Now, imagine a universe just like flatland truly two-dimensional and
entirely flat in every direction but with one exception:
Unbeknownst to the inhabitants
the two dimensional universe is curved into a third physical dimension.
Maybe into a sphere but in any rate into something entirely outside their experience.
Locally their universe still looks flat enough.
But if one of them much smaller and flatter than me takes a very long walk along what seems to be a straight line
he would uncover a great mystery.
Suppose he marked his starting point here and set off to explore his universe.
He never turns around and he never reaches an edge, he doesn't know that his
apparently flat universe is actually curved into an enormous sphere. He doesn't sense that
he's walking around a globe.
Why should this space be curved?
Because there's so much matter in this universe that it
gravitationally warps space closing it back on itself into a sphere.
But our flatlander doesn't know this.
After a long while you'll find he somehow returns to his starting point.
There must be a third dimension.
Our flatlander couldn't imagine a third dimension.
But he could sure deduce it. Now increase all the dimensions in this story by one and you have something like the situation which many
cosmologists think may actually apply to us.
We are three-dimensional creatures trapped in the three dimensions.
We imagine our universe to be flat in three dimensions, but maybe it's
curved into a fourth.
We can talk about a fourth physical dimension, but we can't experience it. No one can
point to the fourth dimension. I mean there's left right and there's forward back there's up-down and
there's some other direction simultaneously at right angles to those familiar three dimensions.
Now, imagine this universe is expanding.
If we blow it up like a four dimensional balloon what happens an astronomer in a given galaxy
thinks all the other galaxies are running away from him.
The more distant the galaxy the faster it seems to be moving this is just what Humason and Hubble found
On the surface of this curved universe there is no boundary or center
the universe can be both finite and unbounded.
The redshift of the distant galaxies seemed to imply to Humason's contemporaries that we were at the center of an expanding universe.
That our place in space was somehow privileged.
But if the universe is expanding whether or not it's curved into a fourth dimension
observers on every galaxy will see precisely the same thing all the galaxies rushing away from them as if they had made some
dreadful intergalactic social blunder. If there's enough matter to close the universe gravitationally
then it's wrapped in on itself like a sphere.
If there isn't enough matter to close the cosmos
then our universe has an open shape extending forever in all directions
this
saddle universe is only one of an infinite number of possible kinds of open universes.
Unlike such closed universes as the sphere open universes have in them an
infinite amount of space.
If our universe is in fact closed off then nothing can get out not matter not like.
We would then be living inside a black hole.
There is one possible way out though a hypothetical tunnel or wormhole
through the next higher dimension a place sucking in matter and light.
Can we find such a wormhole could we survive the trip?
We might emerge in some other place in time perhaps in another universe or perhaps somewhere else in our own.
