In the second kind of solution, the universe is expanding so rapidly that the gravitational attraction can never stop it, though it does
slow it down a bit.
The separation between neighboring galaxies in this model starts at zero, and eventually the galaxies are moving apart at a steady speed.
Finally, there is a third kind of solution, in which the universe is expanding only just fast enough to avoid recollapse.
In this case the separation also starts
at zero, and increases forever.
However, the speed at which the galaxies are
moving apart gets smaller and smaller, although it never quite reaches zero.
A remarkable feature of the first kind of Friedmann model is that the universe
is not infinite in space, but neither does space have any boundary.
Gravity is so strong that space is bent round onto itself, making it rather like the surface
of the Earth.
If one keeps traveling in a certain direction on the surface of the Earth, one never comes up against an impassable barrier or falls over the edge, but eventually comes back to where one started.
Space, in the first Friedmann
model, is just like this, but with three dimensions instead of two for the Earth’s
surface.
The fourth dimension—time—is also finite in extent, but it is like a line with two ends or boundaries, a beginning and an end.
We shall see later that when one combines general relativity with the uncertainty principle of quantum mechanics, it is possible for both space and time to be finite without
any edges or boundaries.
The idea that one could go right around the universe and end up where one started makes good science fiction, but it doesn't have
much practical significance because it can be shown that the universe would
recollapse to zero size before one could get round.
You would need to travel
faster than light in order to end up where you started before the universe came
to an end—and that is not allowed.
But which Friedmann model describes our universe? Will the universe eventually stop expanding and start contracting, or will it expand forever?
To answer this question we need to know the present rate of expansion of the universe
and its present average density.
If the density is less than a certain critical
value, determined by the rate of expansion, the gravitational attraction will be too weak to halt the expansion.
If the density is greater than the critical value,
gravity will stop the expansion at some time in the future and cause the universe to recollapse.
We can determine the present rate of expansion by measuring the velocities at
which other galaxies are moving away from us, using the Doppler effect.
This can be done very accurately. However, the distances to the galaxies are not
very well known because we can only measure them indirectly.
So all we know is that the universe is expanding by between 5 percent and 10 percent every thousand million years. However, our uncertainty about the present average density of the universe is even greater.
If we add up the masses of all the stars that we can see in our galaxy and other galaxies, the total is less than one-hundredth of the amount required to halt the expansion of the universe, even in the lowest estimate of the rate of expansion.
But we know that our galaxy and other galaxies must contain a large
amount of dark matter which we cannot see directly, but which we know must be there because of the influence of its gravitational attraction on the orbits of stars and gas in the galaxies.
Moreover, most galaxies are found in clusters, and we can similarly infer the presence of yet more dark matter in between the galaxies in these clusters by its effect on the motion of the galaxies.
When we add up all this dark matter, we still get only about one-tenth of the amount
required to halt the expansion.
However, there might be some other form of
matter which we have not yet detected and which might still raise the average density of the universe up to the critical value needed to halt the expansion.
The present evidence, therefore, suggests that the universe will probably
expand forever. But don’t bank on it.
All we can really be sure of is that even
if the universe is going to recollapse, it won’t do so for at least another ten thousand million years, since it has already been expanding for at least that long.
This should not unduly worry us since by that time, unless we have colonies beyond the solar system, mankind will long since have died out,
extinguished along with the death of our sun.
slow it down a bit.
The separation between neighboring galaxies in this model starts at zero, and eventually the galaxies are moving apart at a steady speed.
Finally, there is a third kind of solution, in which the universe is expanding only just fast enough to avoid recollapse.
In this case the separation also starts
at zero, and increases forever.
However, the speed at which the galaxies are
moving apart gets smaller and smaller, although it never quite reaches zero.
A remarkable feature of the first kind of Friedmann model is that the universe
is not infinite in space, but neither does space have any boundary.
Gravity is so strong that space is bent round onto itself, making it rather like the surface
of the Earth.
If one keeps traveling in a certain direction on the surface of the Earth, one never comes up against an impassable barrier or falls over the edge, but eventually comes back to where one started.
Space, in the first Friedmann
model, is just like this, but with three dimensions instead of two for the Earth’s
surface.
The fourth dimension—time—is also finite in extent, but it is like a line with two ends or boundaries, a beginning and an end.
We shall see later that when one combines general relativity with the uncertainty principle of quantum mechanics, it is possible for both space and time to be finite without
any edges or boundaries.
The idea that one could go right around the universe and end up where one started makes good science fiction, but it doesn't have
much practical significance because it can be shown that the universe would
recollapse to zero size before one could get round.
You would need to travel
faster than light in order to end up where you started before the universe came
to an end—and that is not allowed.
But which Friedmann model describes our universe? Will the universe eventually stop expanding and start contracting, or will it expand forever?
To answer this question we need to know the present rate of expansion of the universe
and its present average density.
If the density is less than a certain critical
value, determined by the rate of expansion, the gravitational attraction will be too weak to halt the expansion.
If the density is greater than the critical value,
gravity will stop the expansion at some time in the future and cause the universe to recollapse.
We can determine the present rate of expansion by measuring the velocities at
which other galaxies are moving away from us, using the Doppler effect.
This can be done very accurately. However, the distances to the galaxies are not
very well known because we can only measure them indirectly.
So all we know is that the universe is expanding by between 5 percent and 10 percent every thousand million years. However, our uncertainty about the present average density of the universe is even greater.
If we add up the masses of all the stars that we can see in our galaxy and other galaxies, the total is less than one-hundredth of the amount required to halt the expansion of the universe, even in the lowest estimate of the rate of expansion.
But we know that our galaxy and other galaxies must contain a large
amount of dark matter which we cannot see directly, but which we know must be there because of the influence of its gravitational attraction on the orbits of stars and gas in the galaxies.
Moreover, most galaxies are found in clusters, and we can similarly infer the presence of yet more dark matter in between the galaxies in these clusters by its effect on the motion of the galaxies.
When we add up all this dark matter, we still get only about one-tenth of the amount
required to halt the expansion.
However, there might be some other form of
matter which we have not yet detected and which might still raise the average density of the universe up to the critical value needed to halt the expansion.
The present evidence, therefore, suggests that the universe will probably
expand forever. But don’t bank on it.
All we can really be sure of is that even
if the universe is going to recollapse, it won’t do so for at least another ten thousand million years, since it has already been expanding for at least that long.
This should not unduly worry us since by that time, unless we have colonies beyond the solar system, mankind will long since have died out,
extinguished along with the death of our sun.
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