[ ♪ Intro ]
It’s kind of weird thinking about the universe
having a shape.
It’s the universe, right?
It’s … universe … shaped ...
But it does have one.
We just aren’t sure what that shape is.
And some cosmologists have proposed that of
all things, it might be shaped kind of like
a donut.
When we’re talking about the shape of the
universe, we’re really talking about its topology.
The topology of an object has nothing to do
with how many sides it has, or where parts
of it are relative to one another.
It only depends on the number of holes: a
sphere has none, a donut has one, and so on.
A sphere and a donut are both round, but they
have different topologies because there’s
no way to take a sphere and stretch or smash
it to make it look like a donut without, shall
we say, “tearing it a new one.”
On the other hand, a lot of objects we think
of as clearly being different shapes have
exactly the same topology.
A coffee mug has one hole in the handle, so
topologically speaking, there’s no difference
between a mug and a donut.
There are a lot of proposed topologies that
the universe could possibly have, from plain
shapes with no holes to some that are much
more complex.
But one of the most common ideas is what’s
called a 3-torus.
It’s impossible for our puny human minds
to visualize what that looks like from the
outside, because you’d need a fourth spatial
dimension.
A line is one dimensional.
A flat plane: two.
And with the third dimension you get depth.
Usually, when we talk about the fourth dimension,
we mean time.
But in this case, it’s a fourth spatial
dimension — the next level up from 3D.
And as beings who’ve lived our whole lives
in 3D space, we can’t really imagine what
4D would look like.
That doesn’t mean you can’t model a 3-torus,
though!
You just have to step everything down a dimension.
You can take our universe, with its 3 spatial
dimensions, and model it as a two-dimensional
flat plane — think of it like a piece of
paper, except pretend it stretches to infinity
along both axes.
If you take that piece of paper and wrap it
into a cylinder, it stays infinite in one
direction but becomes finite in the other,
because eventually you loop around the cylinder.
If you then wrap the ends of the cylinder
together, making it connect along both axes,
you have yourself a 3-dimensional version
of a 3-torus.
There you go.
Donut universe.
Topology is different from geometry.
It doesn’t care if or how space is curved,
or about the distance or angles between different objects.
Geometry does; it knows the difference between
our mug and donut, and we’re actually pretty
sure we know what the geometry of the universe
is.
Measurements have shown it’s almost definitely
flat, as opposed to positively or negatively curved.
Which, again, gets a little brain-break-y,
because “flat” is not normally an adjective
we use to describe things in 3D.
But cosmologists talk about 3D space as being
“flat” or “curved” because it’s
the best analogy we have for what we’re
trying to describe, which basically boils
down to this:
If you shine two laser beams in parallel,
do they stay parallel?
Or do they eventually cross or diverge?
When we say the universe is flat, we mean
that the beams stay parallel — space isn’t
warped in a way that would curve them toward
or away from each other.
The ‘donut’ universe is actually a topology
with a flat geometry, which our simplified
3D model can't, well, model.
But the idea is that instead of a simple plane
that stretches to infinity in 3 dimensions,
it connects at multiple points.
In other words, it’s finite.
But it mimics an infinite universe because
light wraps all the way around the shape,
so you get the effect of standing in one of
those infinity light boxes.
The 2D version of this is a classic video
game where, if you move to one side of the
screen, you pop up on the opposite side with
the same speed and trajectory.
In 3D space, if the universe were incredibly
small, and you looked directly up, you’d
see the bottom of your own feet.
Or if you looked over your shoulder, you’d
see yourself repeated in an infinitely long line.
But our universe isn’t that small.
So how could we possibly tell if we’re living
in a 3-torus?
Basically, astronomers hunt for recurring
patterns in astronomical images -- the same
cosmological structures showing up in multiple
parts of the sky.
That would mean light is wrapping around the
universe, and we could run models on those
patterns to determine its topology.
Or at least, we could if the true size of
universe is smaller than the distance it takes
the light of everything to reach us.
Because remember, light takes time to get
to us.
There could be things out there so far away
that even though the light coming from them
has been traveling almost since the beginning
of time, it still hasn’t reached us yet.
If there is stuff beyond where the earliest
light we can see originated, the light wouldn’t
have the opportunity to wrap around and create
any repeat images.
The universe could be a donut, and we’d
never know.
That said, results as recent as 2015, courtesy
of the European Space Agency’s now-defunct
Planck satellite, have failed to find any
evidence of a 3-torus topology.
Or any topology.
So as far as we can tell, the universe is
not a donut.
But what if it were?
Well, in day-to-day life - even in certain
fields of astronomy - it wouldn’t matter
very much.
Just like there’s a lot of physics we can
still do with old-school Newtonian equations,
changing how we think about the universe’s
topology wouldn’t require rewriting the
rules of stellar life cycles or planetary
formation.
But there is one bit of cosmology a donut
universe definitely threatens: inflation.
Cosmologists think the universe suddenly expanded
in size when it was super duper young.
When we look at the light left over from the
Big Bang — what’s known as the cosmic
microwave background, or CMB — we can see
evidence of that inflation.
But there’s nothing in the theory that would
cause inflation to produce a universe big
enough to house all the galaxies, yet small
enough to see itself repeated within the observable horizon.
So knowing the universe was a donut would
force astronomers to find a new explanation
for why the CMB looks the way it does.
But one of the cooler consequences of a donut
universe?
Somewhere out there, some of the oodles of
galaxies would actually be the Milky Way itself.
But we wouldn’t be able to tell just by
looking at them, because they’d appear billions
of years younger.
So you could actually wave to yourself, but
you’d be very dead before you received the message.
But hey, it’s the thought that counts.
Thanks for watching this episode of SciShow
Space.
If you want to celebrate your love of the
universe and drink coffee out of a topological
donut every morning, we’ve got your covered!
Head over the DFTBA.com/SciShow to get your
own topological donut!
It’s a coffee mug.
We hope you like it.
And thanks for supporting SciShow Space!
[ ♪ Outro ]
