Time?

[BAndrew]

The edge of space

Consider the following two questions:

1. If the Universe is expanding but at the same time contains the
whole of space, what does it expand into?

2. What is there beyond the edge of the Universe?

We feel as though there must be something beyond our

Universe that can accommodate it as it expands. Believe it or
not these questions are not purely philosophical or metaphysical.
Science has an answer to both. It is just that we are not thinking
about things in the right way. This is where all that stuff about
higher dimensional geometry in Chapter 1 pays off. Na¨ıvely, we

think of the Big Bang as some explosion that happened at some point in
time at a specific location in three-dimensional space. From this point,
all of matter was ejected out and has been flying apart ever since.
Wrong!

First of all, we have learnt that the Big Bang was not like
a supernova explosion with all the matter flying away from a
central point. The expansion of the Universe is a stretching of
space itself, with the matter imbedded within space and carried
along for the ride. Secondly, there is no point in the Universe
where space explorers could travel to, planting a flag which states that: ‘The Big Bang Happened Here’.

Recall the example of the stretching sheet of rubber. The Big Bang
happened everywhere on the sheet at once, and the stretching took place
all over the sheet.

I don’t expect you to feel happy about this just yet. Give me
a couple more pages. I know I have not even answered the two
questions yet. Let’s try and tackle them head-on. Imagine that
you are able to fly off in a rocket at very high speed and carry on
going in a straight line—let’s also assume that you are immortal
and that the rocket has an unlimited supply of fuel. Would you
ever reach a point beyond which you could not go? Some barrier
beyond which there was complete nothingness?

According to Friedmann’s model of the Universe based on
Einstein’s general theory of relativity (which we believe correctly
describes the general features of the Universe), the answer is no,
the Universe does not have an edge. There is no physical boundary
that your rocket would eventually hit when it ran out of space. Nor
would you ever reach a point beyond which there was nothing.
If this abyss could be defined as space, then it is still part of the
Universe, whether or not it contained any matter. So presumably,
your rocket could just keep on going, and you would not have left
the Universe, just entered an empty region of it.

Friedmann in fact found two different types of possible
universe. If there is enough matter for gravity to one day halt the
expansion and cause the Universe to recollapse (corresponding
to the ball rolling back down a steep slope) then we would have
something called a closed universe. If, on the other hand, there is
not enough matter to halt the expansion then we would be living
in an open universe.

Here is where I have to be careful. Friedmann’s model makes
an important assumption: that Einstein’s cosmological constant is
zero. This means that there is no force of antigravity acting at the
moment to complicate things, even if it was responsible for setting
the expansion going in the first place. The following discussion is
therefore simplified5 for the case of no cosmological constant.

Reference: Black Holes Wormholes and Time Machines by Jim Al-Khalili