W
hen thinking of the cosmos one cannot help but be impressed by its sheer size. The clusters of galaxies stretch out into space as far as one can see. So, our next question is: how big is the universe?Here we have to make a distinction between the universe and the observable universe. We see something by the light it sends to us. As already noted, it takes time for the light to get here. The distances involved are so immense that even travelling at 300,000 kilometres per second, it takes four years for light to reach us from even the nearest star. It takes 100,000 years to cross from one side of the Milky Way Galaxy to the other. The fact that the universe came into existence 13.7 billion years ago means we can see only those objects such that the light from them could reach us in less than 13.7 billion years. This defines the extent of the observ- able universe. Beyond the observable universe lies the rest of the universe—presumably. How far does that go on? For
ever. The universe is infinitely big. That is the current thinking.
But what justification can there be for saying that? Is it because we are incapable of imagining what it would be like to come to the edge of the universe? If we did come to an edge, what would lie beyond the edge? Nothing. But wouldn’t that look like empty space and, as such, wouldn’t it be part of the universe—just with nothing in it? So we wouldn’t have come to the end of the universe. That’s why we say it goes on for ever—the universe is infinite.
An alternative solution to the problem is the idea that the universe might be closed. It would be finite in size, but have no edge. How could that be? Imagine a fly crawling over a rubber surface. It carries on in the same direction. All the time it is thinking that it is getting further and further away from its starting point. It assumes that the surface just goes on and on for ever. But then, to its surprise, it finds that, without ever changing direction and retracing its steps, it is back where it started! How is that possible? We who have been observing the fly know the answer. From our bird’s eye view we are able to see that the rubber sheet is not flat; it is in fact a large balloon. The fly has simply gone right round the balloon to where it started.
In the same way—so this theory goes—it might be that if we were in a spacecraft and took off from the north pole and continued going vertically upwards—always keeping to the same direction—we might find that eventually we approached Earth from the opposite direction and landed
on its south pole. That way the cosmos would have a finite size (our complete journey across the cosmos took a finite time) but there was no edge. Such a possibility would require that our space—our three-dimensional space—was some- how curved back on itself, this curvature perhaps being in some unobservable additional dimension in the same way as the fly’s two-dimensional rubber surface was curved back on itself in an unobserved third dimension.
If you are trying to form a mental image of such a curva- ture of three-dimensional space, you can stop right now. It cannot be done. With the rubber sheet it was easy, but when dealing with three-dimensional space we cannot picture any additional dimension. Instead we have to allow the math- ematics to guide us. To use yet another analogy, we are rather in the position of a pilot trying to land an aircraft at night in a fog. He would much prefer to be able to see the layout of the runway approach for himself, but this is not possible. Instead he has to rely on his instruments and readings to guide him home. And that is how it sometimes is with fundamental physics. Explanations in terms of famil- iar mental images might not be possible. The explanations take a mathematical form instead.
I must confess that I have always had a hankering for this finite closed solution to the problem of the size of the universe. It is such a neat, brilliant piece of lateral thinking. It is a possibility allowed by the theory of relativity. The trouble is that the same theory that permits this kind of solution also attributes the curvature to a specific cause. It
is all due to the contents of the universe. The greater the density of matter and energy in the universe the greater the curvature. One finds that there is a particular density— the critical density—such that if the actual density in the universe exceeds this value, the space will curve back on itself and we have a closed universe. So we tot up all the contents of the universe and see what the density is. When we add up all the matter that we can see—that making up the stars and the interstellar gas—we find it comes to no more than 5% of the critical value. But we must not stop there. On examining how the stars rotate about the centre of their galaxy we discover that they are moving much too fast to be held on course by the gravity exerted by the rest of the visible material of the galaxy. This has led to the realisation that the material we can see is but a fraction of the total. The rest is labelled dark matter. ‘Dark’ because it is matter that emits no light. Although we cannot see it, we know it has to be there. Indeed, we know how much of it there is. This we calculate from the strength of the gravitational force req- uired to keep the stars on track as they orbit the centre of the galaxy.
Furthermore it is noticed that the 30 or so galaxies that make up the cluster to which our Milky Way Galaxy belongs (the so-called Local Group) are moving about too quickly to be held together by the gravitational forces exerted by the galaxies—even including the dark matter within the galax- ies. This in turn is interpreted to mean that there is additional dark matter in between the galaxies.
Altogether, dark matter adds up to 25% of the critical density. What the nature of this dark matter is we do not as yet know. I suspect it is only a ques- tion of time before it is identified, but I cannot be sure.
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Adding together the observable matter and the dark matter still leaves a shortfall of 70%. However, this is made up of dark energy—a property of space itself. This we shall be discussing in detail later. Thus it turns out that the actual density of the universe is exactly the critical density! A coincidence? Not really. It is due to inflation. It is built into the mech- anism of inflation that it creates new matter. Most of the matter we see around us today did not, in fact, originate at the instant of the Big Bang; it was created a fraction of a second later during inflation. Moreover, the amount produced is such that the overall density should end up with exactly the crit- ical value. The agreement between this requirement and the experimentally measured value for the mean density of the universe, provides powerful evidence in favour of inflation theory.
So what does this mean in terms of the size of the universe? Because the density is critical—and does not exceed that value—three-dimensional space does not curve back on itself. So the closed universe hypothesis—attractive though it might be—is dead.
T H E S I Z E O F T H E C O S M O S
What is the nature of dark matter?
This, in fact, is not the first time that a beautiful cosmological theory has died. You might have heard of the steady state theory. For a time, this was a rival theory to the Big Bang hypothesis. It held that the universe had no beginning and will have no end. If you were to look at a certain region of space you would see the galaxy clusters moving out from it as a result of the expansion of the universe. But new matter was continu- ally being created, in the form of light elements, and this new matter would collect together to form new stars and galaxies, which in their turn would move out of the region. Essentially the appearance of that region of space would remain un- changed. It was in a steady state, with the loss of material through the recession of the galaxies being exactly balanced by the creation of new matter. Thus there was no need to invoke a one-off Big Bang. It was an aesthetically pleasing alternative which appealed to many cosmologists. The only trouble with it was that, over the years, the evidence for the Big Bang became so overwhelming that the steady state theory had, reluctantly, to be discarded.
And so it is with the hypothesis of the closed, finite universe. The hard evidence is against it, so it too must be set aside. Pity. It means that we are left with the answer that the universe is infinite. But what kind of answer is that? What do we actually mean by saying it is infinite?
I am always suspicious of that word ‘infinite’. Ever since I heard the story of the infinite hotels. You know the one I mean? There was this rich man who built a hotel with an infinite number of bedrooms. Business was good
and every room was filled. So he built another hotel alongside the first. It also had an infinite number of bedrooms. Business was very good and that one was also full. Then disaster struck. One of the hotels burned down in the middle of the night, so the hotelier had an infinite number of guests out in the street freezing to death. But then he had a brain wave. He told everyone in the remaining hotel to look at the number on their bedroom door, double the number, and move to that new bedroom. All those guests had a room to go to. But in doing this, all the odd numbered bedrooms became free. And as there were an infinite number of odd numbered bedrooms, all the guests out in the street from the other hotel had a room in the surviving hotel— despite the fact that the surviving hotel had origin- ally been full! Which just goes to show how wary one has to be of that word ‘infinite’. It leads me to suspect that the assertion that the universe is infinite in size might well be nothing more than a way of disguising the fact that we simply do not know how to answer the question: How big is the universe?
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T H E S I Z E O F T H E C O S M O S
Is the universe infinite in size, and if so, what exactly does that mean?