What do we mean when we say that the Universe is
expanding?
The easiest way to understand this question is to construct a few model
universes, and experiment with them (proper zoning permits first, please, and
do not run them faster than the speed of light within city limits). We know
that our Universe is three dimensional: space, and all of the objects which
exist inside it, have a width, a breadth, and a height.
Look to your left, and then to your right ...
Look in front of you, then check behind ...
Next look up, and then look down ...
Congratulations, you have just verified the three dimensional nature of space,
as we know it!
We can visualize other universes which have a different number of dimensions;
the fact that ours has three does not mean that others must be formed
similarly. We are going to practice visualizing one and two dimensional
universes, because they are simpler than our own, and then manipulate them.
A one dimensional universe contains only one dimension, which we
will call width. We can visualize it as a long piece of string, or a rubber
band. A one dimensional ant can move along this universe just in one
direction or its exact opposite, going forwards or backwards along the single
dimension. The ant's world would seem like living in a subway tunnel,
consisting of a long straight path. How would this universe expand? We
worked this out just a moment ago (see above). Just as if you pulled on the
ends of a rubber band, it would expand uniformly in size along its single
dimension.
A two dimensional universe is made up of two dimensions, width
and breadth. We could draw this universe by sketching on the surface of a
piece of paper, like a floor plan of a single-story house, or by inking
pictures on the surface of a rubber sheet (an uninflated balloon). A two
dimensional ant can move along this universe by going forwards or backwards,
or by going left or right, and her world would look like a gigantic plane (a
huge flat surface). How would this universe expand? Just as if you pulled on
the sides of a rubber sheet or other flexible material, it would expand
uniformly in size along both dimensions, forming a larger and larger square.
A three dimensional universe is made up of three dimensions,
width, breadth, and height. It is easy for us three dimensional ants to
visualize this universe, because we live inside it! How would this universe
expand? Just as if you baked a loaf of bread and it rose while baking, it
would expand uniformly in size along all three dimensions, forming a larger
and larger volume.
A four dimensional universe is more challenging to visualize,
because we ourselves cannot perceive four dimensions around us. But as we
recognize the existence of three distinct dimensions, and can visualize one
and two dimensional universes, we can extend the concept to understand that
such a thing as a four dimensional universe could in theory exist.
