Extra dimensions

... black holes, curve space and time around them, in the way that we've been describing, things fall along the curves in space. If the black holes move around, the curves have to follow them, right? But they can't travel faster than the speed of light either. So what happens is black holes, let's say move around, maybe I've got two black holes in orbit around each other, that can happen. It takes a while. A wave is created in the actual shape of space, and that wave follows the black holes as black holes are undulating. Eventually those two black holes will merge. And as we were talking about, it doesn't take an infinite time, even though there's time dilation because they're both so big, they're really deforming spacetime a lot. I don't have a little tiny marble falling across an event horizon. I have two event horizons, and in the simulations you can see a bobble and they merge together and they make one bigger black hole. And then it radiates in the gravitational waves. It radiates away all those imperfections and it settles down to one quiescent, perfectly silent black hole that's spinning. Beautiful stuff. And it emits E equals MC squared energy. So the mass of the final black hole will be less than the sum of the two starter black holes. And that energy is radiated away in this ringing of spacetime. It's really important to emphasize that it's not light. None of this has to do literally with light that we can detect with normal things that detect light. X-rays, form of light, gamma rays are a form of light, infrared, optical. This whole electromagnetic spectrum, none of it is emitted as light. It's completely dark.

The following is a conversation with Janna Levin, a theoretical physicist and cosmologist specializing in black holes, cosmology of extra dimensions, topology of the universe, and gravitational waves in spacetime. She has also written some incredible books including; How the Universe Got Its Spots, on the topic of the shape and the size of the universe, A Madman Dreams of Turing Machines, on the topic of genius madness and the limits of knowledge, Black Hole Blues and Other Songs From Outer Space, on the topic of LIGO and the detection of gravitational waves, and Black Hole Survival Guide, all about black holes. This was a fun and fascinating conversation. This is the Lex Fridman podcast. To support it. Please check out our sponsors in the description. And now, dear friends, here's Janna Levin.

I should say that you sent me a message about not starting early in the morning, and that made me feel like we're kindred spirits. You wrote to me, "When the great physicist Sidney Coleman was asked to attend a 9:00 AM meeting his reply was, 'I can't stay up that late.'" Yeah, classic. Sidney was beloved.

So you've described the brain breaking idea that a black hole is not so much as super dense matter as it's sometimes described, but it's more akin to a region of spacetime, but even more so just nothing. It's nothing. That's the thing you seem to like to say. I do. I do like to say that black holes are no thing.

Because written in many places about the human beings behind the science, I have to ask you about this, about nuclear weapons. Whereas the greatest of coming together to create this most terrifying and powerful of a technology, and now I get to talk to world leaders for whom this technology, is part of the tools that is used perhaps implicitly on the chessboard of geopolitics. What can you say as a person who's a physicist and who have studied the physicist and written about the physicists, the humans behind this, about this moment in human history, when physicists came together and created this weapon that's powerful enough to destroy all of human civilization? I think it's an excruciating moment in the history of science. And people talk about Heisenberg, who stayed in Germany and worked for the Nazis in their own attempt to build the bomb. There was this kind of hopeful talk that maybe Heisenberg had intentionally derailed the nuclear weapons program, but I think that's been largely discredited, that he would have made the bomb, could he. Had he not made some really kind of simple errors in his original estimates about how much material would be required or how they would get over the energy barriers. And that's a terrifying thought. I don't know that any of us can really put ourselves in that position of imagining that we are faced with that quandary, having to take the initiative to participate in thinking of a way that quantum mechanics can kill people. And then making the bomb, I think overwhelmingly, physicists today feel we should not continue in the proliferation of nuclear weapons. Very few theoretical physicists want to see this continue.

Okay. So can we just return to the collapse of a star that forms a black hole? At which point does the super dense thing become nothing? If we can just linger on this concept. Yeah. So if I were falling into a black hole, and I tried really fast right as I crossed this empty region, but this demarcation, I happened to know where it was, I calculated, because there's no line there. There's no sign that it's there. There's no signpost. I could emit a little light pulse and try to send it outward exactly at the event horizon. So it's racing outward at the speed of light. It can hover there because from my perspective, it's very strange. The spacetime is like a waterfall raining in, and I'm being dragged in with that waterfall. I can't stop at the event horizon. It comes, it goes. It's behind me really quickly. That light beam can try to sit there like a fish swimming against the Niagara, sitting against a waterfall.

Yeah. How are small black holes or supermassive black holes formed just so people can kind of load that in? Is it always a star? No, so this is also why it's important to think of black holes more abstractly. They are something very profound in the universe, and there are probably multiple ways to make black holes. Making them with stars is most plentiful. There could be hundreds of millions, maybe even a billion black holes in our Milky Way galaxy alone that many stars. It's only about 1% of stars that will end their lives in a death state that is a black hole. We now see, and this was really quite a surprise, that there are supermassive black holes. They are billions or even hundreds of billions of times, the mass of the sun and millions to tens of billions, maybe even hundreds of billions. Extremely massive.

Can we get back to space-time? Just going back to the beginning of the 20th century, how do you imagine space-time? How do we as human beings supposed to visualize and think about space-time where time is just another dimension in this 4D space that combines space and time? Because we've been talking about morphing in all kinds of different ways, the curvature of space-time. How are we supposed to conceive of it? How do you think of it? Time's just another dimension? There are different ways we can think about it. We can imagine drawing a map of space and treating time as another direction in that map. We're limited because as three-dimensional beings, we can't really draw four dimensions, which is what I'd require. Three spatial, I'm pretty sure. There's at least three. I think there's probably more, but I'm happy just talking about the large dimensions. The three we see, up-down, east-west, north-south, three spatial dimensions and time is the fourth. Nobody can really visualize it, but we know mathematically how to unpack it on paper. I can mathematically suppress one of the spatial dimensions and then I can draw it pretty well. Now, the problem is that we'd call it a Euclidean space-time. Euclidean space-time is when all the dimensions are orthogonal and are treated equally. Time is not another Euclidean dimension. It's actually a Minkowski in space-time.

Then what does, according to general relativity, does objects with mass do to the space-time? Right, exactly. Einstein struggled for this completely general theory, not a specific solution like a black hole or an expanding space-time or galaxies make lenses or those are all solutions. That's why what he did was so enormous. It's an entire paradigm that says over here is matter and energy. I'm going to call that the right-hand side of the equation. Everything on the right-hand side of Einstein's equations is how matter and energy are distributed in space-time. On the left-hand side tells you how space and time deform in response to that matter and energy, and it can be impossible to solve some of those equations. What was so amazing about what Schwarzschild did is he found this very elegant, simple solution within a month of reading this final formulation, but Einstein didn't go through and try to find all the solutions. He sort of gave it to us.

How was he able to intuit a world of curved space-time? I think it's one of the most special leaps in human history, right? It's amazing.

Well, on that topic, we have to ask you about the information paradox of black holes. What is it? So this is what catapulted Hawking's fame. When he was a young researcher, he was thinking about black holes and wanted to just add a little smidge of quantum mechanics, just a little smidge. Wasn't going for full-blown quantum gravity, but just asking, "Well, what if I allowed this nothing, this vacuum, this empty space around the event horizon, the stars gone, there's nothing there, what if I allowed it to possess ordinary quantum properties, just a little tiny bit, nothing dramatic? Don't go crazy." And one of the properties of the vacuum that is intriguing is this idea that you can never see the vacuums actually completely empty. We talked about Heisenberg, the Heisenberg uncertainty principle really kicked off a lot of quantum mechanical thinking, it says that you can never exactly know a particle's position simultaneously with its motion, with its momentum. You can know one or the other pretty precisely, but not both precisely.

So then from string theory, one of the resolutions is called fuzz balls. I love physics so much. Originating from string theory, this proposal suggests that black holes aren't singularities surrounded by empty space and an event horizon. Instead, they are horizonless, complex, tangled objects, AKA fuzz balls made of strings and brains roughly the size of the would-be event horizon. There's no single point of infinite density and no true horizon to cross. In some sense it says there's no interior to the black hole, nothing of a cross. So I gave you this very nice story that there's no drama, sometimes that's how it's described, at the event horizon, and you fall through and there's nothing there. This other idea says, "Well, hold on a second, if it's really strings, as I get close to this magnifying quality and this slowing time down near the event horizon it is as though I put a magnifying glass on things and now the strings aren't so microscopic, they smear around, and then they get caught like a tangle around the event horizon, and they just actually never fall through." I don't think that either, but it was interesting.

This is probably it though. Oh, boy. So ER equals EPR is an Einstein-Rosen bridge equals Einstein-Podolsky-Rosen bridge. Posits a deep connection between quantum entanglement and space-time geometry, specifically Einstein-Rosen bridge, commonly known as wormholes. It suggests that entangled particles are connected by a non-traversable wormhole, so tiny wormholes connected. Okay.

So another idea to resolve the information paradox is firewalls, proposed by Almheiri, Marolf, Polchinski, and Sully, AMPS. This is a more drastic scenario arising from analyzing the entanglement to requirements of Hawking radiation to preserve unitarity and avoid information loss, they argued that the entanglement structure requires the event horizon not to be the smooth and remarkable place predicted by general relativity, the equivalence principle. Instead, it must be a highly energetic region, a, quote, firewall that incinerates anything attempting to cross it. Okay. So that's a nice solution. Just destroy everything that crosses the... Do you find this at all a convincing resolution to the information? I would say the firewall papers were fascinating and were very provocative and very important in making progress. I don't even think the authors of those papers thought firewalls were real. I think they were saying, "Look, we've been brushing too much under the rug, and if you look at the evaporation process, it's even worse than what you thought previously. It's so bad that I can't get away with some of these prior solutions that I thought I could get away with." There was a duality idea or a complementarity idea that, oh, well, maybe one person thinks they fell in, one person thinks they never fell in, and that's okay, no big deal. They exposed flaws in these kind of approaches, and it actually reinvigorated the campaign to find a solution. So it stopped it from stalling. I don't think anyone really believes that at the event horizon you'll find a firewall. But it did lead to things like the entangled wormholes embroidering a black hole, which was born out of an attempt to address the concerns that AMPS raised. So it did lead to progress.

Is it possible that there's other intelligent alien civilizations out there that are operating on a different membrane? Is this a bit of an out there question, but I ask it more kind of seriously. Is it possible, do you think from a physics perspective, to exist on a slice of what the universe is capable of? I think it is certainly mathematically possible on paper to imagine a higher dimensional universe with more than one membrane. And if things are mathematically possible, I often wonder if nature will try it out.

As we get progressively towards crazier and crazier ideas. So we talked about these microscopic wormholes. My mind is still blown away by that. But if we talk a little bit more seriously about wormholes in general, also called the Einstein-Rosen Bridges, to what degree do you think they're actually possible, as a thing to study, creeping towards the possibility maybe centuries from now of engineering ways of using them, of creating wormholes and using them for transportation of human-like organisms? I think wormholes are a perfectly valid construction to consider. They're just a curve in space-time. The topologically, which has to do with the connectedness of the space, is a little tricky because we know that Einstein's description is completely in terms of local curves and distortions, expansion/contraction. But it doesn't say anything about the global connectedness of the space because he knew that it could be globally connected on the largest scales. This kind of origami that we're talking about, that you could travel in a straight line through the universe, leave our galaxy behind, watch the Virgo cluster drift behind us, and travel in a straight line as possible and find ourselves coming back again to the Virgo cluster and eventually the Milky Way and eventually the earth, that we could find ourselves on a connected compact space-time.

What do you think would lead to the breakthroughs on dark matter and dark energy? I think dark matter might be less peculiar than dark energy. My hope is that they're tied together, because that would be very gratifying. These aren't just separate problems coming from different sectors, but that they're actually connected, that the reason the dark matter is where it is in terms of how much it's contributing to the universe is connected with why the dark energy is showing up right now. I would love that. That would be a solution like no other, right? And like I said, if it revealed something about dark dimensions, that would be a happy day.

I think one of the most incredible things... I have to talk to you about this. One of the most incredible things that humans have ever accomplished is LIGO. We have to talk about gravitational waves. And the very fact that we're able to detect gravitational waves from the early universe is f-ing wild. It's crazy.

So speaking of the human story, you also wrote the book, A Madman Dreams of Turing Machines. It connects two geniuses of the 20th century, Alan Turing and Godel. What specific threads connect these two minds? Yeah, I was really mesmerized by these two characters. People know of Alan Turing for having ideated about the computer, being the person to really imagine that. But his work began with thinking about Godel's work. That's where it began. And it began with this phenomenon of undecidable propositions or unprovable propositions. So there was something huge that happened in mathematics, which is people imagined that any problem in math could technically be proven to be true. It doesn't mean human beings are going to prove every fact about everything in mathematics, but it should be provable, right? It seems kind of... It's not that wild of a supposition.

I'll give you a common example of an exceptionally brilliant person, Terence Tao. Brilliant.

Limitations. There's so many layers to you. So one of which there's this romantic notion of just understanding humans, exploring humans, and there's the exploring science, the exploring the very rigorous, detailed physics and cosmology of things. So there's the kind of artistry. So I saw that you're the chief science officer of Pioneer Works, which is mostly like an artist type of situation. It's a place in Brooklyn. Can you explain to me what that is, and what role does art play in your life?

Yeah. If you could have one definitive answer to one single question, this is the thing I mentioned to you-