Tag Archives: black hole

Simple Rules Don’t Mean a Simple Universe

It’s always fun when nature surprises you.

This week, the Perimeter Colloquium was given by Laura Nuttall, a member of the LIGO collaboration.

In a physics department, the colloquium is a regularly scheduled talk that’s supposed to be of interest to the entire department. Some are better at this than others, but this one was pretty fun. The talk explored the sorts of questions gravitational wave telescopes like LIGO can answer about the world.

At one point during the talk, Nuttall showed a plot of what happens when a star collapses into a supernova. For a range of masses, the supernova leaves behind a neutron star (shown on the plot in purple). For heavier stars, it instead results in a black hole, a big black region of the plot.

What surprised me was that inside the black region, there was an unexpected blob: a band of white in the middle of the black holes. Heavier than that band, the star forms a black hole. Lighter, it also forms a black hole. But inside?

Nothing. The star leaves nothing behind. It just explodes.

The physical laws that govern collapsing stars might not be simple, but at least they sound straightforward. Stars are constantly collapsing under their own weight, held up only by the raging heat of nuclear fire. If that heat isn’t strong enough, the star collapses, and other forces take over, so the star becomes a white dwarf, or a neutron star. And if none of those forces is strong enough, the star collapses completely, forming a black hole.

Too small, neutron star. Big enough, black hole. It seems obvious. But reality makes things more complicated.

It turns out, if a star is both massive and has comparatively little metal in it, the core of the star can get very very hot. That heat powers an explosion more powerful than a typical star, one that tears the star apart completely, leaving nothing behind that could form a black hole. Lighter stars don’t get as hot, so they can still form black holes, and heavier stars are so heavy they form black holes anyway. But for those specific stars, in the middle, nothing gets left behind.

This isn’t due to mysterious unknown physics. It’s actually been understood for quite some time. It’s a consequence of those seemingly straightforward laws, one that isn’t at all obvious until you do the work and run the simulations and observe the universe and figure it out.

Just because our world is governed by simple laws, doesn’t mean the universe itself is simple. Give it a little room (and several stars’ worth of hydrogen) and it can still surprise you.

Thoughts from the Winter School

There are two things I’d like to talk about this week.

First, as promised, I’ll talk about what I worked on at the PSI Winter School.

Freddy Cachazo and I study what are called scattering amplitudes. At first glance, these are probabilities that two subatomic particles scatter off each other, relevant for experiments like the Large Hadron Collider. In practice, though, they can calculate much more.

For example, let’s say you have two black holes circling each other, like the ones LIGO detected. Zoom out far enough, and you can think of each one as a particle. The two particle-black holes exchange gravitons, and those exchanges give rise to the force of gravity between them.


In the end, it’s all just particle physics.


Based on that, we can use our favorite scattering amplitudes to make predictions for gravitational wave telescopes like LIGO.

There’s a bit of weirdness to this story, though, because these amplitudes don’t line up with predictions in quite the way we’re used to. The way we calculate amplitudes involves drawing diagrams, and those diagrams have loops. Normally, each “loop” makes the amplitude more quantum-mechanical. Only the diagrams with no loops (“tree diagrams”) come from classical physics alone.

(Here “classical physics” just means “not quantum”: I’m calling general relativity “classical”.)

For this problem, we only care about classical physics: LIGO isn’t sensitive enough to see quantum effects. The weird thing is, despite that, we still need loops.

(Why? This is a story I haven’t figured out how to tell in a non-technical way. The technical explanation has to do with the fact that we’re calculating a potential, not an amplitude, so there’s a Fourier transformation, and keeping track of the dimensions entails tossing around some factors of Planck’s constant. But I feel like this still isn’t quite the full story.)

So if we want to make predictions for LIGO, we want to compute amplitudes with loops. And as amplitudeologists, we should be pretty good at that.

As it turns out, plenty of other people have already had that idea, but there’s still room for improvement.

Our time with the students at the Winter School was limited, so our goal was fairly modest. We wanted to understand those other peoples’ calculations, and perhaps to think about them in a slightly cleaner way. In particular, we wanted to understand why “loops” are really necessary, and whether there was some way of understanding what the “loops” were doing in a more purely classical picture.

At this point, we feel like we’ve got the beginning of an idea of what’s going on. Time will tell whether it works out, and I’ll update you guys when we have a more presentable picture.


Unfortunately, physics wasn’t the only thing I was thinking about last week, which brings me to my other topic.

This blog has a fairly strong policy against talking politics. This is for several reasons. Partly, it’s because politics simply isn’t my area of expertise. Partly, it’s because talking politics tends to lead to long arguments in which nobody manages to learn anything. Despite this, I’m about to talk politics.

Last week, citizens of Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen were barred from entering the US. This included not only new visa applicants, but also those who already have visas or green cards. The latter group includes long-term residents of the US, many of whom were detained in airports and threatened with deportation when their flights arrived shortly after the ban was announced. Among those was the president of the Graduate Student Organization at my former grad school.

A federal judge has blocked parts of the order, and the Department of Homeland Security has announced that there will be case-by-case exceptions. Still, plenty of people are stuck: either abroad if they didn’t get in in time, or in the US, afraid that if they leave they won’t be able to return.

Politics isn’t in my area of expertise. But…

I travel for work pretty often. I know how terrifying and arbitrary border enforcement can be. I know how it feels to risk thousands of dollars and months of planning because some consulate or border official is having a bad day.

I also know how essential travel is to doing science. When there’s only one expert in the world who does the sort of work you need, you can’t just find a local substitute.

And so for this, I don’t need to be an expert in politics. I don’t need a detailed case about the risks of terrorism. I already know what I need to, and I know that this is cruel.

And so I stand in solidarity with the people who were trapped in airports, and those still trapped abroad and trapped in the US. You have been treated cruelly, and you shouldn’t have been. Hopefully, that sort of message can transcend politics.


One final thing: I’m going to be a massive hypocrite and continue to ban political comments on this blog. If you want to talk to me about any of this (and you think one or both of us might actually learn something from the exchange) please contact me in private.

What’s in a Conjecture? An ER=EPR Example

A few weeks back, Caltech’s Institute of Quantum Information and Matter released a short film titled Quantum is Calling. It’s the second in what looks like will become a series of pieces featuring Hollywood actors popularizing ideas in physics. The first used the game of Quantum Chess to talk about superposition and entanglement. This one, featuring Zoe Saldana, is about a conjecture by Juan Maldacena and Leonard Susskind called ER=EPR. The conjecture speculates that pairs of entangled particles (as investigated by Einstein, Podolsky, and Rosen) are in some sense secretly connected by wormholes (or Einstein-Rosen bridges).

The film is fun, but I’m not sure ER=EPR is established well enough to deserve this kind of treatment.

At this point, some of you are nodding your heads for the wrong reason. You’re thinking I’m saying this because ER=EPR is a conjecture.

I’m not saying that.

The fact of the matter is, conjectures play a very important role in theoretical physics, and “conjecture” covers a wide range. Some conjectures are supported by incredibly strong evidence, just short of mathematical proof. Others are wild speculations, “wouldn’t it be convenient if…” ER=EPR is, well…somewhere in the middle.

Most popularizers don’t spend much effort distinguishing things in this middle ground. I’d like to talk a bit about the different sorts of evidence conjectures can have, using ER=EPR as an example.


Our friendly neighborhood space octopus

The first level of evidence is motivation.

At its weakest, motivation is the “wouldn’t it be convenient if…” line of reasoning. Some conjectures never get past this point. Hawking’s chronology protection conjecture, for instance, points out that physics (and to some extent logic) has a hard time dealing with time travel, and wouldn’t it be convenient if time travel was impossible?

For ER=EPR, this kind of motivation comes from the black hole firewall paradox. Without going into it in detail, arguments suggested that the event horizons of older black holes would resemble walls of fire, incinerating anything that fell in, in contrast with Einstein’s picture in which passing the horizon has no obvious effect at the time. ER=EPR provides one way to avoid this argument, making event horizons subtle and smooth once more.

Motivation isn’t just “wouldn’t it be convenient if…” though. It can also include stronger arguments: suggestive comparisons that, while they could be coincidental, when put together draw a stronger picture.

In ER=EPR, this comes from certain similarities between the type of wormhole Maldacena and Susskind were considering, and pairs of entangled particles. Both connect two different places, but both do so in an unusually limited way. The wormholes of ER=EPR are non-traversable: you cannot travel through them. Entangled particles can’t be traveled through (as you would expect), but more generally can’t be communicated through: there are theorems to prove it. This is the kind of suggestive similarity that can begin to motivate a conjecture.

(Amusingly, the plot of the film breaks this in both directions. Keanu Reeves can neither steal your cat through a wormhole, nor send you coded messages with entangled particles.)


Nor live forever as the portrait in his attic withers away

Motivation is a good reason to investigate something, but a bad reason to believe it. Luckily, conjectures can have stronger forms of evidence. Many of the strongest conjectures are correspondences, supported by a wealth of non-trivial examples.

In science, the gold standard has always been experimental evidence. There’s a reason for that: when you do an experiment, you’re taking a risk. Doing an experiment gives reality a chance to prove you wrong. In a good experiment (a non-trivial one) the result isn’t obvious from the beginning, so that success or failure tells you something new about the universe.

In theoretical physics, there are things we can’t test with experiments, either because they’re far beyond our capabilities or because the claims are mathematical. Despite this, the overall philosophy of experiments is still relevant, especially when we’re studying a correspondence.

“Correspondence” is a word we use to refer to situations where two different theories are unexpectedly computing the same thing. Often, these are very different theories, living in different dimensions with different sorts of particles. With the right “dictionary”, though, you can translate between them, doing a calculation in one theory that matches a calculation in the other one.

Even when we can’t do non-trivial experiments, then, we can still have non-trivial examples. When the result of a calculation isn’t obvious from the beginning, showing that it matches on both sides of a correspondence takes the same sort of risk as doing an experiment, and gives the same sort of evidence.

Some of the best-supported conjectures in theoretical physics have this form. AdS/CFT is technically a conjecture: a correspondence between string theory in a hyperbola-shaped space and my favorite theory, N=4 super Yang-Mills. Despite being a conjecture, the wealth of nontrivial examples is so strong that it would be extremely surprising if it turned out to be false.

ER=EPR is also a correspondence, between entangled particles on the one hand and wormholes on the other. Does it have nontrivial examples?

Some, but not enough. Originally, it was based on one core example, an entangled state that could be cleanly matched to the simplest wormhole. Now, new examples have been added, covering wormholes with electric fields and higher spins. The full “dictionary” is still unclear, with some pairs of entangled particles being harder to describe in terms of wormholes. So while this kind of evidence is being built, it isn’t as solid as our best conjectures yet.

I’m fine with people popularizing this kind of conjecture. It deserves blog posts and press articles, and it’s a fine idea to have fun with. I wouldn’t be uncomfortable with the Bohemian Gravity guy doing a piece on it, for example. But for the second installment of a star-studded series like the one Caltech is doing…it’s not really there yet, and putting it there gives people the wrong idea.

I hope I’ve given you a better idea of the different types of conjectures, from the most fuzzy to those just shy of certain. I’d like to do this kind of piece more often, though in future I’ll probably stick with topics in my sub-field (where I actually know what I’m talking about 😉 ). If there’s a particular conjecture you’re curious about, ask in the comments!

The Universe, Astronomy’s Lab

There’s a theme in a certain kind of science fiction.

Not in the type with laser swords and space elves, and not in cyberpunk dystopias…but when sci-fi tries to explore what humanity might do if it really got a chance to explore its own capabilities. In a word, the theme is scale.

We start out with a Dyson sphere, built around our own sun to trap its energy. As time goes on, the projects get larger and larger, involving multiple stars and, eventually, reshaping the galaxy.

There’s an expectation, though, that this sort of thing is far in our future. Treating the galaxy as a resource, as a machine, seems well beyond our present capabilities.

On Wednesday, Victoria Kaspi gave a public lecture at Perimeter about neutron stars. At the very end of the lecture, she talked a bit about something she covered in more detail during her colloquium earlier that day, called a Pulsar Timing Array.

Neutron stars are one of the ways a star can end its life. Too big to burn out quietly and form a white dwarf, and too small to collapse all the way into a black hole, the progenitors of neutron stars have so much gravity that they force protons and electrons to merge, so that the star ends up as a giant ball of neutrons, like an enormous atomic nucleus.

Many of these neutron stars have strong magnetic fields. A good number of them are what are called pulsars: stars that emit powerful pulses of electromagnetic radiation, often at regular intervals. Some of these pulsars are very regular indeed, rivaling atomic clocks in their precision. The idea of a Pulsar Timing Array is to exploit this regularity by using these pulsars as a gravitational wave telescope.

Gravitational waves are ripples in space-time. They were predicted by Einstein’s theory, and we’ve observed their indirect effects, but so far we have yet to detect them directly. Attempts have been made: vast detectors like LIGO have been built that bounce light across long “arms”, trying to detect minute disruptions in space. The problem is, it’s hard to distinguish these disruptions from ordinary vibrations in the area, like minor earthquakes. Size also limits the effectiveness of these detectors, with larger detectors able to see the waves from bigger astronomical events.

Pulsar Timing Arrays sidestep both of those problems. Instead of trying to build a detector on the ground like LIGO (or even in space like LISA), they use the pulsars themselves as the “arms” of a galaxy-sized detector. Because these pulsars emit light so regularly, small disruptions can be a sign that a gravitational wave is passing by the earth and disrupting the signal. Because they are spread roughly evenly across the galaxy, we can correlate signals across multiple pulsars, to make sure we’re really seeing gravitational waves. And because they’re so far apart, we can use them to detect waves from some of the biggest astronomical events, like galaxies colliding.


Earth very much not to scale.

Longtime readers know that I find astronomy really inspiring, but Kaspi’s talk woke me up to a completely different aspect, that of our mastery of scale.

Want to dream of a future where we use the solar system and the galaxy as resources? We’re there, and we’ve been there for a long time. We’re a civilization that used nearby planets to bootstrap up the basic laws of motion before we even had light bulbs. We’ve honed our understanding of space and time using distant stars. And now, we’re using an array of city-sized balls of neutronium, distributed across the galaxy, as a telescope. If that’s not the stuff of science fiction, I don’t know what is.


By the way, speaking of webcast lectures, I’m going to be a guest on the Alda Center’s Science Unplugged show next week. Tune in if you want to hear about the sort of stuff I work on, using string theory as a tool to develop shortcuts for particle physics calculations.

Entropy is Ignorance

(My last post had a poll in it! If you haven’t responded yet, please do.)

Earlier this month, philosopher Richard Dawid ran a workshop entitled “Why Trust a Theory? Reconsidering Scientific Methodology in Light of Modern Physics” to discuss his idea of “non-empirical theory confirmation” for string theory, inflation, and the multiverse. They haven’t published the talks online yet, so I’m stuck reading coverage, mostly these posts by skeptical philosopher Massimo Pigliucci. I find the overall concept annoying, and may rant about it later. For now though, I’d like to talk about a talks on the second day by philosopher Chris Wüthrich about black hole entropy.

Black holes, of course, are the entire-stars-collapsed-to-a-point-that-no-light-can-escape that everyone knows and loves. Entropy is often thought of as the scientific term for chaos and disorder, the universe’s long slide towards dissolution. In reality, it’s a bit more complicated than that.


For one, you need to take Elric into account…

Can black holes be disordered? Naively, that doesn’t seem possible. How can a single point be disorderly?

Thought about in a bit more detail, the conclusion seems even stronger. Via something called the “No Hair Theorem”, it’s possible to prove that black holes can be described completely with just three numbers: their mass, their charge, and how fast they are spinning. With just three numbers, how can there be room for chaos?

On the other hand, you may have heard of the Second Law of Thermodynamics. The Second Law states that entropy always increases. Absent external support, things will always slide towards disorder eventually.

If you combine this with black holes, then this seems to have weird implications. In particular, what happens when something disordered falls into a black hole? Does the disorder just “go away”? Doesn’t that violate the Second Law?

This line of reasoning has led to the idea that black holes have entropy after all. It led Bekenstein to calculate the entropy of a black hole based on how much information is “hidden” inside, and Hawking to find that black holes in a quantum world should radiate as if they had a temperature consistent with that entropy. One of the biggest successes of string theory is an explanation for this entropy. In string theory, black holes aren’t perfect points: they have structure, arrangements of strings and higher dimensional membranes, and this structure can be disordered in a way that seems to give the right entropy.

Note that none of this has been tested experimentally. Hawking radiation, if it exists, is very faint: not the sort of thing we could detect with a telescope. Wüthrich is worried that Bekenstein’s original calculation of black hole entropy might have been on the wrong track, which would undermine one of string theory’s most well-known accomplishments.

I don’t know Wüthrich’s full argument, since the talks haven’t been posted online yet. All I know is Pigliucci’s summary. From that summary, it looks like Wüthrich’s primary worry is about two different definitions of entropy.

See, when I described entropy as “disorder”, I was being a bit vague. There are actually two different definitions of entropy. The older one, Gibbs entropy, grows with the number of states of a system. What does that have to do with disorder?

Think about two different substances: a gas, and a crystal. Both are made out of atoms, but the patterns involved are different. In the gas, atoms are free to move, while in the crystal they’re (comparatively) fixed in place.


Blurrily so in this case

There are many different ways the atoms of a gas can be arranged and still be a gas, but fewer in which they can be a crystal, so a gas has more entropy than a crystal. Intuitively, the gas is more disordered.

When Bekenstein calculated the entropy of a black hole he didn’t use Gibbs entropy, though. Instead, he used Shannon entropy, a concept from information theory. Shannon entropy measures the amount of information in a message, with a formula very similar to that of Gibbs entropy: the more different ways you can arrange something, the more information you can use it to send. Bekenstein used this formula to calculate the amount of information that gets hidden from us when something falls into a black hole.

Wüthrich’s worry here (again, as far as Pigliucci describes) is that Shannon entropy is a very different concept from Gibbs entropy. Shannon entropy measures information, while Gibbs entropy is something “physical”. So by using one to predict the other, are predictions about black hole entropy just confused?

It may well be he has a deeper argument for this, one that wasn’t covered in the summary. But if this is accurate, Wüthrich is missing something fundamental. Shannon entropy and Gibbs entropy aren’t two different concepts. Rather, they’re both ways of describing a core idea: entropy is a measure of ignorance.

A gas has more entropy than a crystal, it can be arranged in a larger number of different ways. But let’s not talk about a gas. Let’s talk about a specific arrangement of atoms: one is flying up, one to the left, one to the right, and so on. Space them apart, but be very specific about how they are arranged. This arrangement could well be a gas, but now it’s a specific gas. And because we’re this specific, there are now many fewer states the gas can be in, so this (specific) gas has less entropy!

Now of course, this is a very silly way to describe a gas. In general, we don’t know what every single atom of a gas is doing, that’s why we call it a gas in the first place. But it’s that lack of knowledge that we call entropy. Entropy isn’t just something out there in the world, it’s a feature of our descriptions…but one that, nonetheless, has important physical consequences. The Second Law still holds: the world goes from lower entropy to higher entropy. And while that may seem strange, it’s actually quite logical: the things that we describe in more vague terms should become more common than the things we describe in specific terms, after all there are many more of them!

Entropy isn’t the only thing like this. In the past, I’ve bemoaned the difficulty of describing the concept of gauge symmetry. Gauge symmetry is in some ways just part of our descriptions: we prefer to describe fundamental forces in a particular way, and that description has redundant parameters. We have to make those redundant parameters “go away” somehow, and that leads to non-existent particles called “ghosts”. However, gauge symmetry also has physical consequences: it was how people first knew that there had to be a Higgs boson, long before it was discovered. And while it might seem weird to think that a redundancy could imply something as physical as the Higgs, the success of the concept of entropy should make this much less surprising. Much of what we do in physics is reasoning about different descriptions, different ways of dividing up the world, and then figuring out the consequences of those descriptions. Entropy is ignorance…and if our ignorance obeys laws, if it’s describable mathematically, then it’s as physical as anything else.

Don’t Watch the Star, Watch the Crowd

I didn’t comment last week on Hawking’s proposed solution of the black hole firewall problem. The media buzz around it was a bit less rabid than the last time he weighed in on this topic, but there was still a lot more heat than light.

The impression I get from the experts is that Hawking’s proposal (this time made in collaboration with Andrew Strominger and Malcom Perry, the former of whom is famous for, among other things, figuring out how string theory can explain the entropy of black holes) resembles some earlier suggestions, with enough new elements to make it potentially interesting but potentially just confusing. It’s a development worth paying attention to for specialists, but it’s probably not the sort of long-awaited answer the media seems to be presenting it as.

This raises a question: how, as a non-specialist, are you supposed to tell the difference? Sure, you can just read blogs like mine, but I can’t report on everything.

I may have a pretty solid grounding in physics, but I know almost nothing about music. I definitely can’t tell what makes a song good. About the best I can do is see if I can dance to it, but that doesn’t seem to be a reliable indicator of quality music. Instead, my best bet is usually to watch the crowd.

Lasers may make this difficult.

Ask the star of a show if they’re doing good work, and they’re unlikely to be modest. Ask the average music fan, though, and you get a better idea. Watch music fans as a group, and you get even more information.

When a song starts playing everywhere you go, when people start pulling it out at parties and making their own imitations of it, then maybe it’s important. That might not mean it’s good, but it does mean it’s worth knowing about.

When Hawking or Strominger or Witten or anyone whose name you’ve heard of says they’ve solved the puzzle of the century, be cautious. If it really is worth your attention, chances are it won’t be the last you’ll hear about it. Other physicists will build off of it, discuss it, even spin off a new sub-field around it. If it’s worth it, you won’t have to trust what the stars of the physics world say: you’ll be able to listen to the crowd.

Romeo and Juliet, through a Wormhole

Perimeter is hosting this year’s Mathematica Summer School on Theoretical Physics. The school is a mix of lectures on a topic in physics (this year, the phenomenon of quantum entanglement) and tips and tricks for using the symbolic calculation program Mathematica.

Juan Maldacena is one of the lecturers, which gave me a chance to hear his Romeo and Juliet-based explanation of the properties of wormholes. While I’ve criticized some of Maldacena’s science popularization work in the past, this one is pretty solid, so I thought I’d share it with you guys.

You probably think of wormholes as “shortcuts” to travel between two widely separated places. As it turns out, this isn’t really accurate: while “normal” wormholes do connect distant locations, they don’t do it in a way that allows astronauts to travel between them, Interstellar-style. This can be illustrated with something called a Penrose diagram:


Static “Greyish Black” Diagram

In the traditional Penrose diagram, time goes upward, while space goes from side to side. In order to measure both in the same units, we use the speed of light, so one year on the time axis corresponds to one light-year on the space axis. This means that if you’re traveling at a 45 degree line on the diagram, you’re going at the speed of light. Any lower angle is impossible, while any higher angle means you’re going slower.

If we start in “our universe” in the diagram, can we get to the “other universe”?

Pretty clearly, the answer is no. As long as we go slower than the speed of light, when we pass the event horizon of the wormhole we will end up, not in the “other universe”, but at the part of the diagram labeled Future Singularity, the singularity at the center of the black hole. Even going at the speed of light only keeps us orbiting the event horizon for all eternity, at best.

What use could such a wormhole be? Well, imagine you’re Romeo or Juliet.

Romeo has been banished from Verona, but he took one end of a wormhole with him, while the other end was left with Juliet. He can’t go through and visit her, she can’t go through and visit him. But if they’re already considering taking poison, there’s an easier way. If they both jump in to the wormhole, they’ll fall in to the singularity. Crucially, though, it’s the same singularity, so once they’re past the event horizon they can meet inside the black hole, spending some time together before the end.

Depicted here for more typical quantum protagonists, Alice and Bob.

This explains what wormholes really are: two black holes that share a center.

Why was Maldacena talking about this at a school on entanglement? Maldacena has recently conjectured that quantum entanglement and wormholes are two sides of the same phenomenon, that pairs of entangled particles are actually connected by wormholes. Crucially, these wormholes need to have the properties described above: you can’t use a pair of entangled particles to communicate information faster than light, and you can’t use a wormhole to travel faster than light. However, it is the “shared” singularity that ends up particularly useful, as it suggests a solution to the problem of black hole firewalls.

Firewalls were originally proposed as a way of getting around a particular paradox relating three states connected by quantum entanglement: a particle inside a black hole, radiation just outside the black hole, and radiation far away from the black hole. The way the paradox is set up, it appears that these three states must all be connected. As it turns out, though, this is prohibited by quantum mechanics, which only allows two states to be entangled at a time. The original solution proposed for this was a “firewall”, a situation in which anyone trying to observe all three states would “burn up” when crossing the event horizon, thus avoiding any observed contradiction. Maldacena’s conjecture suggests another way: if someone interacts with the far-away radiation, they have an effect on the black hole’s interior, because the two are connected by a wormhole! This ends up getting rid of the contradiction, allowing the observer to view the black hole and distant radiation as two different descriptions of the same state, and it depends crucially on the fact that a wormhole involves a shared singularity.

There’s still a lot of detail to be worked out, part of the reason why Maldacena presented this research here was to inspire more investigation from students. But it does seem encouraging that Romeo and Juliet might not have to face a wall of fire before being reunited.