What is space?

During staff meetings in the Physics Department at Surrey
University where I work, there is always an item on the agenda
called ‘Space’. This is where the different research groups argue
over office space for research students and visiting researcherswho
need a desk for a few weeks and over laboratory space for their
experiments. But when the head of department reaches that point
in the meeting and says something like “And now we come to
Space—”, somebody usually mumbles “—the final frontier”. And
you thought physicists didn’t have a sense of humour!
We all think we know what ‘space’ means, whether it is space
in the sense of ‘there is an empty space over in that corner’ or
‘not enough space to swing a cat’, or space in the sense of ‘outer
space’ of the final frontier variety. When forced to think about it
we would regard space merely as somewhere to put things. Space
in itself is not a substance. This much we would all agree on. But
in that case, can space exist when it doesn’t contain any matter?
Think of an empty box. Even if we pump out all the molecules
of air it contains so that there really is nothing inside the box, we
would still be happy with the concept that the space continues to
exist. The space refers only to the volume of the box.
It is less intuitive when space has no boundaries. The space
inside the box only exists, we think, thanks to the existence of the
box itself. What if we remove the lid and walls of the box? Does
the space still exist? Of course it does. But it is now a region

of space that is part of a larger region inside the room we are
in. Let us try something a bit grander: Our Universe is basically
a very large (maybe infinite) volume of space containing matter
(galaxies, stars, nebulae, planets, etc). What if the Universe were
completely empty and contained no matter at all? Would it still
be there? The answer is yes, since space does not need to contain
matter in order to exist. At this point, the discussion could easily
nosedive—since I am doing all the discussing, and I know what I
am like when I get going—into a highly technical and obscure (yet
much debated) subject known as Mach’s principle. This states that
space, or at least distances and directions within it, is meaningless
when it does not contain any matter. In addition to this, Einstein
has shown in his theories of relativity that space, like time, is, well,
relative. However, I do not want to get too heavy at this early stage
of the book and will assume that although space is not a substance,
it must nevertheless be something!
But if space is not a substance, can we interact with it? Can
matter affect it in some way? It turns out that matter can indeed
affect space itself: it can bend it! Once you appreciate this fact, you
should never again be impressed with claims of cutlery bending
by the powers of the mind (a cheap and rather pointless conjuring
trick).
In the next chapter, I will be asking you to imagine bending 3D
space1. That’s OK, you might think, I can easily bend a 3D object
such as this book. Well, it’s not as simple as that. You see I don’t
mean 3D objects being bent within 3D space but rather bending 3D
space itself.
Think about the curvature of the 1D line to form the letter ‘S’.
We need a 2D sheet of paper to write the ‘S’ on. We say that the 1D
shape is imbedded in the higher dimension. Similarly, bending
a sheet of paper requires the use of our 3D space if we want to
visualize it. It follows that to appreciate what bending 3D space
This is what Einstein’s theory of relativity says
we have to call the combination of the three dimensions of space with the one of
time.means we would have to imagine 4D space in which it could be
bent.