
What Shape Is the Universe, Closed or Flat? - theafh
https://www.quantamagazine.org/what-shape-is-the-universe-closed-or-flat-20191104/
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kevin_bloch
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.

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unzadunza
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.

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YayamiOmate
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.

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ars
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.

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jessriedel
Not remotely feasible. The overall curvature of the universe is swamped by
local inhomogeneities until you get to scales that are much larger than
galaxies. So you'd only be measuring the curvature due to nearby matter unless
you had proves traveling at relativistic speeds and were willing to wait
millions of years.

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keymone
If you know mass distribution between and around probes, could you account for
it? or is it a case where we can only know the mass distribution by observing
the curvature?

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sandworm101
We cannot know the mass distribution that well. We arent even sure about
planet-9, let alone things like dark matter halos.

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ianai
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.

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patrickthebold
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_v...](https://en.wikipedia.org/wiki/Topological_space#Definition_via_open_sets)

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foxes
"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)

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kmill
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.

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rafaelvasco
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;

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tabtab
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-
ma...](https://www.vice.com/en_us/article/j5yngp/the-universe-is-made-of-tiny-
bubbles-containing-mini-universes-scientists-say)

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.

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hombre_fatal
What's up with the Pikachu references? I don't get the joke.

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earthboundkid
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

