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So you’ve decided to jump into a black hole. Good news: as long as the black hole is big enough you
can sail through the event horizon without harm and get to experience the interior of the black
hole before you’re annihilated by the central singularity. Or so we once thought. These days,
quite a few physicists believe that the only way to avoid horrible contradictions
in fundamental physics generated by black holes is for all them to be surrounded by
screens of extreme energy that prevent anything from ever entering the event
horizon. Sounds outlandish? Welcome to black holes. So let’s find out why
many of our most brilliant physicists take these black hole firewalls deadly seriously.
Einstein’s general theory of relativity has been wildly successful at describing the behaviour
of space and time and gravity and its crazy predictions have been verified over and over,
from time dilation to black holes to gravitational waves. And it all started with this one idea—what
Einstein called his happiest thought—that there is a fundamental equivalence between the feeling
of floating you have when falling and the same feeling of floating in the absence of
gravitational fields. All of general relativity came from following this equivalence principle to
its logical conclusions, plus the thing about the speed of light being constant for everyone. That’s
why it makes physicists very sceptical when a new idea appears to violate this principle. But what
if the alternative to violating equivalence is violating something that’s even more fundamental?
In recent episodes, we saw how the prospect of black holes either destroying or duplicating
quantum information violates something called unitarity which is as foundational to quantum
mechanics as the equivalence principle is to general relativity. TLDW: if black
holes both swallow quantum information and also radiate that information as Hawking radiation,
then the same bit of quantum info is in two places at once and physics breaks. But if
you don’t let quantum information fall into the black hole in the first place
then you violate the equivalence principle, because this principle tells us that nothing
special or weird should happen to anything falling through an event horizon—as long
as that horizon is large enough so there’s no observable tidal force.
This catch-22—violate unitarity or equivalence—is the black hole
information paradox. One way around this is to argue that qubit duplication is fine
as long as there’s no observer—no conceivable reference frame—that can access both versions
of the information. Now this is black hole complementarity, and in our previous episode
on the topic we followed the adventures of Alice and Bob as they attempted to outsmart
reality and observe both the swallowed and the Hawking radiated qubit. But reality was
too smart for them—it seemed impossible for one observer to ever see duplicate qubits.
For a while, this black hole complementarity was thought to have solved the black hole information
paradox, but it turns out it’s not as neat a solution as we had hoped. Not long after these
early Alice and Bob expeditions were conceived, a new thought experiment appeared that may have
found a way to outsmart reality after all. The thought experiment didn’t just reveal
a way to detect quantum cloning, but also necessitated the appearance of a firewall—a
screen of extreme energy that prevents anyone ever entering a black hole in the first place.
This final proposal saves unitarity, but violates the equivalence principle so utterly that many
physicists despise the idea. And yet some argue that the chain of logic behind the
firewall is so robust that we need to seriously consider throwing equivalence out the window.
So how did we end up in this unfortunate state of contradictory affairs? Well,
to understand that we need to go back to the black hole information paradox and understand it
in terms of not just quantum information, but also quantum entanglement. Quantum entanglement is when
a pair of quantum objects are correlated with each other in a sort of fuzzy way,
such that the information about their individual states is undetermined—it’s in a superposition of
multiple states at once. But this superposition of states is correlated between the entangled pair,
such that the measurement of one defines the properties of the other. We have episodes on
this crazy stuff if you want to dig into that weird hole. But for now just know that quantum
entanglement is ubiquitous and the information about quantum systems is largely woven into webs
of entanglement. That’s why entanglement is important for the information paradox.
So let’s look at entanglement in black holes. As a black hole grows, so does its entropy. This is
the finding by Steven Hawking and Jacob Bekenstein that led to the black hole information paradox in
the first place. Entropy is basically a measure of the information that’s hidden in a system
that we can’t access. Black hole entropy grows because almost all the details about the stuff
that fell in is lost to us. Most physicists think that this information has to be somehow encoded
on the horizon and then must escape as Hawking radiation, because if it didn’t then it would
blink out of existence when that same Hawking radiation causes the black hole to evaporate.
The high entropy at the horizon means that the degrees of freedom on that horizon are
highly entangled with each other—the quantum information about their original pre-falling-in
state is scrambled across the horizon. Now when the first particle of Hawking
radiation leaks out it contains almost no information about the stuff that fell in
because that information is spread across its entanglements with other horizon particles.
But as more and more particles leave, we can start to see patterns. Information about the
material that orginally fell in could, in principle, be slowly reconstructed from
the Hawking radiation. That really only becomes possible when the particles of
Hawking radiation are no longer exclusively entangled with the inaccessible horizon,
but rather with their entangled other particles of Hawking radiation.
There’s a very specific transition point when the qubits remaining on the horizon are mostly
entangled with qubits in the expanding cloud of Hawking radiation—we would say that at this moment
the entanglement between the black hole and the Hawking cloud is at its maximum,
and it happens when around half the mass of the black hole is evaporated,
although in terms of time it’s about 90% of the way to complete evaporation. This moment is called
the Page time, after Don Page who figured out how the entanglement entropy of black hole horizons
must first rise as information and then shrink. After this time it
becomes increasingly possible to find and decode pairs of entangled Hawking qubits.
So let’s consider a single qubit that’s still encoded on the horizon at around
the Page time. It’s entangled with a distant particle of Hawking radiation.
It now wants to join its quantum sibling and become Hawking radiation itself.
So a popular way to describe Hawking radiation is like this:
in the vacuum of space, pairs of matter and antimatter particles are constantly appearing
and vanishing. If this happens at an event horizon, one of these particles can be captured,
leaving the other free to escape and effectively become a real particle of Hawking radiation. A
more precise way to describe this is in terms of quantum field theory—and we obviously have
an episode on this. We can describe the vacuum of space as consisting of equal parts positive and
negative frequency modes of the quantum fields in that space—equal and opposite vibrations in those
fields that cancel each other out perfectly. Black hole horizons perturb these modes,
and the non-perfect cancelling leads to a non-perfect vacuum. The quantum fields end up in
excited states, and this manifests as particles—of Hawking radiation. However you like to describe
Hawking radiation, we have one thing being swallowed by the black hole and one escaping.
And listen, because this is very important—these pairs of swallowed and radiated things have to be
entangled with each other. In fact it’s been argued that the fabric of space is stitched
together by the entanglement between these virtual particles or modes. The entanglement
of adjacent fluctuations is fundamental. In fact, it seems that without this entanglement there
is no space. That’s something we’ll come back to another time, but keep it in mind for now.
OK, so back to our qubit sitting at the horizon waiting to radiate away. It’s entangled with a
distant qubit of Hawking radiation, but it also needs to be entangled with an
adjacent qubit just below the horizon. Without the latter there is no partner
particle or mode that it can sacrifice to the black hole in order to escape. So this
qubit must be entangled twice—with both the Hawking cloud and the black hole interior.
You might say it’s quite promiscuous in its entanglement. Naughty qubit
and quantum mechanics does have rules about these things. In fact,
we know that entanglement has to be monogamous. Monogamy of entanglement says that if a pair of
qubits are maximally entangled with each other then neither qubit can share any entanglement
with a third qubit outside this pair. Monogamy of entanglement is closely related to the no-cloning
theorem, and absolutely violates unitarity to violate this monogomy.
If we want to avoid over-entangling our black hole it seems we need to break one of these
entanglements. Because the entanglement over the Hawking radiation holds the information we want
to preserve, it’s probably safer to break the entanglement between qubits above and below the
horizon. Unfortunately there are dire consequences to doing that. It takes energy to break any
entanglement. You can calculate the amount of energy required to break the links between the
swallowed and radiated particles at the horizon. And it is a lot of energy. In fact in order
for all of the Hawking radiation to break its entanglement connection with the black hole there
would need to be a screen of energy just above the horizon so intense that nothing could ever cross
that horizon without being completely thermalized. Severing entanglement requires a firewall.
Incidentally, the firewall solves the violations of unitarity in two ways:
it breaks the entanglement between the Hawking radiation and the interior of the black hole,
so monogamy of entanglement is saved. And it also stops anyone observing the interior of the black
hole by turning them to plasma. That makes it extra impossible to even think about observing the
same qubit both inside and outside the black hole. And this firewall wouldn’t be visible to a distant
observer—the extreme gravitational redshift of the radiation emerging from a miniscule
Planck length above the horizon would turn that radiation into very faint Hawking radiation.
OK, so firewalls sound cool and useful even if they ruin our trip
into the black hole. Unfortunately, the firewall hypothesis pretty thoroughly
violates the sacred idea we started with: the equivalence principle.
More formally, the equivalence principle states that there’s no experiment you can
do on the local patch of spacetime to distinguish between this freefall or gravity-free floating,
or between standing still against a gravitational field with a certain
g-force versus acceleration absent gravity with the same g-force.
So, if Alice is in freefall towards an event horizon, the equivalence principle says that
she should measure a quantum vacuum consistent with empty space and should see no local sign
revealing the location of the event horizon. But the firewall is a hell of a sign. It reveals to
Alice that the vacuum is massively altered by some apparently non-local influence.
The black hole firewall paradox is a refinement of the black hole information paradox. It’s also
called the AMPS paradox after the physicists who first outlined it in 2012: Ahmed Almheiri,
Donald Marolf, Joseph Polchinski, and James Sully. Whether or not firewalls exist—and physicists are
still divided on this—the main point of the AMPS paper was to show that the black hole
information paradox is still a paradox. In particular, it’s not fully solved by black
hole complementarity. As we saw in our episode on the topic, it’s possible to hedge around the
problem of quantum cloning by noting that no possible observation can detect that cloning.
But the firewall paradox grants a way to cheat. For example, Alice could descend
very close to the event horizon to see if there’s a firewall. If there is then the
equivalence principle is violated. That’s bad. If there isn’t, she has evidence that quantum
entanglement must exist across the event horizon. She could then back out and see
that quantum entanglement also exists between the horizon and the past Hawking radiation,
revealing that monogamy of entanglement is violated and with it unitarity. Also bad.
So the power of the firewall argument is that Alice can learn whether the
exterior and interior of the black hole are entangled without having to enter
the black hole. That seems to defeat the main value of black hole complementarity,
even if this complementarity seems to be still needed for other things.
If firewalls do exist, then it’s not just that the black hole interior is inaccessible,
it means the black hole interior may not exist. Breaking the entanglement between
the vacuum modes across the horizon is the same thing as breaking the stitching of the
fabric of space itself. In a regular black hole, that spatial fabric ends
at the central singularity. If firewalls exist, then it’s like the singularity has
expanded to the event horizon, and that there’s literally nothing—not even a vacuum—beneath it.
So, what’s it all mean? Well this is not a solved problem. Some, including the AMPS four,
argue that breaking the equivalence principle is less radical than breaking unitarity,
and so favour the firewall. But breaking equivalence is radical enough, and many
would prefer a solution which doesn’t violate either. For example we have Leonard Susskind
and Raphael Bousso, who both point to other very general options. If we don’t want to
break unitarity or the equivalence principle, we have to admit that the theories we use
to describe the happenings above the event horizon are themselves broken. For example,
that the quantum field theory we’re using to describe these vacuum modes
and Hawking radiation break down. But this is the same QFT that works perfectly well
in situations that are really no more extreme than the event horizon of a large black hole.
There are some other pretty funky notions. For example Gary Horowitz and Juan Maldecena have
a scheme to reframe quantum field theory with both forward and backward causal directions,
which enables the information swallowed by the black hole to effectively teleport back out to
the horizon qubit. This avoids the need to break entanglement and so ignite firewalls. Or maybe a
full theory of quantum gravity will help us to avoid information-swallowing black holes
after all. For example, fuzzballs of string theory propose that matter unravels into giant
balls of elementary strings below the event horizon. These happen to offer a way to move
quantum information from below the horizon back into the universe, again avoiding the firewall.
Long story short is that the black hole firewall paradox tells us that our current ways of thinking
about black holes need to be cleaned up. Many believe that this little glitch in the
consistency of our best theories of nature is the most promising path to a deeper theory that could
unite quantum mechanics and general relativity. These ideas may even lead us to an idea we’ll
explore soon—which is to an understanding of how space emerges from quantum entanglement,
and how, if we unstitch that entanglement, we get firewalls at the end of space time.
Twelve years ago on July 4th, 2012 the ATLAS and CMS collaborations announced the discovery
of a new particle to a packed auditorium at CERN. It was revealed to be the Higgs
Boson - the particle that makes the existence of matter and interactions as we know them
possible. To celebrate the fireworks of that collision we’ve designed our very own limited
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then you’ll need to put your order in by June 23rd. Check out pbsspacetime.com/shop
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