The Black Hole Information Paradox

The Black Hole Information Paradox


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.

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