Thank you to Brilliant for supporting PBS. Black holes are a paradox. They are paradoxical because they simultaneously must exist but can’t, and so they break physics as we know it. But many physicists will tell you that the best way to fix broken physics is with string. String theory, in fact. And in the black holes of string theory - fuzzballs - are perhaps even weirder than the regular type Einstein’s general theory of relativity
tells us that if the density of matter is sufficiently ridiculous, ultimate gravitational
collapse is inevitable. The matter should contract to a single point
of infinite density - the singularity - which is surrounded by a surface from which even
light can’t escape - the event horizon. And we see these black holes - or at least
their incontrovertible evidence - in many places out there in the universe. But black holes are also impossible. At the central singularity, the known laws
of physics break down - general relativity comes into irreconcilable conflict with quantum
mechanics. There’s our first paradox. And at the event horizon another paradox arises. On the one hand, general relativity insists
that no information from the matter that fell into a black hole should be observable on
the surface - the so-called no-hair theorem, which says that the only properties that we
can observe from outside a black hole are its mass, electric charge, and angular momentum. That’s not very many bits of information. On the other hand, if we calculate the amount of information that goes into a black hole to build it up, we get a prodigiously large
number - 10^10^77 bits for a black hole the mass of our Sun. Black holes should have an enormous number of so-called microstates - hidden configurations - and this translates to an enormous entropy. The formula for black hole entropy was discovered by Jakob Bekenstein, who, incidentally, also inspired the colourful phrasing that black
holes “have no hairs” to describe the absence of observable microstates in a black hole, which, on the surface, seems to contradict his black hole entropy formula. Here’s an analogy. We can describe the behavior of the air in
this room with very few numbers: its bulk motion, its temperature, pressure, etc. But these few numbers emerge from the motion of every air molecule — and to describe that we’d need the positions and momenta
of 10^27ish particles. So the air has the very high entropy of lots
of information that is hidden under very few macroscopic properties. But in the case of air, the hidden information still exists and is, in principle, still measurable. Not so in the black holes of general relativity. The no-hair theorem says that there’s no
information beyond charge, mass and spin that’s observable above the event horizon. The information contributing to black hole
entropy could be beneath the horizon, but if we add one more fact we run into serious
trouble. Black holes evaporate by emitting Hawking
radiation. We talked about this previously, but the TL;DW is that Hawking radiation should be completely random, and so leaks away the black hole’s
mass without any of the information that went into building the black hole. When the black hole eventually vanishes, so
does its enormous information content. And that violates a very deep and fundamental law - the law of conservation of quantum information. This threat of erasure of quantum information in a hairless black hole is the black hole information paradox. So yeah, black holes seem to be paradoxes. And yet they definitely exist. But you know what doesn’t exist? Actual paradoxes. When we see an apparent paradox in physics, it’s really a clue pointing to a gap in our understanding. Solving the paradox can lead us to new knowledge. While we’ve covered these black hole paradoxes before, and have even hinted at possible solutions - we’ve never actually solved them. That’s what we’ll try to do today. Ultimately, the black hole paradoxes stem
from the disagreement between quantum mechanics and general relativity. The impossibility of the central singularity
is the most obvious place where we need a theory of quantum gravity. But this is also the problem at the event
horizon. A theory of quantum gravity would have really helped Stephen Hawking in deriving his eponymous radiation. But such a theory didn’t exist back then
in the 70s and still doesn’t. Instead Hawking used a hack - something called the semi-classical approximation. He was able to describe the black hole using pure general relativity but then analyze its effect on the surrounding quantum fields,
which only worked if the gravity at the horizon was relatively weak, in which case quantum
gravity effects shouldn’t play a part. But that assumption may be wrong. If gravity starts to get quantum even above
the event horizon, then it may be possible to actually encode information on that surface in a way that saves that information from destruction as the black hole evaporates. And it turns out that our most advanced theory of quantum gravity can do this quite neatly. Black hole paradoxes may be solved by string theory. In string theory, black holes are not hairless
at all - in fact all of those strings make them positively fuzzy. And so we come to fuzzballs. Well, very nearly. First a spot of string theory. We’ve covered this horrendously complex
topic in detail before, so I’m only going to give you the crudest overview. In string theory, all elementary particles
are oscillations in 1-dimensional strands that themselves are embedded within complex,
many-dimensional spaces. String theory immediately solves the problem of the black hole singularity, because instead of collapsing all of a black hole’s mass
into a single point, it gets distributed around the ring structure of these strings. Lose that pesky infinite density and we can
start making sense of physics again. It turns out that though, that string theory
can make sense of the black hole event horizon also. The first step towards this was in 1996, when Andrew Strominger and Cumrun Vafa created a black hole using string theory - in theory-space, not actually. Now I’ll come back to the some of details
later - for now just the result. These guys found a way to count the microstates on the horizon- the number of possible configurations of stringy structures - the 1-D strings themselves and higher-dimensional structures called D-branes. And the number they found exactly agreed with the Bekenstein formula for black hole entropy. It was hard to believe that this was a mere
coincidence — it seemed they’d stumbled on the mechanism by which information could be encoded on the event horizon. The infinitesimal strings and branes of string theory might be the analog of the molecules that store the entropy of our room full of
air. I should add that Strominger and Vafa did
this for the somewhat unrealistic case of a black hole horizon with 4 spatial dimensions, but it was a decisive step and it gave us a compelling reason to think that string theory might explain where the microstates of black holes live. But in order to solve the information paradox, we still have to get that information out of the black hole as it evaporates. The breakthrough came quickly. A year after the Strominger-Vafa result, Samir Mathur at Ohio State dug into that model to see if it could reproduce properties of black
holes beyond the entropy. And it did, almost too well. For instance, the profile of the radiation
emitted by the strings precisely matched that of traditional Hawking radiation. This was another stunning match to theory,
and also a way for stringy black holes to leak out their information. It was looking pretty good, but I realize
that I haven’t really told you what these stringy black holes look like, or how they
form, or how structure can actually be supported on the event horizon. For that we need to finally get to the idea
of the fuzzball. First, a thing that’s weird about even regular
black holes. If you were to dial up the strength of gravity,
black holes would get bigger. That’s different to pretty much everything
else in the universe, which are crunched down to smaller size if you increase the power
of gravity. This property of black holes is actually quite hard to reproduce in theories of quantum gravity. But while he was exploring stringy black holes, Samir Mathur found that the strings that formed the black hole would increase in size as the
strength of gravity increased. In fact, if you have a bunch of strings dense
enough to form a black hole in general relativity, it wouldn’t actually collapse. Rather it would grow to produce an agglomerate of strings with the same radius as a classical black hole. If this is right, then black holes don’t
have an empty event horizon at all, but rather a real surface that looks like a tangled nightmare of strings and branes, like the hairball coughed up from some hyperdimensional quantum cat. A fuzzball. Just as the neutron star’s gravitational
field is so intense that atomic nuclei are crushed into a soup of neutrons, a star collapsing into a fuzzball will see its constituents crushed into a soup of elementary strings. The most amazing element of the fuzzball paradigm is the discovery that quantum gravity effects might not just be important at the center
of the black hole but instead may pile up to the horizon scale. The ability for strings to maintain structure
in this extreme gravity comes down to an effect specific to string theory called fractionation. The tension of a string is inversely proportional to its length: tight rubber bands are naturally small because they are difficult to stretch
and vice versa. But in string theory, when you merge a large
number of strings, the tension of the resulting object is effectively smaller than for
each individual string - proportional to the number of strings merged. That means by crushing an enormous number of strings together, the resulting monstrosity can be stretched to enormous scales. The normally Planck-length strings can therefore pile up into fuzzballs with sizes ranging from kilometers to light years. The resulting fuzzball doesn’t have a local
event horizon - in that there’s no single surface of no-return. But from a distance, fuzzballs would look
like black holes. Light trying to escape would still be massively redshifted - sapped of energy by the gravitational field - rendering the object effectively black. It would still cause massive gravitational
lensing, time dilation, etc. All classical effects of black holes from
general relativity would be preserved. But if you approach the fuzzball you start
to see this surface of stringy material with a thickness of about a Planck length. And what happens if you punch through that
surface? Well, that’s where things get properly weird. In fact there is no interior. A fuzzball is really a fuzzsphere, or fuzzshell. It’s not that the interior is empty, but
rather that space and time literally end at the surface. As a fuzzball is forming, all of the matter
- now dissolved into stringy mess, is pushed up to the surface and the interior grid of
spacetime is deleted from the universe. This last thing is the weirdest and coolest
thing about fuzzballs, so let’s explore a bit further by dropping a few dimensions. Instead of the 4 spatial dimensions of a Strominger-Vafa or the 3 dimensions of regular black holes, let’s think about a 1-D black hole. One dimension means a line, so a 1-D black
hole is just a segment of a line with a point of infinite density on it. The event horizon is just the pair of equidistant points on the line inside of which escape is impossible. Now let’s try a string-theoretic version. In string theory we have extra compact dimensions - spatial dimensions that are coiled up on the Planck scale so we can’t see them. Adding a single coiled dimension to our 1-D
black hole turns our line into a drinking straw. The extra dimension is the distance around
the straw. For a fuzzball, spacetime closes on itself
at the event horizon. The extra compact dimensions contract and pinch off, so all spatial dimensions end in that direction. As a side benefit, this eliminates the problem of the gravitational singularity at the center of a black hole. There is no central singularity because there is no center. The emergence of fuzzballs in string theory
radically changed our vision of what a black hole could be and provided a satisfying potential resolution to several paradoxes. However, this picture is not yet complete. The model has only been carried out for simplified and nonrealistic-cases like the Strominger-Vafa black hole. Constructing fuzzballs that more closely match real astrophysical black holes remains a major theoretical effort. I should also add that fuzzballs are not the
only quantum extension of the GR black hole. We can come back to those another time. Black holes, or something like them, definitely exist. And they’re one of our best hopes for understanding the union of general relativity with the quantum. Perhaps that’ll come when we find evidence
of fuzziness surrounding those distant holes in the fabric of space time. Thank you to Brilliant for supporting PBS. To understand astrophysics, Brilliant believes it helps to have a solid understanding of relativity. Brilliant has a lesson on special relativity
that includes interactive challenges and problems to solve. A hands-on approach can guide you through thinking strategies for challenging subjects like relativity. It starts out explaining relativity in terms
of boats passing each other on a river, then goes into some puzzles that require changing perspective (like the ball stack bounce), and then goes into the speed of light and
even time travel! To learn more about Brilliant, go to Brilliant.org/Spacetime. Hey everyone, I’d like to invite you to
participate in PBS Digital Studios’ annual audience survey. The Space Time audience has always had a great showing on the annual survey and we’d love for that to continue this year. Your feedback really helps us understand what
you’re interested in and you even get to vote on potential new shows! And we really do spend quite a bit of time
analyzing and discussing the results. There’s a link in the description below. If you have a few minutes, we’d love your
input. And, as always, if you've joined us on Patreon, we can't emphasize enough how helpful your support is in keeping this show going. But today, on behalf of one of our generous
contributors, we want to give a very special Big Bang shoutout dedicated to the memory of Ernest H Anderson Jr. Earnest was a geophysicist who’s PhD examined Martian Atmospheric Haze and he worked with the most famous planetary scientist of all - Carl Sagan. Earnest was also a part of the Apollo XI mission, working in the Air Force in Colorado tracking and predicting solar radiation bursts. We tend to talk about the famous scientists
on this show, but it’s the dedication, passion, and hard work of scientists like Earnest that
really carry the grand scientific project for all humanity. So it is our honor to honor Ernest H Anderson Jr., who passed away in 2018, and has returned to the stars. So we’re going to take a short release break
to take a breath and get some mind-bending episodes written. We will return in December with said episodes, and with the comments responses from last episode - because we’re also taking a comments break. See you all very soon.
The hard part I have with accepting string theory is that it hasn't made any testable claims yet. The math is definitely compelling, but there has to be some physical basis for believing it's real.
The other thing that I'm a little bit confused about it, is why a singularity at the center of a black hole is problematic, but a carved-out space at the center of a fuzzball that is not part of the universe is fine?
Man… still no idea what he’s talking about, but I keep watching
The most important takeaway from this is that we need to start replacing the word "Black Hole" with "Fuzzball". Personally I'm excited to hear re-releases of Soundgarden's "Fuzzball Sun" and Muse's track "Supermassive Fuzzball" from their album "Fuzzballs and Revelations".
Also, saying someone has a black hole for a heart is an insult, but a fuzzball for a heart sounds like a compliment.
It amazes me how easily Matt explains these complex things. I don't get all the details but is enough to have a view of the deep physics problems around.
They are doing an excellent job.
Why's this start at the end?
Now they have to reshoot the last part of Interstellar.
Cooper: Newton's third law, Brand. To go anywhere you have to leave something behind. Detach.
An hour later
Cooper comes over Brand's radio
Cooper: Umm, actually nevermind Brand. I'm sitting on the event horizon now, looks like there is no way to get inside the black hole. Can you come back and pick me up?