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Old 11-05-2019, 02:47 PM
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A spherical Universe?


Science magazines have been publishing articles in the past 2 days after a paper in Nature Astronomy suggesting the Universe is not flat but spherical.

What current laws of physics point to this and if true which established laws of Physics will have to be binned?
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Old 11-05-2019, 03:04 PM
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A link with the claims would be nice.
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Old 11-05-2019, 03:05 PM
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Huh. I've always just assumed the universe is spherical.
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Old 11-05-2019, 03:11 PM
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I recall from a very long time ago that a "flat" universe does not mean two-dimensional, but rather that if you got in a spaceship and went in a particular direction, you could go on forever. But a "spherical" universe means you would eventually return to your starting point, just like if you flew all the way around Earth. Is that what is being referred to here?
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Old 11-05-2019, 03:30 PM
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Current measurements are heavily in favour of a flat universe - https://map.gsfc.nasa.gov/universe/uni_shape.html

Looks like this article, or something like it, are at the root of the question - https://www.sciencealert.com/wild-ne...urved-not-flat

The articles look to be based on https://www.nature.com/articles/s41550-019-0906-9 where the authors argue that anomalies in the gravitational lensing of the cosmic microwave background radiation can be explained by a curved/closed spacetime geometry.
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Old 11-05-2019, 03:37 PM
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The laws of physics are perfectly fine with either possibility (or with a hyperbolic universe, which is the opposite of spherical, sort of like the shape of a Pringle). It's not consistency with the laws that's the issue; it's observations. And even there, it's complicated by the fact that a spherical (or hyperbolic) universe with a very large radius looks an awful lot like a flat one, so even if our observations suggest that the Universe is flat, we can never actually rule out the possibility that it's spherical but just really big.
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Old 11-05-2019, 04:28 PM
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I recall from a very long time ago that a "flat" universe does not mean two-dimensional, but rather that if you got in a spaceship and went in a particular direction, you could go on forever. But a "spherical" universe means you would eventually return to your starting point, just like if you flew all the way around Earth. Is that what is being referred to here?
Basically, yes.

If I understand this correctly, some guys basically were looking at the latest and greatest data for the cosmic background radiation and came to some interesting conclusions. One problem we have with our current understanding of physics is that there is more gravitational lensing in the cosmic background than there should be if the universe is flat. We can correct that mathematically by adding in a "lensing factor" of sorts, but then we don't understand what that lensing factor actually means from a real world point of view. It's just a fudge factor in the math.

What this paper says is that if you look at the best numbers we have now and assume a curved universe, we can actually get rid of the lensing fudge factor.

And that's all that the paper says. It's only looking at background radiation and lensing and stuff related to that.

Others have pointed out that while the curved universe gets rid of this mysterious lensing fudge factor that we have been using, it breaks other things. So either way, whether the universe is flat or curved, there are things going on that don't match up with our models of how we think they should behave.

Still, it is interesting that, according to this study, the lensing factor does go away if you assume a curved universe.

Last edited by engineer_comp_geek; 11-05-2019 at 06:06 PM. Reason: fixed word changed by stupid autocorrect
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Old 11-06-2019, 05:20 AM
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Some of the terminology here may confuse laymen. Since I am often a confused layman myself, let me try to help.

For laymen, "sphere" is often used to denote what mathematicians call a "3-ball" (three-dimensional ball). Technically a "sphere" "or "2-sphere" is the shape that corresponds just to the surface of a 3-ball. (Flatlanders living on a 2-sphere, e.g. the surface of the Earth, would think about only two dimensions. The 3rd dimension arises for us when we contemplate a 2-sphere because it is convenient for us to imagine it as the surface of a 3-ball.)

But in this thread, "sphere" refers not to 2-sphere but to 3-sphere — the (3-D) boundary of an imaginary 4-dimensional ball.

One way to understand a 2-sphere is to cut two disks out of thin sheets of plastic, glue their edges together and then pull on and stretch the plastic till you get the desired spherical shape. To do something similar to get a 3-sphere, you'd start with two 3-balls, glue the complete surface of one, point-by-point, to the complete surface of the other (*) and continue from there. (* - This will be impossible, although you might imagine a 4-D creature doing this in 4-D space.)
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Old 11-06-2019, 05:42 AM
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Is this new? I always heard the universe is curved so that if you go forward long enough you'll end up back where you started.
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Old 11-06-2019, 07:17 AM
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Until around 1999, it was an open question whether the Universe was closed, flat, or open. Some may have preferred one model over another, but without any real evidence.

Since then, the evidence has all been that the Universe is flat, or very close to it (and had some surprises that we didn't expect in 1999).

There may be something to this new study, but it'll face a serious uphill climb if it disagrees with two decades of evidence.
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Old 11-06-2019, 08:45 AM
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Is this new? I always heard the universe is curved so that if you go forward long enough you'll end up back where you started.
No, that was always just one possibility, and the recent evidence (until this study, at least) has pointed against it.
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Old 11-06-2019, 09:00 AM
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Huh. I've always just assumed the universe is spherical.
Originally this is what I thought as well. Starting from a single point and moving out in all directions. I had to revise that idea due to the fact that there was not an equal amount of matter and anti-matter - leading me to assume that the universe is actually asymmetrical.
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Old 11-06-2019, 10:53 AM
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Well consider there's no space for the point to expand into; it is its own space. So why would it have to be radially symmetrical like an explosion?
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Old 11-06-2019, 11:07 AM
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Huh. I've always just assumed the universe is spherical.
Yeah, it's equally awful no matter what angle you look at it from.
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Old 11-06-2019, 08:37 PM
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One reason folks might have thought the Universe was closed, when its shape was still undetermined, was the expanding-balloon analogy. It's only an analogy, and no analogy is perfect, but it's a lot closer analogy for a closed universe than it is for an open one.
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Old 11-07-2019, 12:06 AM
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On rare occasions, I, like many others, sometimes have trouble visualizing a universe with 4 dimensions of space. The depictions of the different universe geometries seem to always use a 2D plane in our 3D space and show how it deforms when placed into a different geometry. Trying to scale that slice up to a full 3D space in a new geometry hurts the head.

I wonder what various objects, like a cube, would look like in a saddle universe. Or, what would a cube constructed in a saddle universe would look like after it has undergone a transformation into our presumed-flat universe.
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Old 11-07-2019, 12:45 AM
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On rare occasions, I, like many others, sometimes have trouble visualizing a universe with 4 dimensions of space. The depictions of the different universe geometries seem to always use a 2D plane in our 3D space and show how it deforms when placed into a different geometry. Trying to scale that slice up to a full 3D space in a new geometry hurts the head.

I wonder what various objects, like a cube, would look like in a saddle universe. Or, what would a cube constructed in a saddle universe would look like after it has undergone a transformation into our presumed-flat universe.
4 dimensions of space? I guess you could visualize that with some effort, but there are lots more videos showing what things look like near a black hole, or in variously shaped 3-d spaces
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Old 11-07-2019, 08:44 AM
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What do you mean by a cube? In a curved space, there exists no object with all of the same properties as a cube. You can pick and choose some of them, but depending on what you pick, you'll get different shapes.
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Old 11-08-2019, 07:53 AM
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Is this new? I always heard the universe is curved so that if you go forward long enough you'll end up back where you started.
Kind of like the old video game Asteroids...you leave off one side of the screen and re-enter the opposite side.

https://boards.straightdope.com/sdmb...ight=asteroids
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Old 11-08-2019, 08:11 AM
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Well, the "Big Bang Theory" has held prominence for ages. If the universe did indeed come into being in that manner, the explosion would send matter in all directions from a central point. It would have to expand as an ever growing spherically shaped entity. How could it possibly be flat? I've never heard of any serious theory maintaining that the universe is flat
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Old 11-08-2019, 08:58 AM
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Well we don't know the natural shape of a universe. Perhaps the shape requiring the least amount of effort is saddle shaped.

But I think you're considering "flat" as the surface of a sphere - somewhere it's possible to start at point A and return to point A. But that's a 2-D surface on a 3-D object. It's more like (but not) being inside the sphere and trying to get back to your starting point by going in a straight line.
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Old 11-08-2019, 10:46 AM
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Well, the "Big Bang Theory" has held prominence for ages. If the universe did indeed come into being in that manner, the explosion would send matter in all directions from a central point. It would have to expand as an ever growing spherically shaped entity. How could it possibly be flat? I've never heard of any serious theory maintaining that the universe is flat
The Big Bang didn't fling material out of a central point into the surrounding space. It created the very fabric of space (and time) itself!

This means it's not quite as intuitive for a couple of reasons:

1) you might expect that our ever expanding universe is adding new "space" at the edges as it spreads into infinity. That's not quite right. Our current understanding is that the smallest unit of measure possible in our universe is something called the Planck Length. The same way that the picture on your TV is granular at the level of a pixel, our universe is granular at the level of a Planck. And instead of growing at the edges (adding new pixels to the edge of the TV screen) our universe grows by adding new Plancks in between existing ones (push two pixels in the middle of the screen aside and put in a new one in between).

2) If you were to walk along the surface of the Earth, what you'd find is that you are NOT walking in a straight line. You are curving along the surface of the Earth. A curved space time isn't like that. If our universe was curved, you could move in a truly straight line -- ie if you started on Earth and walked forward, you'd eventually need to leave the surface at a tangent to the curve of the Earth. But even though you're TRULY moving in a straight line, in a curved universe you'd end up back where you started.

3) Except that you could never make it. The fastest speed anything can move at within the universe is the speed of light, but two points can move away from each other at an effective speed that's faster than light! that's because they aren't literally moving apart faster than light, rather the space between them is growing because new planck-sized bits of space are appearing between them.

So yeah -- our universe expanding rapidly in all directions doesn't actually have any bearing on whether or not the fabric of space time is flat or not. We can't figure out the curvature of space just because our observable universe (The area that light can actually reach us from) is a "sphere".

By the way, space obviously DOES curve -- in the presence of matter, which curves space time in a way we see as gravity. But the question is whether the universe itself, absent any matter, is flat or not.
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Old 11-08-2019, 11:49 AM
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Well, the "Big Bang Theory" has held prominence for ages. If the universe did indeed come into being in that manner, the explosion would send matter in all directions from a central point. It would have to expand as an ever growing spherically shaped entity. How could it possibly be flat? I've never heard of any serious theory maintaining that the universe is flat
This is a very common misconception. The way that the Big Bang is taught, people often think of all matter being squished down into a point, and then expanding outward into a 3d space that already existed. The 3d space did not exist.

Think of it this way. Stick a flag somewhere out in space. This flag never, ever moves. It stays right where it is, always. Now stick another flag out in space, say 100 million miles away from it. This second flag also never, ever moves. Even though neither flag moves, they both end up moving away from each other. Both flags are not moving. So how can they move away from each other if neither one is moving? The space itself between them is expanding. And it's not just these two flags. Space everywhere is expanding.

Now, rewind the universe backwards in time. Again, those two flags never move, at all. But they keep getting closer to each other, just because as you go back in time, the space itself is getting smaller. As every point in space gets closer and closer together, eventually all of the points is space itself squish down into a single point.

So it's not that matter started out as a single point and expanded into an already existing space, but instead, matter and space itself were all squished down to a single point. That point two feet away from you? That was squished down into that single point. That flag that's 100 million miles away, that point also gets squished down to the single point. And, importantly, the flag never moved. Space itself squished.

Admittedly, this is kinda hard to grasp, since we are constantly thinking of everything in terms of an already existing 3d space.

Here is another analogy that might help. Imagine that instead of being a 3d person, you only have two dimensions. As far as you are concerned, the universe is a flat sheet of paper. You can go in the X direction, and you can go in the Y direction, but you can't go up off of the paper. There is no Z direction in this imaginary 2d universe. Now, imagine that instead of being a piece of paper, the universe is actually the surface of a balloon. The tricky part here is not to think of the balloon as a 3d object in 3d space, like we are used to thinking, but instead think of only the surface of the balloon. You can go in any direction along the surface of the balloon, but you can't go up off of the surface, and you can't go down into the inside of the balloon. You can only go around along the surface of the balloon. There are only 2 dimensions in your universe.

When the Big Bang happened, the "balloon" was completely deflated, so all of the bits of the balloon are packed down right next to each other. Then the balloon inflates, and they all spread out away from each other. The balloon keeps getting bigger and bigger, so if you draw a dot on the surface of the balloon and draw a dot about an inch away from it, neither dot moves, but as the balloon inflates, the dots keep getting farther away from each other.

A "flat" universe is like your piece of paper. Only it's a stretchy piece of paper, and it keeps expanding. A "curved" universe is like the balloon. If you keep going in one direction along the surface of the balloon, you'll eventually get back to where you started.

So the real universe is kinda like that, except in 3 dimensions instead of 2. If you pick a direction and go that way forever, do you keep going, or do you come back around to where you are now, even though you never turned? That's the flat vs. curved universe theories.

Last edited by engineer_comp_geek; 11-08-2019 at 11:51 AM.
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Old 11-08-2019, 12:07 PM
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I'm sure I'm not the only one who's thought of this but...
You know how on very small scales there duality - like a photon can be a wave or a particle depending on how you look at it?
Could there be some kind of duality on very large scales?
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Old 11-08-2019, 03:39 PM
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What kind of duality are you thinking of? As it stands, your question is too vague to answer.
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Old 11-08-2019, 04:07 PM
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That the universe could be flat, curved, AND closed depending upon how you measure it.
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Old 11-08-2019, 04:21 PM
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I can't see any way that could work, at least not in the sense that we're talking about here.
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Old 11-08-2019, 04:35 PM
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So no Nobel prize for zoid?
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Old 11-08-2019, 11:52 PM
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If the space between everything is expanding like a balloon, wouldn’t it appear that “stuff” farther away would appear to be accelerating faster? Like if you were toward the center of the balloon, and looking at the edges, the edges would accelerate quicker than the objects closer to you, but the volume increases consistently, Ie. constant speed of light.
It’s probably already been explained or debunked over my head in this thread, but these threads with expert folks are fascinating.
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Old 11-09-2019, 12:53 AM
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If the space between everything is expanding like a balloon, wouldn’t it appear that “stuff” farther away would appear to be accelerating faster?
Yes. This is called "Hubble's Law" and as the name implies, credit for the discovery generally goes to a guy named Edwin Hubble (though technically another guy discovered it first).

This is the same guy that the Hubble space telescope is named after.
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Old 11-09-2019, 03:12 AM
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If the space between everything is expanding like a balloon, wouldn’t it appear that “stuff” farther away would appear to be accelerating faster? Like if you were toward the center of the balloon, and looking at the edges, the edges would accelerate quicker than the objects closer to you, but the volume increases consistently, Ie. constant speed of light.
It’s probably already been explained or debunked over my head in this thread, but these threads with expert folks are fascinating.
You're not quite getting the balloon analogy. It's meant to be a 2-dimentional analog, so the inside and outside of the balloon are not part of the analogy. Just the surface. So there is no center of this 2D analog, just as there is no center of the universe.
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Old 11-09-2019, 07:42 AM
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So no Nobel prize for zoid?
Well de Sitter space allows slicings where the spatial sections can be flat or curved and can be closed too. It depends on your coordinate choice. de Sitter space can be regarded as a cosmological model, but it's lack of matter makes it an unrealistic one.
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Old 11-11-2019, 09:05 AM
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This month, in Universe shapes:

The Universe is 41 times more likely (?) to be closed than flat.

Or

There's a 99% chance the Universe is closed. (This article has some nice art and explanation of some of this.)

Next month: there's a 1 in 42 chance that the Universe sits on the back of a Hyper-Turtle.
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Old 11-11-2019, 03:49 PM
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And again, this all depends on these few specific new results being correct, which they might or might not be.
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Old 11-11-2019, 05:07 PM
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Kind of like the old video game Asteroids...you leave off one side of the screen and re-enter the opposite side.

https://boards.straightdope.com/sdmb...ight=asteroids
I was never sure, are those games spherical worlds, or toroidal? Or is it possible to distinguish the two given what we know (that going past the top of the screen brings you back to the bottom, and going past the left edge brings you to the right side, and vice versa)?
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Old 11-11-2019, 05:31 PM
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Most edgeless video game worlds (including Asteroids) are toroidal, and yes, it's possible to tell the difference.

If our Universe is toroidal, or some other non-trivial topology, however, it's on scales too large for us to see any of the repetition. And yes, we've looked.
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Old 11-11-2019, 06:47 PM
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Okay, if the universe is "flat" and finite, it has an edge, right? What would the edge of space be like?

I once saw a science fiction movie where a spaceship was propelled to the edge of space. It was like a solid wall, that wasn't an actual thing, but just the absence of space. I don't think that's accurate ... or is it?
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Old 11-11-2019, 06:52 PM
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An Asteroids screen is flat, finite, and edgeless. And there are other similar arrangements.

Personally, I favor rhombic dodecahedrons, just because they're cool.
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Old 11-11-2019, 07:07 PM
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I thought we'd established that an Asteroids screen is a torus? And a torus isn't "flat," is it?
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Old 11-11-2019, 07:48 PM
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I thought we'd established that an Asteroids screen is a torus? And a torus isn't "flat," is it?
Your basic Asteroids torus is perfectly flat, in the sense that it has zero curvature everywhere, which is clear since it locally looks like 2-d Euclidean space.
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Old 11-11-2019, 08:07 PM
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I don't know what that means.

But Asteroids space is curved, so that the top of the screen meets the bottom, and the left meets the right... isn't it?

Maybe we're using different meaning of "curved" and "flat."
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Old 11-11-2019, 08:19 PM
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Whatever you mean by "flat", if a flat piece of paper is "flat" then so is an Asteroids screen because they are indistinguishable on a local basis. Yes, the top of the screen meets the bottom, but that is a large-scale phenomenon (imagine you are an ant, then you couldn't tell without walking all the way around). There are no seams or bends. Also keep in mind this is an Asteroids flat torus and not a bagel-shaped surface.
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Old Yesterday, 07:45 AM
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To a topologist, the local curvature doesn't matter. A sphere and a cube are the same topology. A simple handle coffee cup and a donut (torus) are the same topology.

As to an arcade game with a toroidal geometry there are two primary mappings: The top and bottom edges wrap through the center of the donut and the sides go around the hole or vice versa. Once you introduce such a mapping then there is a distinction that can be made.

The terminology can be a bit muddled in terms of talking about a purely Mathematical model or something that is more of a Physics notion.
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Old Yesterday, 08:22 AM
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Okay, if the universe is "flat" and finite, it has an edge, right? What would the edge of space be like?....
This might be helpful: https://www.youtube.com/watch?v=AwwIFcdUFrE
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Old Yesterday, 12:13 PM
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To a topologist, the local curvature doesn't matter. A sphere and a cube are the same topology. A simple handle coffee cup and a donut (torus) are the same topology.
Quite true, but I want to consider not only the topology of the toroidal surface, but the additional Riemannian manifold structure where we can measure lengths, angles, etc., and in particular the curvature is defined at every point, and in the case of the arcade screen is zero, which is not the case if you twist it into a doughnut.

If you try to cram a flat torus into three-dimensional Euclidean space it ends up very wrinkled...
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Old Yesterday, 01:52 PM
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Quote:
Originally Posted by DPRK View Post
Quite true, but I want to consider not only the topology of the toroidal surface, but the additional Riemannian manifold structure where we can measure lengths, angles, etc., and in particular the curvature is defined at every point, and in the case of the arcade screen is zero, which is not the case if you twist it into a doughnut.
I'm a topologist, not a geometer, but yes, the torus can be given a metric in which the Gaussian curvature is everywhere 0. It's just the metric inherited by quotienting the plane. See Wikipedia's section on the Flat Torus.
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Old Yesterday, 04:41 PM
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You can't embed a torus into a three-dimensional space without giving it some curvature. But who said anything about wanting to embed it into 3-dimensional space? The Universe is presumably not embedded into any space larger than itself, and it has whatever topology it has independent of any embedding or lack thereof.
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Old Yesterday, 05:42 PM
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Yeah, there's that Math vs. Physics issue. Yeah, Math people like to be able to define flat toruses. Physics people know that's crazy. And these are people who love to model particles in 11 (or is it 13?) dimensions.

A lot of Math is crazy and impractical. Until it isn't.
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Old Yesterday, 06:10 PM
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Physics people know that's crazy.
We do?
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Old Yesterday, 07:48 PM
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Tori are not that crazy. Maybe Seifert–Weber space or something...
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