6 ms·

What Shape Is the Universe, Closed or Flat?

87 points by theafh 7y ago

kevin_bloch 7y ago
Maybe I was way off the first time I read it, but I could have sworn that Stephen Hawking's "Black Holes and Baby Universes" already claimed, decades ago, that the universe looped like that. If I remember right, there was some analogy likening us to ants crawling on the surface of the Earth, but I could be conflating it with something else.
tabtab 7y ago
Atheists are going to have a hard time if it turns out the Universe is shaped like a giant Pikachu :-) Some models suggest our universe is just one "foam-bubble" in a big ocean of universes. Hell, the mole on your face may contain its own universes. It really could be "turtles all the way down", or Pikachus all the way down. https://www.vice.com/en_us/article/j5yngp/the-universe-is-made-of-tiny-bubbles-containing-mini-universes-scientists-say https://www.vice.com/en_us/article/j5yngp/the-universe-is-ma... Because of our Earthly experience, we tend to assume there's an absolute limit to the quantity of "stuff", but perhaps that's not true: there is infinite stuff, we just can't touch most of it.
- hombre_fatal 7y ago
  What's up with the Pikachu references? I don't get the joke.
  - earthboundkid 7y ago
    The universe is the dream of an enormous sleeping Pokémon called Slumblord. If it should ever wake, all of our reality will disappear in an instant and be forgotten. “Worship not God but Regigigas, on whom the world rests.” — Henry David Thoreau
rafaelvasco 7y ago
The bubble shape makes much more sense to me than the linear plane shape. Whatever the truth is, the most accepted model today is most likely wrong;
ars 7y ago
Time for Einstein Gravity Probe C. Einstein suggested we could directly measure the curvature of the universe by comparing distances between probes located at angles to each other. They would need to be pretty far apart from each other for this to work, but they can be very small: just an RTG and an antenna. So hopeful light enough to build up an enormous velocity.
- tasty_freeze 7y ago
  For the satellites to communicate to each other they need some combination of a powerful transmitter and a large receiving antenna, so that puts a limit on just how small they can be.
  - ars 7y ago
    I was thinking a laser rather than radio. In radio terms: very very high gain. The receiver can be a mylar reflecting dish, which would be lightweight. Use a gyroscope to steer the entire probe (both for transmitting and receiving). They only need to communicate very very sporadically, and you only need a single bit of data transmitted (amongst each other). Make some kind of schedule where the probes face each other, measure distance (i.e. time between send and reply), then steer toward the next probe. To earth you would basically use Hubble to read the data (and let each probe send duplicate data back to earth).
- namirez 7y ago
  You are right but this has already been done using the CMB data and the universe seems flat with a 0.4% uncertainty. I don't think there is any need for artificial probes for it. Source: https://arxiv.org/abs/1502.01589 https://arxiv.org/abs/1502.01589
  - ars 7y ago
    That's exactly the point of the article - the CMB data is far less clear than advertised.
    - 7y ago
ianai 7y ago
Seems like it would have to be open since the boundaries are permanently expanding. The set can’t contain its accumulation points if new points will always be created. Granted, infinite sets like aleph-0 and -1 are typically considered both open and closed, iirc. Been a while since I took topology.
- patrickthebold 7y ago
  I'm pretty sure when the article says 'closed' the really mean 'compact' in the topological sense. If you have a topological space, the entire space is always both open and closed. https://en.wikipedia.org/wiki/Topological_space#Definition_via_open_sets https://en.wikipedia.org/wiki/Topological_space#Definition_v...
  - foxes 7y ago
    "Closed manifold" means compact with boundary. I think physics might also just mean something with positive "Ricci curvature". Certainly closed 3-manifolds are all equivalent to 3-spheres [0]. I think 4-manifolds are more complicated? In relativity, the idea is all time-like (basically path of ordinary matter) curves will all converge, while the other case, time-like curves always diverge (so open). [0] https://en.wikipedia.org/wiki/Poincaré_conjecture https://en.wikipedia.org/wiki/Poincaré_conjecture
    - kmill 7y ago
      Typo: a "closed manifold" is compact without boundary. The Poincaré conjecture states that closed simply connected 3-manifolds are all diffeomorphic to the 3-sphere. Even stronger, every closed 3-manifold whose fundamental group is finite is a quotient of the 3-sphere by a discrete subgroup of its group of isometries, SO(4) (called the elliptization theorem, which is what Perelman proved). I've been told some astronomers once looked into whether the cosmic background radiation suggested that we lived in Poincaré dodecahedral space. Thurston's geometrization conjecture (all proved as of 2012) is that all closed 3-manifolds can be built out of certain 3-manifolds with standard Riemannian geometries by gluing them together along their torus boundaries and by introducing wormholes, essentially. Some interesting cases are the spherical geometries (constant positive curvature, classified above) and hyperbolic geometries (constant negative curvature, also classified by Perelman). The only actually flat closed 3-manifolds are the 10 finite-order mapping tori of the torus -- one example is S^1 x S^1 x S^1, where the 3-dimensional version of the game Asteroids would be played. There are infinitely many closed hyperbolic 3-manifolds. I don't understand why space can't be negatively curved. Jeff Weeks has a cool program for flying through different spaces: http://geometrygames.org/CurvedSpaces/index.html http://geometrygames.org/CurvedSpaces/index.html 4-manifolds are definitely more complicated. Lots of techniques that work for 3-manifolds and (5+)-manifolds don't work.
unzadunza 7y ago
I read a book a long time ago (Poetry of the Universe: A Mathematical Exploration of the Cosmos, by Robert Osserman) about the shape of the universe. In it he talks about quasars. If you observe 2 of them in opposite directions, each 13 billions light years from earth, then they must be 26 billion light years from each other. But the universe is only a little less than 14 billion years old so how can this be? He argues that the universe must be a hypersphere. I read this more than 20 years ago, and I'm no cosmologist, so forgive me if I butchered that summary.
- YayamiOmate 7y ago
  But that's not the only explanation. If you strech space in each direction you get the same effect. If you have a baloon with a band attached to two opposite points on it's surface and blow the ballon, the distance between points (the band length) on the surface will change 2 times as the distance from the middle. Moreover, if you place some markers on the band the distance between them will also strech. You get that effect in plain Euclidean 3d space. It's not that surprising even for nice orthogonal geometry.

87 points by theafh 7y ago

Maybe I was way off the first time I read it, but I could have sworn that Stephen Hawking's "Black Holes and Baby Universes" already claimed, decades ago, that the universe looped like that. If I remember right, there was some analogy likening us to ants crawling on the surface of the Earth, but I could be conflating it with something else.

tabtab 7y ago

Atheists are going to have a hard time if it turns out the Universe is shaped like a giant Pikachu :-) Some models suggest our universe is just one "foam-bubble" in a big ocean of universes. Hell, the mole on your face may contain its own universes. It really could be "turtles all the way down", or Pikachus all the way down. https://www.vice.com/en_us/article/j5yngp/the-universe-is-made-of-tiny-bubbles-containing-mini-universes-scientists-say https://www.vice.com/en_us/article/j5yngp/the-universe-is-ma... Because of our Earthly experience, we tend to assume there's an absolute limit to the quantity of "stuff", but perhaps that's not true: there is infinite stuff, we just can't touch most of it.

hombre_fatal 7y ago
What's up with the Pikachu references? I don't get the joke.
- earthboundkid 7y ago
  The universe is the dream of an enormous sleeping Pokémon called Slumblord. If it should ever wake, all of our reality will disappear in an instant and be forgotten. “Worship not God but Regigigas, on whom the world rests.” — Henry David Thoreau

rafaelvasco 7y ago

The bubble shape makes much more sense to me than the linear plane shape. Whatever the truth is, the most accepted model today is most likely wrong;

ars 7y ago

Time for Einstein Gravity Probe C. Einstein suggested we could directly measure the curvature of the universe by comparing distances between probes located at angles to each other. They would need to be pretty far apart from each other for this to work, but they can be very small: just an RTG and an antenna. So hopeful light enough to build up an enormous velocity.

tasty_freeze 7y ago
For the satellites to communicate to each other they need some combination of a powerful transmitter and a large receiving antenna, so that puts a limit on just how small they can be.
- ars 7y ago
  I was thinking a laser rather than radio. In radio terms: very very high gain. The receiver can be a mylar reflecting dish, which would be lightweight. Use a gyroscope to steer the entire probe (both for transmitting and receiving). They only need to communicate very very sporadically, and you only need a single bit of data transmitted (amongst each other). Make some kind of schedule where the probes face each other, measure distance (i.e. time between send and reply), then steer toward the next probe. To earth you would basically use Hubble to read the data (and let each probe send duplicate data back to earth).
namirez 7y ago
You are right but this has already been done using the CMB data and the universe seems flat with a 0.4% uncertainty. I don't think there is any need for artificial probes for it. Source: https://arxiv.org/abs/1502.01589 https://arxiv.org/abs/1502.01589
- ars 7y ago
  That's exactly the point of the article - the CMB data is far less clear than advertised.
  - 7y ago

ianai 7y ago

Seems like it would have to be open since the boundaries are permanently expanding. The set can’t contain its accumulation points if new points will always be created. Granted, infinite sets like aleph-0 and -1 are typically considered both open and closed, iirc. Been a while since I took topology.

patrickthebold 7y ago
I'm pretty sure when the article says 'closed' the really mean 'compact' in the topological sense. If you have a topological space, the entire space is always both open and closed. https://en.wikipedia.org/wiki/Topological_space#Definition_via_open_sets https://en.wikipedia.org/wiki/Topological_space#Definition_v...
- foxes 7y ago
  "Closed manifold" means compact with boundary. I think physics might also just mean something with positive "Ricci curvature". Certainly closed 3-manifolds are all equivalent to 3-spheres [0]. I think 4-manifolds are more complicated? In relativity, the idea is all time-like (basically path of ordinary matter) curves will all converge, while the other case, time-like curves always diverge (so open). [0] https://en.wikipedia.org/wiki/Poincaré_conjecture https://en.wikipedia.org/wiki/Poincaré_conjecture
  - kmill 7y ago
    Typo: a "closed manifold" is compact without boundary. The Poincaré conjecture states that closed simply connected 3-manifolds are all diffeomorphic to the 3-sphere. Even stronger, every closed 3-manifold whose fundamental group is finite is a quotient of the 3-sphere by a discrete subgroup of its group of isometries, SO(4) (called the elliptization theorem, which is what Perelman proved). I've been told some astronomers once looked into whether the cosmic background radiation suggested that we lived in Poincaré dodecahedral space. Thurston's geometrization conjecture (all proved as of 2012) is that all closed 3-manifolds can be built out of certain 3-manifolds with standard Riemannian geometries by gluing them together along their torus boundaries and by introducing wormholes, essentially. Some interesting cases are the spherical geometries (constant positive curvature, classified above) and hyperbolic geometries (constant negative curvature, also classified by Perelman). The only actually flat closed 3-manifolds are the 10 finite-order mapping tori of the torus -- one example is S^1 x S^1 x S^1, where the 3-dimensional version of the game Asteroids would be played. There are infinitely many closed hyperbolic 3-manifolds. I don't understand why space can't be negatively curved. Jeff Weeks has a cool program for flying through different spaces: http://geometrygames.org/CurvedSpaces/index.html http://geometrygames.org/CurvedSpaces/index.html 4-manifolds are definitely more complicated. Lots of techniques that work for 3-manifolds and (5+)-manifolds don't work.

unzadunza 7y ago

I read a book a long time ago (Poetry of the Universe: A Mathematical Exploration of the Cosmos, by Robert Osserman) about the shape of the universe. In it he talks about quasars. If you observe 2 of them in opposite directions, each 13 billions light years from earth, then they must be 26 billion light years from each other. But the universe is only a little less than 14 billion years old so how can this be? He argues that the universe must be a hypersphere. I read this more than 20 years ago, and I'm no cosmologist, so forgive me if I butchered that summary.

YayamiOmate 7y ago
But that's not the only explanation. If you strech space in each direction you get the same effect. If you have a baloon with a band attached to two opposite points on it's surface and blow the ballon, the distance between points (the band length) on the surface will change 2 times as the distance from the middle. Moreover, if you place some markers on the band the distance between them will also strech. You get that effect in plain Euclidean 3d space. It's not that surprising even for nice orthogonal geometry.