Black Holes
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 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 time scales. 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, and 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 any other influence within the black hole. 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? But 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. But 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. And 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, Hawking had to hack both general relativity and quantum-field theory to do the 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 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 activity and quantum-field 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-field 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 Hawking. 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, who 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 universe is required. The 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 the 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 by transferring quantum information to Hawking radiation, you may still violate the law of conservation of information just as much as you would by deleting it. From the point of view of an observer falling into the black hole, they aren't frozen at the horizon. They fall straight through, 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 conservation of information. Specifically, it would violate 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 those 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 complimentary observables, like position and momentum, that can't both be perfectly measured at the same time. Black-hole complementarity argues that the interior and exterior of a black hole are 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 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 realized that the three-dimensional gravitational and quantum-mechanical interior of a black hole could be fully described by interactions on a 2D surface that did not include gravity.
This led him to realize that the union of quantum mechanics and gravity may require that the entire 3D universe be a projection on a 2D 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 has 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 the 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 of one to better reflect the scrambled information in Hawking radiation. The idea of black-hole complementarity and the results it led 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 the 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 spacetime. Black holes represent the ultimate victory of gravity. Einstein's general theory of relativity reveals them to be regions of frozen time and cascading space.
But the first hint of the existence of black holes appeared long before Einstein. They were glimpsed as dark stars in the mathematics of Isaac Newton's law of universal gravitation. So, to continue your own mathematical journey into black holes, Newton's gravity is the place to start. Brilliant.org has a really comprehensive series on gravitational physics that will take you from Newton's law all the way through gravitational field and celestial mechanics.
And Brilliant leads you on this journey in a series of clear, very gettable steps. You will be solving increasingly complex problems along the way to really training your brain to think like a physicist. Learning about physics is much more than facts and memorizing. But when done right, it can give you a whole new way to look at the universe itself.
Brilliant, math and science done right, is proud to support "Space Time". To learn more about Brilliant, go to brilliant. Last week we talked about the no-hair theory of black holes, and you all had some hairy questions. EpsilonJ asked, what would happen if you fired a continuous beam of electrons at a black hole and how would the charge affect the Penrose diagram? Great question.
If you keep injecting charge into a black hole, then it does maintain an electric charge. That charge only decays if the black hole is left to its own devices. And it turns out that a charged black hole has a pretty weird Penrose diagram. The exterior looks pretty similar to a regular black hole, but the inside is very different. The electric charge within the black hole produces a negative pressure that actually halts the cascade of space within the black hole and propels it back outwards.
In the mathematics, it looks as though anything falling into a charged black hole is ejected into a separate universe. That's a universe of weirdness that we'll do an episode on at some point. Destroctive Blade asks how it can be that the outside of a black hole can feel its electric charge given that the electromagnetic field is communicated by photons and photons can't escape the black hole. Good observation.
So, we talked about a black hole's electric charge in terms of the classical electromagnetic field which has an existence independent of electric charge. But quantum-field theory imagines the electromagnetic force as being transmitted by virtual photons. Now it's important to note the distinction between virtual photons and real photons. Virtual particles in general are just a way to mathematically account for the infinite ways a quantum field can communicate its influence. Virtual particles don't have the same restrictions as regular particles.
They can have any mass, can travel faster than light, and can even travel backwards in time. Check out our episode on the path integral and Feynman diagrams for more info on this wackiness. In this picture, virtual particles can escape a black hole to communicate the influence of the charge within, but it's important not to take the existence of these particles too seriously. The electromagnetic field outside the black hole knows about the charge inside the black hole.
But whether that's because of virtual-particle interaction with the interior or just the persistence of the field at the event horizon is a matter of interpretation. HebaruSan noticed that, in our graphic, the Earth completed 1.75 orbits in the supposed 8 minutes it took the Sun's gravitational field to vanish. Yeah, that was due to time dilation.
There's a very certain special frame of reference, like when you're trying to throw together a quick graphic and forget that "Space Time" viewers notice everything. In these frames of reference, sometimes 21 months takes 8 minutes due to "ran out of time" dilation.
