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.
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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.