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As predicted we got a lot of questions from people about our trilogy of shows on the size, shape and centre of the universe. Today we’ll do our best to clear them all up.As always, if you’re still confused drop us an email to email@example.com
- Is the Universe a Donut? — COSMOS
- Hypertorus — Loughborough University
- Book: Flatland by Edwin A. Abbott
- Book: Hyperspace: A Scientific Odyssey through Parallel Universes, Time Warps and the Tenth Dimension by Michio Kaku
- Pamela and Fraser re-live the Dark Matter analogy on 365 Days of Astronomy podcast
If the Universe was small enough, would a star’s light be visible to different observers in the same intensity in all directions?
If the Universe is expanding, there must be an edge that is farthest from the center. How can everything be the same distance from the center?
- Balloon Analogy in Cosmology
- The Expanding Universe — SDSS
- Does the fact that the Universe is expanding mean it lacks a physical edge? –Scientific American
Is there an extra spatial dimension?
- How many dimensions are there? — Info Please
- Imagining Other Dimensions — PBS
- Brian Greene — TED talk (You Tube Video)
- Ant on a wire analogy — RedOrbit
If the Universe is expanding, are we expanding, too?
- Physicsforum discussion on this question
- If Universe is expanding, does that mean atoms are expanding?
- Chemical bonding — GSU
- Nuclear bonding energies
Original episodes the listen and check show notes for more information:
We want to get more questions from you. As you know, we have our special question shows that we do just for high school students as part of our work with GLAST. So get your high school class together, we will send you the recording equipment, help you with getting questions recorded, answer your questions personally and send it back so that your class can have the questions answered.
Anything else Pamela?
Dr. Pamela Gay: We want to help you.
Fraser: We want to help you learn. We want to help you get A’s in your Astronomy class. So take the time to ask your teacher, students, classmates, ask your kids. We would love to be able to do a question show for your class.
OK. Let’s get on to the show then. As predicted we got a lot of questions about our trilogy of shows on the size, shape, and center of the universe. A general question we received a lot of comments that people were unsatisfied with us saying that the universe is a donut.
I think we need to clear that up. Pamela, is the universe a donut?
Pamela: No giant entity living in spatial dimensions greater than three is going to come along and bite us â€“ no.
Fraser: So why do we say that it’s a donut? Why do we even bring that up?
Pamela: It’s a word that people are familiar with and it denotes a shape that we’re familiar with. One of the mathematical forms that are attributed to the possible shape of the universe is a hypertorus.
When I say hypertorus people generally look at me like I’m a strange person. When I say like a torus in four dimensions, they look at me a little bit less strangely and then say â€œI’m not quite sure what a torus is.â€
When I say it’s shaped like a donut but in four dimensions, they know what a donut is. It is just a way of communicating some kind of confusing vocabulary words using an image that we’re all familiar with.
Pretty much everyone has seen a donut at some point in life. We all have watched the Simpsons.
Fraser: Right, but we’re not actually talking about a donut; we’re talking about a shape.
Pamela: A four dimensional hypertorus.
Fraser: Right but the point being that it’s a shape that permits two parallel lines to stay parallel forever. In the same way that if the universe was a sphere that two parallel lines don’t stay parallel.
If you start off on a sphere and you start your two lines going, they will spread away from each other as they cross the equator of the sphere and then come back together when they reach the pole again.
Or if it’s a cone you get a similar problem. But when you get a torus, the lines will stay parallel when you move in any direction.
I think the other shape of the universe that has been postulated is a dodecahedron, a twenty-sided dice for you D & D fans out there. I think I get that as well.
Imagine you have one of these twenty-sided die and you run your two lines along one of the faces of the die and then go over to the next facet of the die and the lines stay parallel.
But if it was a sphere, you would get the lines spreading apart, right? Or again, if you had a cube you could take the cube and the two lines will stay parallel and they’ll go over one facet of the cube and they will be parallel and go over another facet and they will stay parallel.
They’ll come right back to where they started again and will remain parallel. Yet it was a shape.
Pamela: This is even true with both the cube and the dodecahedron. If the two lines end up going across opposite sides of a corner such that they pass on two different bases of the object, they still stay parallel and they come back together as they turn the next corner.
And that staying parallel and the fact that you can also draw lines at right angles to them that stay at right angles. Those two different characteristics define a unique geometry. As we try and look for evidence of the geometry of space, these are shapes that we know how to look for the evidence of.
Fraser: I guess that’s the point. Cosmologists are looking at the flat nature of the universe, which they think they have the evidence based on the W-map data that the universe is flat.
Listen to the whole show on that to get how that was arrived at. It’s kind of the same situation. If anyone has read that Flat Land story where you are trying to talk to a two-dimensional creature and trying to explain what a sphere is. There is no way that their little two-dimensional minds and comprehend it.
The only thing that you have is you can take a sphere, push it through the plane that they are on and show how they get a circle, then a bigger circle and then they get an even bigger circle and then a smaller circle and then they get a small circle and that is a sphere.
They may understand that projection of the sphere on to their two-dimensions but they can’t really understand what that three-dimensional object is. They just can see its shape as it passes by.
I think that’s the same thing we have right now. Our universe has a shape; we can’t understand that shape. The best we can do is Cosmologists can come up with a projection of that four-dimensional shape into our three-dimensions.
Pamela: They are working in pure mathematics. They’re designing things in super-computers by giving the computers sets of rules such as â€œthese things must be trueâ€ based on what we’ve observed. The computers are building the shapes that the human mind in general can’t visualize.
Fraser: Even if they finally come up with the shape of the universe that fits the mathematics and can show it’s projection into our three-dimensions in the same way that you can take a sphere and push it through a plane and show a two-dimensional creature what a sphere looks like yet not really show them.
Even when they finally have an answer, and say, â€œIt is this, it has this kind of mathematicsâ€, you and I with our three-dimensional brains won’t be able to visualize it. You can’t comprehend it because it is in four-dimensions.
Pamela: It leaves us with unsatisfactory analogies. Sometimes that’s all we have is ugly mathematics with elegant results and the inability to see things in our own head.
Fraser: So a torus might be the wrong thing; a dodecahedron might be the wrong thing. It might be a shape that in four-dimensions makes perfect sense but which we have no analogy for in our three-dimensions.
Pamela: But we’re looking for the evidence. That is what is eventually going to answer this for us, what we find in the cosmic microwave background.
Fraser: When we talk about a flat universe and how things can wrap back again, where you can end at your starting point, a cube is a great example. Take a cube, draw two parallel lines you’ll see that they remain parallel.
Take a sphere like a ball and you will see that your parallel lines don’t remain parallel. That’s all we’re really getting at in trying to explain.
To be worried if the donut breaks is not going to happen. It is just an analogy. I hope that clears things up for people when we talk about it.
For now, we’re just going to use the word donut wily nilly from here on out.
Pamela: If you want to try this for yourself, go get some narrow Christmas or general wrapping ribbon and try wrapping up a box, a basketball, or a kid’s inner tube from the pool. You’ll see what we mean by keeping the ribbons parallel to one another.
Fraser: Perfect. That’s a great way to do it. I’m going to put you on the spot here because there is one other thing I want you to do.
You were interviewed and you had a great description for dark matter and dark energy which I thought was wonderful. It was one of the best descriptions of it I think I have ever seen. It really gets the point across.
Do you want to have another run at that?
Pamela: Sure. Basically, I constantly I have cranky people asking, â€œWhat’s this stuff, this dark energy that we don’t know anything about? I don’t believe it exists because we don’t know anything about it.â€
No, that’s not true. It’s like your car making a weird noise and you don’t know the source of the noise but you can diagnose that the weird noise occurs when you are going uphill between 30 and 40-miles per hour and the noise seems to be generating from the front right-hand quadrant of your car.
You know all of these things about the noise. You know how to cause it, you know what it causes â€“ noise, vibration, perhaps even causes your car to spit blue smoke. You have all of these different symptoms that there is something weird going on with your car.
You and the mechanic are trying to find the source and you may not know the exact source but you know exactly how to cause the effect. With dark energy, we know what it does; we know where it is and how to see it in our observational data.
We just can’t point to a specific particle and determine this particle, field or something that we have an exact mathematical description of all of its’ properties.
We can’t do that yet but we can say dark matter and dark energy really do both exist the same way I can’t say what is wrong with my car but that rattle really does exist.
Fraser: This has just exactly happened to me. Our car at highway speeds shifting somewhere between fourth and fifth gear was having trouble finding its gear. Also when we were really slowing down to come to a stop it would kind of stutter.
I went in to the mechanic and he said it sounds like there is a problem with the transmission. Usually it’s a problem with this I don’t know, solenoid coil or something like that.
They essentially recommended we get a used transmission from a car that was a lot younger because it could take them a long time to diagnose what the problem is.
They figured it was probably the transmission, they weren’t really sure what it was so we put in a used transmission from a much younger car and it runs really smoothly now, the problem is gone away but we never really found out what it was.
Pamela: We may never fully understand dark energy â€“ I hope that’s not the case. Sadly we can’t go out there and swap out the space between the stars to see if we can make the problem go away.
This is something left for a problem for future generations of graduate students.
Fraser: So Astronomers have a lot of repeatable, dependable observations they are able to make on both dark matter and dark energy and they are learning more and more every day but they still don’t know what’s causing it and they may never know.
Pamela: They know it’s reproducible.
Fraser: Yes, they know it’s reproducible. They know the observations are there. People don’t like the word, but I think that’s just too bad. It’s there.
Pamela: So, make fun of us for stupid names but don’t tell us that we’re making stuff up that’s not there.
Fraser: Right, just to pad the pockets or to get more funding or to build new telescopes or to throw something over on the public is really baseless. Now I think you can use that analogy with your friends.
When someone says dark matter â€“ I don’t like it, use the car analogy and I think you’ll get a lot of distance from it. So, on with the actual show.
Chris Town writes and asks: â€œIf the universe was small enough and there were stars emitting light (as stars do) in all directions would the star’s light be visible to an observer on the exact other side in the same intensity in all directions?â€
I think this is where we talk about if light comes back to where it began, if you look far enough you can see your own back, which so far hasn’t been proven.
But if the universe was small enough and it was true that you could see a star, would you be able to see the star in all directions because it’s emitting light in all directions if you’re standing beside it?
Pamela: This is one of these things where it gets into some really neat side-affects. So, imagine that you’re here on Earth and just like you and I are, I’m sitting here in Illinois and you’re sitting there in Vancouver. Right now if I sent two undergrads running because they’re everywhere and I can do that, and I told one of them to run straight towards you on the shortest path and I told the other one to run straight towards you on the longest paths and take swimmers, they could both get to you by going in a straight line.
One would probably have to go through many oceans, across Africa and back around through Russia and Siberia. They would both eventually reach you on a straight line. One of them would get there much faster than the other.
It’s the same thing with light coming from the star. It could be that the light comes the short path through the universe that gets to you first. Then the star lives and it dies and after the light from the shortest path winks out as the star dies along that shortest path, you might just start getting the light from the longest.
You will get these fascinating time delays depending on just how long the different paths are, so yes, you could see the front and the back of the star at the same time.
Fraser: But at different ages.
Pamela: At different ages and that’s kind of cool to think about.
Fraser: Yeah. It would be almost like different brightness because of how far the light had to travel. I can almost imagine you would see white in the sky because you would be seeing the light from all directions at the same time but it would vary in brightness depending on where the star actually was. Is that right?
Pamela: It leads to a lot of weird confusion. How do you figure out that you’re looking at the same object in two different places?
This is where with the cosmic microwave background where we have looked to see if we can see the front and the back of the universe. Can we see the same thing repeated across the sky? Instead of looking for a single object, a single point source, we’re looking to match patterns in different places. Perhaps you see the same family of objects in two different places in the sky.
Fraser: And we could even more complicate it if the light was being lensed by dark matter in-between and shifting its directions. You would see patches.
I guess this is exactly what the people working with W-map are trying to do; they’re trying to match up the two sides of the universe to see if they are looking in the front door and back door at the same time.
But there is so much complexity and variation going on at the same time that it must be really hard to do. I think that answers the question. You would see the light in many directions and yet it would be really hard to know.
Brett Muenster asks: â€œIf the universe is expanding then there must be an edge where things are more distant from the center. How can everything be the same distance from the center?â€
Pamela: Well, this is again where we have to come back to our balloon analogy. It’s so hard for us as three-dimensional creatures to imagine our universe stretched across the surface of a fourth-dimension basically.
Our expanding universe doesn’t have to have an edge. It doesn’t have to have anything inside it. It’s a new shape that we can’t fully imagine in our mind. So, yes, we’re expanding, but depending on if we’re finite or infinite there may not be an edge.
How do you define what the edge is because if you step off of it, aren’t you in a new place? Haven’t you gone past the edge and you find a new edge? Just like looking at the surface of the balloon, you can’t say where’s the edge of that surface but you can watch that surface expand. It’s expanding into an extra dimension.
Fraser: Yeah, that’s it. I think that’s the best we can do. Take a balloon â€“ where is the edge of the balloon? There is no edge of the balloon. Yet, as you blow up the balloon, the points are getting further and further apart and then you can ask yourself how can those points be expanding? Well, they just can.
Then take that exact analogy, move it up to our three-dimensions and there you are. Don’t worry if it doesn’t make sense because it can’t make sense. You can’t imagine.
Pamela: But it’s fun to try especially late at night with friends. So go out, have a great star party. At the end of the star party, build yourselves a campfire, watch the sun rise and contemplate the shape of space.
Fraser: All right. I hope Brett’s happy with that answer.
Okay Casper Fairhall asked this question. Use the familiar metaphor of space like the surface of a balloon like we just described. Since this surface in our universe comprises three spatial plus one time-dimension does this mean that there is an extra spatial dimension in the same way that a two-dimensional surface of a balloon requires a third spatial dimension?
Pamela: Yes. This is one of the really cool things about particle physics and astronomy. It looks like your universe is probably only a small fraction of all there is â€“ which we already knew.
There are particle physicists that think that our universe isn’t just three dimensions plus time but it’s eleven dimensions, twenty-three dimensions, they come up with all these different numbers. As the Large Hadron Collider starts spitting out data, hopefully we will be able to narrow the number of models.
But it seems almost certain that our universe is made up of way more than three dimensions plus time and we just don’t experience those dimensions because they’ve collapsed down into things that are beyond our ability to observe.
Fraser: So, it’s at least four dimensions.
Pamela: At least four dimensions and probably at least eleven. Isn’t that cool and creepy all at the same time?
Fraser: Yeah, and once again there is no easy way to understand. One of the best analogies I have ever heard to try and explain and understand an additional dimension I think it was Brian Green when he said imagine you have a piece of wire.
From our point of view, that wire is one dimension. Then imagine an ant is crawling around that wire. If you zoom in and zoom in and zoom in and really take a good close look at the ant on the wire, you will have the ant able to go in an additional dimension around the wire.
So not only can the ant go back and forth along the wire, the ant can actually go around it almost like a cylinder so they’re going to be able go around the long way.
There you go. What you thought was really one dimension was really actually two dimensions, or actually three dimensions. There’s where the extra dimensions can come it.
It might be that those extra dimensions are curled up really small inside the dimensions that we already have. That’s a way that at every point in space you can actually move in more directions than you thought.
Pamela: And we just don’t know how many dimensions are out there and we leave that one for the particle physicists.
Fraser: Yeah. Well, lets move on to the next question. I think we’ve seen this one a few times before as well.
This is from Steve McIntosh. â€œThe universe is expanding at twenty kilometers per second or something like that. Even if it were two centimeters per second, wouldn’t we also be expanding? We’re in space too so what keeps us together?â€
So we talk about the Big Bang, the expansion of the universe and yet here we are apart from big turkey dinners, I don’t really feel like I’m expanding at kilometers per second. What’s going on?
Pamela: Well, there are two different things here. First of all the expansion rate of the universe is measured in kilometers per second per mega-parsec. A mega-parsec is about three thousand light years across.
So every more than three thousand light years of space is expanding about seventy kilometers per second. So in the grand scheme of things, that is a really itty-bitty tiny amount. That said, we’d still probably notice it, especially over the entire course of humanity. And we don’t.
It’s not like our bodies are a whole lot bigger and we have to consume a whole lot more food or anything like that. That’s because the size of us and the size of our planet and our solar system and even the size of our galaxy is dictated by gravitational and chemical reactions.
In order for my body to have a given size, I have to eat food and my cells have to divide and a bunch of different biological processes have to go on around me. My body occupies a set volume of space. The total volume of space can expand all at once and those chemical bonds are still going to hold me to the same size.
There are several different ways to think about this. Imagine that you are in an inflatable pool of water. That particular pool of water has maybe a twenty-meter radius or something and it is an above ground pool.
If a dog comes a long and bounces on the side of the pool, it might knock one of the sides down and all of a sudden the volume of the water spreads out. Now if you look down on it, the water is covering a larger area of land.
So originally if you look down in the pool it covered a twenty-meter diameter area. As the water flows out of the pool it is now covering an eighty-meter diameter or a hundred-meter diameter area.
You’re not expanding with the water as the water flows to fill a larger and larger surface area. You’re staying the same size.
In the case of the universe, the universe is spread out like that water was spreading out except it’s doing it in all the dimensions where the water just spreads out across the surface.
Just like you standing in the pool, you stay the same size as the universe around you expands. Our galaxy is held together gravitationally. So the distance between the Earth and the sun is set by their masses and they hold on to each other and they are not going to expand as the space around them expands.
The stars in our galaxy hold on to each other; and even the Andromeda galaxy and we gravitationally hold on to each other. In this case a little bit too tight. In about five billion years, we’re actually going to ram ourselves into the Andromeda galaxy as we gravitationally merge.
So the chemical bonds are stronger. The gravitational bonds are stronger. While there are forces out there pushing the universe apart accelerating the universe apart, those forces aren’t affecting the chemical and gravitational bonds that dictate the type of stuff that we live in that we experience and the size of our bodies.
I wish this were explained more. I remember as a small child (I was a geeky child and read far too much and didn’t understand it) being greatly disturbed thinking what would happen when all of a sudden my shoulders had expanded and my fingers couldn’t touch together anymore.
Not a concern. We’re held together through forces that just really ignore the expansion of the universe.
Fraser: I guess a good analogy is you take a fridge magnet. The force of gravity is pulling on that fridge magnet and holding and turning the Earth into a sphere and keeping you down to the ground.
And yet the teeny tiny little fridge magnet is able to resist the pull of gravity and stick on the fridge. In the same situation, the nuclear bonds that are holding our atoms, the chemical bonds that are holding our molecules together, the force of gravity, magnetism, all of these things just overwhelm the expansive force.
Then I guess the question then is, if we didn’t have those things what would we have?
Pamela: Then I don’t think we would have a universe. But go on.
Fraser: Sure, but let’s say if we had expansion. Would everything expand as with it?
Pamela: Yes. In that case if there were nothing holding the atoms together, nothing holding the stars and the planets together, everything would be carried apart.
There would be a much lonelier universe because nothing would have ever had the chance to form. So we’re glad that we have chemistry and gravity and that these forces are as strong as they are. If they weren’t, we wouldn’t have had the chance to form all of these wonderful structures that let to life.
Fraser: I know one of the concerns has been with dark energy one of the thoughts was this thing was constant as the big rip, right? Where if the amount of dark energy is changing over time that the acceleration of the universe’s expansion is changing.
Imagine if dark energy is a wind that is blowing to help expand the universe or inflate the balloon and someone is cranking up the speed of that dark energy you could get a situation where dark energy gets stronger and stronger and now suddenly it is able to stop the rate of galaxies pulling together.
It’s so strong that it’s actually starting to blow star systems apart. And then suddenly it’s so strong that your atoms start to come apart. So that could be possible except that they don’t think dark energy is changing.
Pamela: Right. And we are all grateful for this. It’s one of these real issues of what if gravity changes with time. What if the strength of dark energy changes with time?
As near as we can tell, all of these things are constants. It’s always fun and it makes for great science fiction to consider what if these things that we count on for being constant weren’t constant.
But we’re safe. We’re okay right now.
Fraser: Okay, good. Well I think that covers the questions that we received although I’m sure this is not going to be the end of it. As always, if you have questions for us, send them in and we’d be happy to answer them.
Pamela: And if you’re a high school student, have your teacher send them in.
Fraser: Yes, have your teacher send them in. So, if you’re a high school student and you want us to call your teacher or anything, just let us know. We want to get more of these high school question shows done so please let us know.
This transcript is not an exact match to the audio file. It has been edited for clarity. Transcription and editing by Cindy Leonard.
Haven’t heard the whole thing yet, but a dodecahedron is a 12 sided polyhedron or a 12 sided dice per your D&D terms.
I’ve only just begun listening to the podcast a few weeks ago and its great, my only problem is that Pamelas voices is just too dam sexy and i lose all concentration on the subject.
Wrapping paper on torus ain’t easy. The torus in math and in reality a little different (at least that’s how I think I should explain it – I don’t really know), since the inner radius of a torus is always < outer radius of a torus, making the wrapping paper crease on the inside part. I wonder if this can still be considered “flat”, since wrapper paper doesn’t quite wrap a real torus well. (Please clarify this puzzle – I have been so confused by it and can tolerate no longer. Thanks.)
So I get how a star would look different if you looked at it, say, to the right and then turned left to wait for the light to travel around the universe the opposite/long way. But I think the question that prompted the answer was asking something else. That is, I think I want to ask something else.
So I’m looking at a star from point A. The star is 10 million light years away. Let’s say I travel really fast in a straight line towards the star, pass through the center, and go another 10 million light years. If I turn back and look at the star from this direction, will it look the same as it did at point A? If I travel back to the center of the star and move straight up for 10 million light years and look down on the star, will it look the same?
My instinct says yes because I would think that a sphere would burn more or else consistently all over its surface. My brain tells my instinct not to be so cocky but can’t say why. Would the star look the same if you observed different sides of it from the same distances?
Karen, some stars are rotating so fast, that they bulge at the equator, and would look slightly different from different vantage points.
Pamela says in this episode that a megaparsec is “about three thousand light years across”. Since a parsec is about 3.2 lightyears, wouldn’t a megaparsec be about 3.2 million light years, not 3.2 thousand? Wouldn’t 3.2 thousand be a kiloparsec?
Whenever I try to picture space having a torus geometry, I think about that old-school video game, Asteroids.
It’s a 2D game, you can fly your spaceship up, down, left and right. When your ship flies past the upper part of the screen, it appears at the bottom. When your ship flies past the bottom part of the screen, it appears at the top; and similarly right to left and left to right.
Is this space a torus geometry?
It would be nice if people were respective of each other no matter there view point. The univese is a BIG place. So there are alot of scenarios that can be had, even the imaginative are not to be discounted. That’s why we have fiction (no matter what catagory) and it could possibly be true if you suggest it. I like all therories but some have to be questioned, others dicounted, some discredited and others (most of them) looked at seriously. So can we not look like we’re talking to some one who doesn’t know anything about cars and help each other to Know about the vast nature that surrounds us, the universe.
A recent issue of New Scientist quoted a comment that time passes more slowly in regions of high gravity. I believe also that as an object approaches a black hole, time for the object is slowed relative to the world outside.
So what would have happened just after the Big Bang, when the entire universe was, say, the size of a pea? Perhaps one could say yes, time passed _very_ slowly, but since everything was running at the same rate, it didn’t matter. But would that affect the speed of light? Would light have taken years to travel this small distance? Does light march to a different drum from the rest of us? – though now the drums are indistinguishable.
I am learning alot from you two. I did not know the Milky Way is now only thought to be in two spiral arms not 4. That’s a huge change in thinking. Thanks for the info. Tom, Cape Cod
dont have time to read all the comments to see if someone has pointed this out….but a DoDecahedron has twelve (12) sides, not 20.