Cosmic Queries – The Shape of the Universe with Delilah Gates

What is the shape of spacetime? Neil deGrasse Tyson and comedian Chuck Nice discover the structure of the universe, spacetime geometry, and relativity with theoretical physicist at Princeton Gravity Initiative, Delilah Gates.

Speaker names marked ? are inferred from speaking time and the show’s known hosts — they are not voice-verified.

• 0:00Neil deGrasse Tyson?

  Coming up on StarTalk Cosmic Queries, I've got Chuck Nice with me, and we have as our guest theoretical physicist Delilah Gates, and she's an expert on everything spacetime geometry. We're going to learn what that is. We're going to find out if in a spherical universe, whether we can see the back of the head of our own Milky Way. Does the rest of the universe abide by Newton's laws or Einstein's laws? Is the universe curved? And is there a center of the universe? Next on StarTalk.

• 0:35Neil deGrasse Tyson?

  Welcome to StarTalk, your place in the universe where science and pop culture collide. StarTalk begins right now.

• 0:47Neil deGrasse Tyson?

  This is StarTalk Cosmic Queries Edition. I've got Chuck Nice with me to help me out here. Chuck, how you doing, man?

• 0:54Chuck Nice?

  Hey, Neil, what's happening?

• 0:56Neil deGrasse Tyson?

  All right, all right. This is Cosmic Queries on Gravity and Spacetime Geometry. What do you think of that?

• 1:03Chuck Nice?

  Oh, my. I think, you know, why aren't we being a little, you know, you know, we really should be as elementary as possible, you know?

• 1:12Neil deGrasse Tyson?

  Just the basics, get the basics out there.

• 1:15Chuck Nice?

  We need to get these basics out of the way, and I think this is a great time to do it, you know? Yeah.

• 1:22Neil deGrasse Tyson?

  So.

• 1:22Chuck Nice?

  Not everybody, yeah, go ahead.

• 1:25Neil deGrasse Tyson?

  Yeah, yeah. So whatever I know about this is not enough to do a whole show on it. And so we got to get, we have to, we've, we've, we found one of the world's experts on this subject, and she's with us today, Delilah Gates. Delilah, welcome to StarTalk.

• 1:41Chuck Nice?

  Hi, thanks for having me.

• 1:44Neil deGrasse Tyson?

  Yeah, yeah. And from your resume here, you have freshly minted PhD, like 18 months ago or something.

• 1:51Chuck Nice?

  That's right.

• 1:52Neil deGrasse Tyson?

  Am I getting that right?

• 1:52Chuck Nice?

  That's absolutely right. Oh, wow. You know what? I thought, I thought that was it. You got that new doctor smell. I thought.

• 2:01Speaker 02

  Well, as long as it's a pleasant one, I'll take it.

• 2:04Neil deGrasse Tyson?

  There you go.

• 2:06Chuck Nice?

  Absolutely, absolutely.

• 2:07Neil deGrasse Tyson?

  So you got your PhD in physics from Harvard a couple of years ago, and now you're at the Princeton Gravity Initiative. So what is that? What does that even mean?

• 2:20Speaker 02

  So, yeah, the Gravity Initiative is a center here at Princeton. And most of the people involved with it are postdocs and affiliated professors and a few grad students. And we are a bunch of people who ask questions about compact objects, by which I mean objects that have the strongest gravity that we have in our universe. That's black holes and neutron stars. And also people who study questions of math related to general relativity and gravity as well.

• 2:48Neil deGrasse Tyson?

  So is that because what Einstein realized was that there are entire branches of mathematics that you need, that the physicists might not have expertise in? And then the mathematicians come in to help out? Is that kind of what happens there?

• 3:01Speaker 02

  That's kind of what happens. It's actually an interesting back and forth. So of course, discovering Einstein's equations and the solutions to it that describe the shape of spacetime around things like black holes was revolutionary. And of course, new math needed to be introduced to be able to calculate these objects. But additionally, just the fact that we now know our universe hosts these objects, black holes, neutron stars, these strong gravity environments, leads to just mathematical questions about whether spacetime itself is stable, for instance. And so the mathematicians have a back and forth interplay with the physicists when it comes to asking questions about gravity.

• 3:45Neil deGrasse Tyson?

  Delilah, that completely spooked me when you said spacetime might not be stable.

• 3:51Chuck Nice?

  Exactly.

• 3:51Neil deGrasse Tyson?

  Okay.

• 3:52Chuck Nice?

  It's like, yeah, what happened? Did we break up with another universe in the multi-universe?

• 3:58Speaker 02

  The question of stability shouldn't be as scary as it sounds. Certainly, we think it should be stable. It hasn't broken yet. We're still all here to ask these questions, so we don't think it's broken yet. It's more so just, though, mathematically, understanding if something is stable is a little bit different from, you know, just by fiat saying we exist, therefore it is. So we...

• 4:20Neil deGrasse Tyson?

  And Chuck, it has nothing to do with emotional stability, just to be clear, okay?

• 4:25Chuck Nice?

  That's where I'm gonna go immediately.

• 4:29Neil deGrasse Tyson?

  So Delilah, is there, tell us what spacetime is and spacetime geometry, just so we're all on the same page.

• 4:36Speaker 02

  Absolutely. So let me back up a little bit and just talk about, you know, our own intuition. We live in a world where we're able to move around and we kind of can get this feel that there are three dimensions in which we can move. We can move back and forth, we can move left to right, or we can move up and down, right? And so that feels like three dimensions. And, you know, for a long time, we used classical mechanics and Newtonian gravity to describe what was going on in that situation. But when Einstein came along with special relativity, he told us that time, the way we perceive sequences of events, is also related to the dimensions that feel like spatial dimensions to us. So

• 5:19Speaker 02

  what we actually have to do is think of space and time as being one object. And to move from thinking about them as just one object, this object also has a shape. And this is when Einstein added general relativity to tell us about what that shape is. There's this relationship between the shape of quote unquote spacetime, this fabric that we all live in, which has to do with the way we're allowed to move physically through space, as well as the way we perceive time flowing in space. This one object is shaped by the stuff that's in it. So gravity is given to us by general relativity. From Einstein tells us, energy and matter tell spacetime how to be shaped, and the way that spacetime is shaped tells matter how to move throughout spacetime, what paths it

• 6:04Speaker 02

  should take.

• 6:06Neil deGrasse Tyson?

  Wow. All right. And so when you have your, when you have your, your, your high-gravity objects, that tests your ideas and the mathematics at their limits, in a way, right? Because I guess all, everything that you described is happening here and now around us, but it's not manifesting in any important way that we would change our lives based on it, right?

• 6:29Speaker 02

  That's right. It's true that, for the most part, we can use You know, classical mechanics and Newtonian gravity for the way things are. And we don't have to appeal to-

• 6:38Neil deGrasse Tyson?

  Delilah, it was good enough, it was good enough for my grandparents, okay?

• 6:41Speaker 02

  I mean, hey, it's honestly good enough for all of us when we drive our cars, when we throw baseballs, you know? We don't have to think about, oh my goodness, how is the baseball warping space and time as I throw it to my friends?

• 6:52Neil deGrasse Tyson?

  In my generation, we were, that was good enough for us.

• 6:55Speaker 02

  I think most of us actually live our physical intuitive lives without having to appeal to it. But, you know, even, even in the time of Einstein, it became relevant. It was, you know, first tested general relativity and the corrections it makes to Newtonian's gravity was first tested using solar eclipses. So even the way our sky appears, you know, is affected by, by general relativity. Even though we don't need it for the way we intuitively move about our day for both, for the most part.

• 7:30Neil deGrasse Tyson?

  Plus, as I understand it, the entire Apollo program used just Newtonian gravity. So like, it was good enough for us to get to the moon-

• 7:38Speaker 02

  Absolutely.

• 7:38Neil deGrasse Tyson?

  -to you young whippersnappers that are trying to do something extra with it. So, so we have questions that we solicited from our Patreon fan base. And if you want to ask questions too out there, you can join our Patreon. And there's a pretty affordable lowest level where you get to ask these questions. And so Chuck, you, you compile them?

• 7:57Chuck Nice?

  Yeah, these are all specifically for Delilah.

• 8:01Neil deGrasse Tyson?

  Good, cool.

• 8:01Chuck Nice?

  Christine Dolman says, hello, Dr. Tyson, Doc, Dr. Gates and Sir Chuck. No, that's Lord Chuck, Christine. I'm a teacher and a young scientist. I love facilitating the study of geometry. How are two and three dimensional shapes represented across the universe? Spheres are easy, but what about the rest? Aha, yes. The spheres, the spheres happen even here, naturally, underwater. And for some reason, everything becomes a sphere, so. What's going on there? And what about the rest?

• 8:37Speaker 02

  Well, I guess, you know, when thinking about the shapes of various things, often the question is, you know, what is energetically easy? Spheres are easy. And it's because, you know, you can make things smooth and try to, you know, fit a minimal surface area around a maximal amount of volume.

• 8:58Speaker 02

  For, if you think about, a fun thing is if you think about water and space. If you have a drop of water, it's roughly spherical when it floats in space, unencumbered by the force of gravity. Of course, if you touch it a little bit, it'll, it'll vibrate and wiggle. But it, it wants to be spherical because of the surface tension, trying to find an easy way to relax. But I will say, what about the rest about shapes throughout space? If we're thinking about objects, one thing that I think is profound is that in physics, we kind of think that things are generic. We think that the laws of physics here are the laws of physics everywhere. And we try to come up with, with theories that describe the whole of what happens anywhere in the universe. And of course, this is what we want.

• 9:43Speaker 02

  I do hope the way I throw a ball is the same way I would throw it on one side of the earth or another side of the earth, or if I went to the moon, as long as I calculate for the change in the mass of the, the planet I'm standing on. So the shapes should all be described in the same way, depending, regardless of where we are in the universe.

• 10:05Neil deGrasse Tyson?

  Oh, that's very clean.

• 10:07Speaker 02

  That's very clean. Okay.

• 10:08Neil deGrasse Tyson?

  On earth as it is in the heavens.

• 10:13Chuck Nice?

  That was good.

• 10:14Neil deGrasse Tyson?

  All right. Chuck, give me another one.

• 10:16Chuck Nice?

  Great question, Christine Toldman. Thanks. This is Trevor C. Mills. Trevor is coming to us from Augusta, Georgia. He says, "Greetings, Dr. Tyson, Dr. Gates, and Chuck. I know that currently it is not believed that wormholes, sizable ones at least, have the ability to be stable. Is this due to the geometry of spacetime itself? If so, what about the geometry of spacetime prevents stable wormholes? And if not, then does, then what does?"

• 10:52Chuck Nice?

  Prevent stable wormholes.

• 10:55Neil deGrasse Tyson?

  Ah. You know, when people ask that, I try to ask them how old they are, because if they're like 12 or 13, then you got to check the basement, see if they're making something down there. Because they get the nemesis of superheroes.

• 11:07Neil deGrasse Tyson?

  Sounds like an innocent question, you know, on the surface.

• 11:10Chuck Nice?

  Yes, yeah, there is an addendum here is, and if I were to create a wormhole, would I be able to get one billion dollars?

• 11:22Speaker 02

  Hey, I'm sure if we created a wormhole, you know, someone would try to, try to use it to make money.

• 11:28Neil deGrasse Tyson?

  In various ways. So, so Deli, we, we mentioned instabilities earlier, and here we're talking about the stability of a wormhole. So what's up with that?

• 11:35Speaker 02

  So I will say, as a caveat, my expertise is not math, so this is a question, the mathematical side, as a mathematician of general relativity or spacetime geometries, but from my understanding, this goes to the question of the way how things change when you add additional matter. Often when we solve for the shape of spacetime in Einstein's equations analytically,

• 12:04Speaker 02

  we only do it in specific circumstances where everything, all the matter is only, say, in the black hole or the neutron star, very compact. But of course, you know, if you want to jump through a wormhole, you're yourself matter. And if you are matter, you cause, according to Einstein's equations, the shape of spacetime to change slightly. So when mathematicians try to understand the stability of spacetime, of certain spacetime objects, like black holes or wormholes, what they really have to do is add a little bit to the mathematical description of the shape to account for adding, say, a person trying to jump through the wormhole. And then you have to calculate whether or not the equations break down, or can settle

• 12:46Speaker 02

  back down into their original form, once the person has moved through the wormhole. And that's a hard thing to do. I don't know what the generic rules are about what make this up, but typically stability is not an easy thing to prove. It's still an open question whether spinning black holes are stable.

• 13:04Neil deGrasse Tyson?

  All right. So, so what you're saying is the, it's still not a completely solved problem, which is interesting, which keeps open the doorway for science fiction writers. And I don't have a problem with that, you know, as long as we. We give them a little bit of latitude, let them run with it.

• 13:18Speaker 02

  It also keeps the door open for mathematicians who want to study the area.

• 13:22Neil deGrasse Tyson?

  Mm hmm, mm hmm, mm hmm. All right, what do you have next?

• 13:26Chuck Nice?

  All right, here we go. This is, uh, let's see here. Let's, uh, let's move away from home and go to Quinton in Switzerland. Quinton says, "If the universe has a closed spherical, spherical shape, could one of the galaxies in the sky that we look at be the Milky Way in its past state?" Oh, wow. So can we look out and then see around?

• 13:56Neil deGrasse Tyson?

  Oh, just, oh, come around the backside?

• 13:59Chuck Nice?

  Should we come around the backside?

• 14:01Neil deGrasse Tyson?

  Is that the back of your head, Chuck?

• 14:03Chuck Nice?

  Yeah, exactly. How did that happen, man?

• 14:06Neil deGrasse Tyson?

  Move out of the way, Chuck.

• 14:08Chuck Nice?

  I see I need to get a shape up in the back of my head.

• 14:13Neil deGrasse Tyson?

  Actually, we're gonna take a quick break, but when we come back, we're gonna find out the answer to whether if the universe is spherical, does looking out in one direction end up coming right back so that you can see the back of your own head? Or at least the back of the Milky Way's head? When StarTalk continues with our guest, Delilah Gates.

• 14:43Speaker 03

  I'm Joel Cherico, and I make pottery. You can see my pottery on my website, cosmicmugs.com. Cosmic Mugs, art that lets you taste the universe every day. And I support StarTalk on Patreon. This is StarTalk with Neil deGrasse Tyson.

• 15:04Neil deGrasse Tyson?

  We're back. StarTalk, Cosmic Queries, talking about spacetime geometry and gravitation with freshly minted PhD.

• 15:13Neil deGrasse Tyson?

  Delilah Gates, who is now at Princeton University in their Gravity Initiative program. That's just so audacious. It's like, no, there's still some gravity we don't understand, and we gotta figure this out, and let's get some smart people all in the same place at the same time. See what I did there?

• 15:30Chuck Nice?

  Yeah.

• 15:33Neil deGrasse Tyson?

  Look at that. See, see how clever I was with that? State time jokes. I know.

• 15:42Neil deGrasse Tyson?

  So, so this is a question from Switzerland. Just read it back real quick, Chuck.

• 15:47Chuck Nice?

  Sure thing, sure, sure, sure thing. This is Quentin from Switzerland. He said, if the universe had a closed spherical shape, could one of the galaxies in the sky be the Milky Way in its past state?

• 16:00Chuck Nice?

  Interesting.

• 16:01Speaker 02

  So this is a great question. And in principle, the answer is if the universe had a closed spherical geometry, then indeed we could see the, our own Milky Way in the sky. But there is one problem, however.

• 16:16Speaker 02

  Or one other element you need to consider. Even if the universe is spherical, you also have to consider its size. There would have had to be enough time since the Milky Way started for the light from it to reach us. So even if the universe was spherical, but the universe was too big, the light from the, from our universe that went around, ball the back around, and then to come back at us, wouldn't have had enough time. So in principle, the answer is yes, but you also need to consider how large the universe is to understand whether or not one would be our, our own galaxy that we're seeing in our sky.

• 16:52Neil deGrasse Tyson?

  Then what's the answer for this universe? Then we should know that, right?

• 16:55Speaker 02

  Well, we-

• 16:55Neil deGrasse Tyson?

  Are we big enough, or are we small enough for that?

• 16:57Speaker 02

  Yeah, we don't, we, we don't see any evidence that, that the observable universe, in the observable universe, in, in all the light we can see, from starting close to the Big Bang with things like the cosmic microwave background, we don't see any evidence that our universe is closed and spherical.

• 17:17Neil deGrasse Tyson?

  Okay.

• 17:17Speaker 02

  Another thing is, we also, if you-

• 17:21Speaker 02

  Talk about whether the universe is closed. It doesn't have to be a sphere. There are other closed geometries, like tori. And different.

• 17:29Chuck Nice?

  I don't, I don't, I don't know what a tori is.

• 17:32Speaker 02

  A tori is a donut.

• 17:33Neil deGrasse Tyson?

  It's the pearl of Taurus, dude.

• 17:34Speaker 02

  Yeah, a Taurus.

• 17:35Neil deGrasse Tyson?

  It's a pearl of Taurus, dude.

• 17:36Chuck Nice?

  Now, I know.

• 17:37Speaker 02

  It's not, it's not, it's not, it's not a, it's not a, it's not an astrology sign. It's a, it's a, it's a donut.

• 17:45Chuck Nice?

  That's it, okay. That's the first time I ever heard tori, okay.

• 17:49Neil deGrasse Tyson?

  It's a pearl of Taurus. Alright, so what you're saying is we're in an open universe, not a closed universe?

• 17:55Speaker 02

  We think we're, we're death, there's definitely no evidence we're in a closed one. And there's also no evidence that we are on a geometry that is curved, like a sphere. You could, for instance, if you, even if you didn't know the universe was big enough that you couldn't have seen the light from yourself wrapped back around, you might say, that doesn't matter, I can just look at the overall curvature of the spacetime. And we don't have any evidence that the curvature of the spacetime isn't flat. We, we, all of our evidence is, has an error constraining around it, constraining it around being flat geometry.

• 18:31Neil deGrasse Tyson?

  So, in other words, the uncertainties, even in our understanding of the flat universe, do not include the possibility of us being closed?

• 18:39Speaker 02

  Well, yes, that's correct, that's correct.

• 18:42Chuck Nice?

  Wow.

• 18:42Neil deGrasse Tyson?

  Right, okay.

• 18:43Chuck Nice?

  So, but intuitively, when you think about it, if the universe, not if, we know the universe is expanding, and you look into space, it, doesn't it have to be expanding in all directions all at once? Which, the only thing that we know that goes in all directions all at once is, you know, like a sphere and an ellipse, or something like that. So intuitively, your mind goes to, oh, it's gotta be shaped like that.

• 19:06Speaker 02

  Um, I think, you know, one would, one, um, one intuitively from geometry that we understand might suspect that, but actually, I think that's a little bit of, of... Of where you have to actually use your math to tell you that you should be careful of your own intuition because at large scales, we don't necessarily intuitively have to live by the rules of, say, Newtonian gravity.

• 19:30Chuck Nice?

  Ah.

• 19:32Speaker 02

  Just because, consider, you know, just a plane. If you were a two dimensional being and you lived on a plane, that plane could go on forever without having to be wrapped around such that it didn't have a, um, such that it closed in on itself. So it could just be you're on an infinite plane. Um, and then, of course, you can extend that into 3D to have an infinite volume.

• 19:52Chuck Nice?

  Right.

• 19:52Speaker 02

  So intuitively, this is a case where we got to check our math and tell ourselves we don't necessarily have to be in a closed universe.

• 20:00Chuck Nice?

  I love it.

• 20:02Neil deGrasse Tyson?

  Yeah, so Chuck, stop using your damn intuition, okay?

• 20:06Neil deGrasse Tyson?

  That's what.

• 20:07Chuck Nice?

  Believe me, that, we gave up on that a long time ago.

• 20:12Neil deGrasse Tyson?

  I, I opened one of my books with, with this statement, "The universe is under no obligation to make sense to you."

• 20:19Chuck Nice?

  Yeah, it's very cool.

• 20:21Neil deGrasse Tyson?

  Put that out there.

• 20:22Chuck Nice?

  We like it. We like that.

• 20:24Neil deGrasse Tyson?

  What more do you have, Chuck? Keep coming from our Patreon members.

• 20:27Chuck Nice?

  Mm-hmm. Let's keep on going with Patreon member Dylan, who says, "Greetings, Dr. Tyson, Dr. Gates, Chucky Baby." Oh, my God, I haven't heard that since. What was that show where the guy went, "Chucky Baby, Chucky Baby, Chucky Baby"? Damn.

• 20:41Neil deGrasse Tyson?

  I don't remember. I don't remember.

• 20:42Chuck Nice?

  All right. "Undergrad Astrophysics at NAU in Flatstaff, that's where you'll find me. General relatively allows for three possible shapes of the universe, Euclidean, positive and negative curvatures. Curious on which shape you most lean towards." So we just got finished talking about, uh, you know, how we got to check the math not to be, uh, relying on our intuition. But now, uh, we have a question directly to you, Doc. Well, where do you come down on the whole shape issue?

• 21:18Speaker 02

  Um, well, I tend to, I tend to be conservative and trust my colleagues. And so there's amazing experimentalists out there who have so far shown us that we shouldn't expect that the universe overall has a curvature. So I definitely lean towards it being, being flat. I will say, you know, when people ask this question, I want to caveat, this is on large scales. Of course, gravity, the gravity tells us that there is curvature where there's matter. So certainly around black holes, the spacetime is very curved, but it's like on large scales. If you average it, we think it's supposedly flat.

• 21:57Chuck Nice?

  Yeah. And to your last point, we have pictures of that. That's of course, we think that because we, we've actually seen it, not the black hole itself, but how light interplays around the black hole. So we know that what you just said, you know, that it's.

• 22:11Speaker 02

  Absolutely. Speaking of black holes, we had a question earlier about the, this idea of seeing the back of our, our Milky Way, if we were in a closed spherical, small enough geometry for our universe, even if we're not, a place where you can potentially see the backside of your own head is actually around a black hole. Black holes have a region around them called the photon sphere. And this is a region where light can wrap around many times around the black hole, coming pretty close to its original position before either spiraling out very far away from the black hole or falling into the black hole. So if you want to see the back of your head, go near a black hole.

• 22:52Neil deGrasse Tyson?

  So the light is basically in orbit around the black hole.

• 22:55Speaker 02

  That's right.

• 22:55Neil deGrasse Tyson?

  Is that a fair way to say that?

• 22:56Chuck Nice?

  So cool.

• 22:57Neil deGrasse Tyson?

  Yeah. So you look straight ahead and you will see light that headed backwards and came around to the front of your face. And that would be your, your nap, the nappy back of your head.

• 23:08Speaker 02

  That's right.

• 23:09Neil deGrasse Tyson?

  Go to the barber shop.

• 23:10Chuck Nice?

  There we go. That's what we're talking about.

• 23:12Neil deGrasse Tyson?

  Right, right.

• 23:13Chuck Nice?

  Wow, that is so cool.

• 23:14Neil deGrasse Tyson?

  That would make for a weird picnic, you know? Do you know who you're looking at? Who, you see the front and the back of them at the same time? And then you walk towards them, but you don't know which one you look, I mean, that would, that's, that's, that's something somebody needs to do in a movie.

• 23:29Speaker 02

  Oh, absolutely. I imagine it'd be very disorienting.

• 23:31Chuck Nice?

  Yeah.

• 23:32Neil deGrasse Tyson?

  Yes, completely.

• 23:33Chuck Nice?

  Worst movie theater ever. Down in front.

• 23:43Chuck Nice?

  Oh wow. Oh, that's a fascinating, fascinating, fascinating little.

• 23:47Neil deGrasse Tyson?

  The photon sphere, very cool, okay.

• 23:49Chuck Nice?

  Photon sphere, love it, love it. All right, here we go, this is Tegan Messier. And Tegan says, hello, Dr. Gates. This is Tegan from British Columbia here. Uh, what shape do you think our universe is? We already said that. Um, I heard an idea that it could be shaped like the DNA molecule, since the DNA is the best way to store information that we are aware of. Any thoughts on this? So now, the reason why I read this is because there are a lot of people who actually make connections between our own physiology, our brain, our neurosynaptical systems, and the universe itself. Uh, do you see any connection there?

• 24:34Speaker 02

  I will say there's, uh, the shape of DNA is a kind of funny and wide shape, so there is no reason to expect that to be the shape of our universe. But I do think there are a lot of, uh, beautiful analogies between, um, humanity, our own DNA, um, the structures, shapes of things here on Earth, and the shape of things, uh, that we see in the sky, like, um, the shape of where matter is, following the galaxies, and dark matter, if we run simulations to see where the stuff is clumped. It has, um, interesting patterns that feel a lot of like, kinds of natural, quote-unquote, patterns we'd see here, um, on Earth. And I think, uh, one of my favorite, um, analogies between humanity and the universe is the fact that we are all made up of cells,

• 25:19Speaker 02

  and yet we are conscious, and so we're tiny cells, uh, that somehow have become conscious and can ask questions about ourselves. In the same way, um, we are made up of the same stuff as the rest of the universe. Um, and so humanity and any other sentient life out there, uh, that's asking such questions is really, you know, made up of these tiny things and then able to query itself about itself. Where the universe is asking itself about itself. And I think that's pretty, pretty, pretty darn cool.

• 25:52Neil deGrasse Tyson?

  Damn.

• 25:53Chuck Nice?

  Damn.

• 25:54Neil deGrasse Tyson?

  Damn.

• 25:54Chuck Nice?

  Alright, goodnight ladies and gentlemen, that's our show.

• 26:00Neil deGrasse Tyson?

  You can't follow that with anything, right?

• 26:01Chuck Nice?

  Yeah, what do you do with that?

• 26:04Neil deGrasse Tyson?

  So, I think it was in the Carl Sagan era, there was the phrase,

• 26:10Neil deGrasse Tyson?

  "Humans are a way for the universe to know itself." And, that sounds all poetic, but it's kind of egocentric, because it implies

• 26:18Chuck Nice?

  It is.

• 26:18Neil deGrasse Tyson?

  that we are the ultimate source of how the universe can know itself, when it could have made some way smarter aliens in the other sector, okay?

• 26:25Speaker 02

  Well, I did say, us and any other sentient beings out there. I do think it's humorous to think we're alone.

• 26:31Neil deGrasse Tyson?

  Completely, of course, yes, yes.

• 26:35Chuck Nice?

  Look at that, we are not alone. Look at that, so, all you extraterrestrial enthusiasts out there, we're not alone. You just heard it here. Okay, uh, this is Brian Lacy. Hello, it's Brian from Baltimore. I've heard of toroidal shapes, like the donut, and that our universe may even be that. How does it work in, wait a minute, here's the questions, because we just touched on that. So just to let you know, I'm not crazy. How does this work in upper dimensions? So that's the difference from what we just touched upon about the tori. So, you know, how do things change once we get to other dimensions?

• 27:17Speaker 02

  So if we add dimensions, actually, you know, depending on what we're describing, things don't change too much. We can think about, we know how to measure the curvature of shapes. Actually, it turns out, intrinsically, which means we don't have to embed them in higher dimensions to know how to measure their curvature. So, you know, you might think I can measure the shape of a circle, because I can hold an object that's a circle. But if I lived on the circle, I wouldn't be able to describe its shape, unless it was small enough for me to walk all the way around and come back to the same point. But in geometry, this isn't quite true. There are intrinsic ways, in principle, to measure curvature. So, we can get at the curvature, even if we live in the spacetime.

• 28:01Speaker 02

  And so the same measures we would use to say is spacetime curved in our 3 plus 1, that means 3 space plus 1 time.

• 28:11Speaker 02

  Spacetime that we live in, we could play the same mathematical games and use similar experiments that we've developed to measure the the shape of spacetime in higher dimensions. It turns out.

• 28:24Neil deGrasse Tyson?

  So what does what does a higher dimensional torus look like? Like, what is that?

• 28:30Speaker 02

  Well, it's a it's a shape I can't draw on a piece of paper because we only have so many dimensions. But it's more or less in a way the same similar to what we have now. You could think of having describing a torus, at least topologically. You can describe a torus as as a as taking a closed object like a sphere and then puncturing it. And you can count, you can describe tori by how many punctures they have. There's the doughnut, which has one puncture. You know, you've seen inner tubes where they're where you when you go down a like a water slide where two people can sit on it. That's a torus with two holes, or we call the holes genus.

• 29:13Speaker 02

  And so you can do the same game in higher dimensions. And you can say, starting with a closed shape, and I puncture holes into it, and I can describe it by how many holes it has.

• 29:21Chuck Nice?

  Whoa, that is really dope. That is cool.

• 29:26Neil deGrasse Tyson?

  Next time I'm on a two-seater water slide, I'll be thinking of this conversation. For sure.

• 29:34Chuck Nice?

  Absolutely.

• 29:35Speaker 02

  I think that's one of the fun things about being a physicist is you can you can think about analogies to the stuff you're learning in physics and math, geometry, etc. When you come across everyday objects, and it makes them, in my mind, feel even more exciting to to think about.

• 29:51Neil deGrasse Tyson?

  Mm hmm. Mm hmm. All right.

• 29:54Chuck Nice?

  All right.

• 29:55Neil deGrasse Tyson?

  Chuck, keep it going.

• 29:57Chuck Nice?

  This is Hi Do, and Hi Do says, Hello, Dr. Gates, Dr. Tyson, Lord Nice. I've always wondered if the golden ratio ever applied to anything astrophysical in nature. If not, why? We hear it used often with terrestrial architecture, art, music, etc. Do you ever find these examples in astrophysics?

• 30:22Speaker 02

  Wow, so maybe Neil can tell us more, but to my understanding, I'm not sure that the golden ratio tends to pop up in any astronomical observables or measures to my knowledge.

• 30:38Neil deGrasse Tyson?

  I haven't, I haven't seen it either.

• 30:41Speaker 02

  Yeah. I think one thing that does, you know, in a sense, pop up more often is pi. But that's because pi is related to spheres.

• 30:50Chuck Nice?

  Cool.

• 30:51Speaker 02

  So a lot of equations, like Einstein's equation, for instance, has pi in it.

• 30:58Neil deGrasse Tyson?

  It is where pi shows up in the, in the, in the most unlikely places that you'd ever think.

• 31:03Speaker 02

  Yes.

• 31:03Neil deGrasse Tyson?

  And there it is. Like, how'd you get it? Who let you in?

• 31:06Speaker 02

  Who ordered that? Hey, you, you, some of us order pizza pies and some of us order the number pie.

• 31:14Chuck Nice?

  There you go.

• 31:16Neil deGrasse Tyson?

  All right.

• 31:16Chuck Nice?

  All right. Let's move on. This is Zubersing. He says, hello, Dr. Gates, Dr. Tyson and Chuck. Here's my question. How does the, how does the geometry of spacetime change in the presence of massive objects like a black hole? And how does this affect motion of objects in the vicinity of those massive objects? So, I mean, if you want to talk truly massive, it'd have to be, you know, the black holes at the center of our galaxies.

• 31:50Speaker 02

  Absolutely. So, you know, we all know that our planets, for instance, in our solar system, orbit the sun. And so this is, this effect where we can get matter to travel around an object many times is the name, namely, one of the biggest features of having mass really concentrated. And so when we concentrate mass even more into a smaller area and we get even heavier objects, these effects get more and more pronounced. Namely, for black holes, the defining feature of them is that you have so much gravity that not only is it Planets or other massive objects that can get on paths that are closed,

• 32:34Speaker 02

  you also can get the same thing happening to light. And you can even get it such that you have the event horizon, gravity so strong that even light can't escape from the black hole if it gets too close. So it's just a bigger and more pronounced effect of what you probably know from your astronomy classes or science class when you learn about planets being able to be on orbits. And like I mentioned, the photon sphere earlier, you can get light bending around black holes multiple time. And of course, you have the defining feature of them, the event horizon, the surface around the black hole, the area from which if light gets caught, if light goes to that that area, then it won't be able to escape the gravity and leave the planet,

• 33:19Speaker 02

  leave the black hole, excuse me.

• 33:22Chuck Nice?

  That's pretty cool. Yeah, no, you just said, you know, what the photon sphere again. And what just popped into my head as a question is, how are you recognizing the same light as opposed to the new light that's coming in from behind the black hole? So how are you identifying these are the same photons that we just registered whenever?

• 33:44Speaker 02

  Great question. So if you are thinking about the problem from a mathematical standpoint, you can do the following. You can say, I have, I can shoot light from different positions around the black hole and watch and calculate all the paths that it can take. And so it's when you do that, if you say, I have a source here and an observer here, I shoot off light and I watch the different paths that connects my observer and my source, or my source and my observer, then you can just look at the different paths to see how many times it winds. In actuality, in the real world, we don't have experiments that are so powerful yet

• 34:28Speaker 02

  that we can necessarily easily detect the light from an object, being the light that wound many times. But in principle, one could look at, say, a black hole that has stuff spiraling around it, and they could look for statistically correlations in the image to know that they saw light from that object that wound different amounts of time.

• 34:58Neil deGrasse Tyson?

  Okay, alright. Chuck, we gotta take a break. We'll be coming back for our third and final segment of Cosmic Queries, Spacetime Continuum Edition, when StarTalk returns.

• 35:24Neil deGrasse Tyson?

  We're back, StarTalk, Cosmic Queries. We're talking about the Spacetime Continuum with Dr. Delilah Gates of Princeton University. Do I understand correctly that you make an appearance in a Netflix series, what's it called here, A Trip to Infinity, is that correct?

• 35:40Speaker 02

  That's correct. There's a Netflix special called A Trip to Infinity, which I appear in, and it has experts, mathematicians, physicists, philosophers, and we take the chance to discuss what it's like to try to grapple with the concept of infinity, what it means to mathematicians and physicists and philosophers, and try to give people a way to understand it. I think it's wonderfully done, has beautiful animations, and can give anyone the sense of awe that I feel and that I think many physicists and scientists feel who think about these kinds of problems when we do our work.

• 36:21Chuck Nice?

  I love it. I have it bookmarked, and I haven't watched it, but now I'm gonna watch it.

• 36:25Neil deGrasse Tyson?

  Alright Chuck, last segment.

• 36:27Chuck Nice?

  Last segment, we'll make it quick. I mean, I'll keep things moving, but first, let me just give the PS to Zubr Singh, who I promised that I would, but he says, "My educational background is in the humanities, but because of Neil and Cosmos, I am now a huge fan of astrophysics." Love what he's doing. Just wanted to say that, okay? Okay, let's do this. This is Colby LaPressey, who says this. "Hey, it's Colby from South Carolina here. Hi Neil, how's Chuck? Hi Dr. Gates. Why do we always see galaxies appear closer and closer together when we look deeper and deeper in space? Does this have any indication of the shape of the cosmos?

• 37:04Chuck Nice?

  I get that we're looking back, but what's the deal?"

• 37:08Speaker 02

  I think the deal is twofold. I think, one, as we can see further and further away, of course, if you think about having a forest, and you can only see the trees a certain distance, and then you can add on distances, it seems more dense. Not that they weren't always there, but just because you have farther depth. in your vision, so it seems more crowded because you're seeing further and further away black galaxies stacked on top of each other. So that's one. And then two,

• 37:37Neil deGrasse Tyson?

  but it's a line of sight. So that's a line of sight thing.

• 37:39Speaker 02

  That's a line of sight thing. And then I think

• 37:41Neil deGrasse Tyson?

  Right, right. It's not that they're actually next to each other. They're they're just lined up in your line of sight.

• 37:46Speaker 02

  Exactly.

• 37:46Neil deGrasse Tyson?

  And they feel like they're crowding.

• 37:47Speaker 02

  Exactly. And I think

• 37:48Chuck Nice?

  And in photography, in photography, that's called depth of field. And when you use a longer lens to take a picture, you can squish things together with a telephoto lens. But go ahead.

• 37:56Speaker 02

  Absolutely. So there's the depth of field. But then also, because we are the way we view things, we view things kind of, you know, from one position, if you view things, you view things in a cone, if you have a conical view outward. So additionally, you can stack more things kind of directly behind each other. So it looks denser. But you also, as you look out, you see a conical kind of field of view. And so you have, based on just the shape of a cone, right? You can fit less things here than you can fit at the top of the cone. And so the top of the cone, the things that are farther away, you can also see more of those. So it's I think it's part of it is depth, as well as the fact that we view things conically. So it looks like we're seeing more and more. And then,

• 38:39Speaker 02

  but it's not actually a statement necessarily about something having fundamentally changed. Those galaxies were there. They've been there for a long time. It's just we have new technology.

• 38:52Neil deGrasse Tyson?

  And by the way, galaxies do collide. So it's not that that does happen. But I want to add something here. And that is, in the past, because if you look out in space, you're looking back in time, the universe was smaller than it is today. So this angle of view that you send out to the edge of the universe actually encloses much more of the universe in the early time than it does in the later time, simply because the universe was smaller. It's an interesting phenomenon that we that we see. So we have to adjust the measures of the distances between things that we get from the angle that we see. So

• 39:35Neil deGrasse Tyson?

  so there would be distortions on this cone that Delilah was talking about. Yeah. So the cone doesn't go straight out. The cone actually focuses back a bit as you go out there. And so cramming in more of the universe into the field of view. It's a pretty cool effect, actually. Yeah.

• 39:53Chuck Nice?

  Let's keep going. Great question there, Colby. We appreciate you. This is Woody from Adelaide who says. Adelaide, Australia? Yes, sir. Australia, okay. Yeah, we're getting them from all over the world today, man. Right, alright. People are interested in this, uh, this subject. Woody says, "I often see visualizations and descriptions of the fabric of spacetime, where a 3D structure stretches and bends, but is it possible for spacetime to be anything like a fluid near or inside of an event horizon?" Oh, I like that. Wow, look at that.

• 40:29Speaker 02

  So, I'll start with the fact that we don't know what happens inside of an event horizon. We can make mathematical speculations, but like Neil said, the universe has, uh, is not obligated to be understandable by us or be, um, in accordance with what we've so far calculated. And since an event horizon by definition is a region from which light cannot escape, we can get no information about what's behind it, at least as far as our understanding is today. Um, but if we even think about the spacetime that we have outside of black holes, um, we can think of it in a way, um, as something that is in motion.

• 41:10Speaker 02

  Um, because sources of, that's things like black holes, galaxies, planets, all these things are moving. So, the shape of spacetime around them is also always dynamically changing and adjusting as the matter moves on top of it. Um, and in fact, in able to, in order to understand, um, the gravitational wave detections that we have from LIGO, um, and the other, um, experiments, COGRA and such, um, we have to dynamically calculate the way spacetime changes, uh, stretches, uh, and contracts because of the two massive objects spinning in on each other to emit gravitational waves.

• 41:50Speaker 02

  So, in fact, yes, the universe is like a fabric or a geometrical shape, but it's not rigid.

• 41:59Neil deGrasse Tyson?

  Not rigid.

• 42:00Chuck Nice?

  Not rigid, okay.

• 42:01Neil deGrasse Tyson?

  Right, right.

• 42:02Chuck Nice?

  Wow, look at that.

• 42:03Neil deGrasse Tyson?

  Okay.

• 42:03Chuck Nice?

  Fascinating stuff, fascinating stuff.

• 42:05Neil deGrasse Tyson?

  All right, another one, check.

• 42:06Chuck Nice?

  Let's keep moving on, okay, here we go. This is Bruce Ryan. Bruce Ryan is from Alexandria, Virginia. He says, "I once heard Neil say that there is no center of the universe." Hey, what's up with that? If the universe started from a single point, there has to be a center at some moment. Okay.

• 42:27Neil deGrasse Tyson?

  All right, Delilah, dig us out of that one.

• 42:29Speaker 02

  So, this is the, again, where our intuition is fooling us if we think about what we're used to. But in fact, we know, for instance, that the universe is probably not shaped like a sphere, but for a moment, suppose it was. If it was shaped like a sphere, and you're a person who lives on this sphere, who's to say what point is more special than any other point on that sphere? And so, when we say that the universe is expanding, it's not talking about, it's not talking about expanding away from any one given point that's the center, it's the whole thing expanding in size. Think of drawing a point on the surface of a balloon, and then blowing up the balloon.

• 43:14Speaker 02

  All points on the surface of the sphere get farther and farther away from each other, but none of them is more special than the others. And this is what we mean when we say there's no center to the universe, despite the fact that it's expanding.

• 43:26Neil deGrasse Tyson?

  I like to think of it that there is a center, but you can only find it if you go back in time. So, it's a place in time, not in space.

• 43:35Speaker 02

  Yes, yes.

• 43:36Neil deGrasse Tyson?

  What do you think of that?

• 43:37Chuck Nice?

  Excellent, a place in time. See, my answer is the center of the universe is, in the words of Little Richard, "Me."

• 43:46Neil deGrasse Tyson?

  Okay.

• 43:50Neil deGrasse Tyson?

  Little Richard, the only one who have ever said me? Is that you gotta go to him?

• 43:54Chuck Nice?

  He's the only one that ever said it like that.

• 43:56Neil deGrasse Tyson?

  Like that, that's right.

• 43:57Chuck Nice?

  Like that, yes, which I love. Sorry, just wanted to give him a shout out. Love that guy, he's dead, but who cares? All right.

• 44:04Neil deGrasse Tyson?

  All right, quick, a quick last one. Give it to me.

• 44:06Chuck Nice?

  Can we get a last one in? All right, let me find something here that is.

• 44:10Neil deGrasse Tyson?

  Delilah, you gotta go on soundbite, soundbite mode.

• 44:13Speaker 02

  All right.

• 44:13Neil deGrasse Tyson?

  Delilah, okay, all right, let's go.

• 44:16Chuck Nice?

  All right, this is Jesse Desmond. Okay, I picked the wrong one, cuz I don't even know what this is, but I'm gonna do it anyway. Could the Mandela? Could the Mandela effect be the result of a parallel universe colliding with ours? Imagine two bubbles colliding, but instead of bursting, uh, they form a double bubble.

• 44:35Speaker 02

  I hesitate to say yes to that. I, just because I don't understand how mathematically we would set up the situation to describe this, and mathematics is king in theoretical physics. You have to write down your theory and then test it, so. If we don't have that, I hesitate to put any weight behind it, sorry.

• 44:54Neil deGrasse Tyson?

  And, and, remind us of the Mandela effect described here, is that?

• 44:59Speaker 02

  The Mandela effect is this effect where we misremember, like, like, large swaths of people will remember something falsely, like, um, Luke, I am your father in Star Wars. I think he just says, I am your father. I think there's no Luke before it.

• 45:13Chuck Nice?

  Yeah, he never says Luke.

• 45:13Speaker 02

  Or Berstein bears versus Berenstain bears. So it's this thing where it seems like as a whole, lots of people seem to misremember something, which feels uncanny.

• 45:24Neil deGrasse Tyson?

  Right, right, right. There's another one, like, uh, it was, uh, played again, Sam. There is no again. He just says, play it, Sam, I'm pretty sure.

• 45:34Chuck Nice?

  Oh, cool.

• 45:35Neil deGrasse Tyson?

  Yeah, I think, or, or the, the inverse of that. But what people misremember that collectively are certain about what their memory is, and it's just all wrong. So what is it we're, we're misremembering about Mandela?

• 45:47Chuck Nice?

  That he's not Dr. Martin Luther King.

• 45:54Speaker 02

  I think it might be when he died is what people misremember.

• 45:57Neil deGrasse Tyson?

  Right. Okay.

• 45:59Chuck Nice?

  Okay.

• 46:00Neil deGrasse Tyson?

  All right.

• 46:01Chuck Nice?

  All right.

• 46:01Neil deGrasse Tyson?

  Well, there you have it. He's got the name. So the day we do discover parallel universes intersecting in ways that are interesting, Mandela is remembered for this. This is cool. I like that. Yes. And not Luke. Not Star Wars.

• 46:16Chuck Nice?

  Not the Luke effect.

• 46:18Neil deGrasse Tyson?

  Let there be some social justice gained by the collision of two parallel universes. Well, Delilah, it's been delightful to have you on and congratulations on your recently minted PhD. Good luck. Sometimes you need a little bit of that going forward in this universe. And if you make any new discoveries or you hear about anything very cool, give us a holler. We'll put you right back on because it's clear.

• 46:42Chuck Nice?

  Tell us first.

• 46:45Speaker 02

  Will do.

• 46:45Chuck Nice?

  Tell us first, Delilah.

• 46:47Speaker 02

  Thank you so much for having me.

• 46:49Chuck Nice?

  Don't let the Princeton people call the New York Times. You call New York Times first.

• 46:55Speaker 02

  You got it.

• 46:56Neil deGrasse Tyson?

  Really good. This has been StarTalk Cosmic Queries Edition with Dr. Delilah Gates, a newly minted PhD at Princeton University, right down the block from us in New York. Chuck, always good to have you, man. Always a pleasure. Neil deGrasse Tyson here, as always, bidding you to keep looking up.