantum mechanical interior of a black hole could be fully described by interactions on a 2-D surface that did NOT include gravity. This led him to realize that the union of quantum mechanics and gravity may require that the entire 3-D universe be a projection on a 2-D structure. Leonard Susskind formalized this idea in the context of string theory, in what we now know as the holographic principle. This is definitely something we’ll come back to, because, besides giving a concrete mechanism by which information can be stored on the surface of a black hole, it may imply that the entire universe is a hologram.

Exactly how the information on an event horizon gets attached to Hawking radiation is still contentious, but a number of physicists have proposed possibilities. Stephen Hawking himself also jumped into that game, suggesting that quantum tunneling from within the black hole could interact with the holographic horizon and carry information back out into the universe. But to enter that game, Hawking had to concede the old bet and admit that information does escape black holes. He gave John Preskill an encyclopedia of baseball, but joked that maybe he should have given him the ashes, to better reflect the scrambled information in Hawking radiation.

The idea of black hole complementarity and the results it lead to are by no means fully accepted. They are, of course, untested. But black hole complementarity introduces yet another paradox: it suggests that each particle of Hawking radiation should be simultaneously entangled with the interior of the black hole and with all past Hawking radiation. This violates the principle of monogamy of entanglement. We’ll have to come back to this also, and to the proposed solution: the black hole firewall.

It never fails to amaze me how one little loose thread – a seemingly insignificant quirk in theory – can lead to massive discoveries, and complete reframing of physics. That cute little 1974 paper in which the young Stephen Hawking showed that black holes must leak, very slightly, has led to radical new ideas about the nature of information and entropy, exploded the field of string theory, and hinted at the possible holographic nature of space time.