MATT O’DOWD: Thank

you to Brilliant.org for supporting PBS

Digital Studios. 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. [MUSIC PLAYING] 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.org/spacetime. 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.