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.