Is there really a fourth dimension?

If you already know a little about Einstein’s theory of relativity
(which I am assuming you do not) then you might well be a little
worried at this point. After all, didn’t Einstein say something
about time being the fourth dimension? In Chapter 6 I will
discuss Einstein’s theory of special relativity in which time and
space are linked together in a quite surprising way, into something
called four-dimensional spacetime. For now, we can understand
it in the following simple way. Go back to the example of the
submarine requiring the three numbers to fix its position. If it
is moving, stating those numbers is meaningless unless we also
state when the submarine was at that position. And so we now
require four numbers to correctly locate its position: latitude,
longitude, depth and the time when it had those values. However,
we should not lose sight of the fact that time is not the same as
the three dimensions of space. We are free to move forwards and
backwards along any one of the three spatial axes, but are restricted
to moving forwards only along the time axis (from past to future).
The question here is whether there could exist, beyond our senses,
a fourth dimension of space.
A hundred years ago, some of the world’s most respected
scientists believed that the spirit world, the realm of ghosts and phantoms, was four-dimensional and included our 3D space
within it. The inhabitants of this higher dimensional world would
occasionally pass through our 3D one but would otherwise be
invisible to us. Nowadays of course, hardly any serious scientists
(by which I mean not counting those of the fruitcake persuasion)
believe this. This is not to say that higher dimensions are ruled out.
In fact, some new, as yet untested, theories in physics suggested
that there may be even more than four dimensions of space, all of
which are beyond our grasp. Two theories currently in vogue,
known as superstring theory and M-theory4, suggest that our
Universe actually contains nine, and ten, dimensions of space (plus
one of time), respectively. But all the extra unwanted dimensions
are curled up so small that we can never detect them. You may
think this just a load of hogwash but the truth is that either of these
exotic theories could well turn out to be the one that describes the
ultimate underlying reality of our Universe.
Even if the three dimensions of space we know of are all there
is, we will see in the next couple of chapters that it is useful to have
an extra dimension up our sleeve to help us understand a certain
aspect of Einstein’s theories of relativity: curved space.