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Authors: Stephen Hawking
Tags: nonfiction
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the universe.
The Expanding Balloon Universe
As a result of the expansion of the universe, all galaxies are moving directly away from each other Over time, like spots on an inflating balloon, galaxies that are farther apart increase their separation more than nearer galaxies Hence, to an observer in any given galaxy, the more distant a galaxy is, the faster it appears to be moving
Friedmann derived only one model of the universe. But if his assumptions are correct, there are actually three possible types of solutions to Einstein’s equations, that is, three different kinds of Friedmann models—and three different ways the universe can behave.
In the first kind of solution (which Friedmann found), the universe is expanding sufficiently slowly that the gravitational attraction between the different galaxies causes the expansion to slow down and eventually to stop. The galaxies then start to move toward each other, and the universe contracts. 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. Finally, there is a third kind of solution, in which the universe is expanding only just fast enough to avoid collapse. The speed at which the galaxies are moving apart gets smaller and smaller, but it never quite reaches zero.
A remarkable feature of the first kind of Friedmann model is that in it 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. This is rather like the surface of the earth, which is finite but has no boundary. If you keep traveling in a certain direction on the surface of the earth, you never come up against an impassable barrier or fall over the edge, and you eventually come back to where you started. In this model, space is just like this, but with three dimensions instead of two for the earth’s surface. The idea that you could go right round the universe and end up where you started makes good science fiction, but it doesn’t have much practical significance, because it can be shown that the universe would collapse to zero size before you could get around. It is so large, 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! Space is also curved in the second Friedmann model, though in a different way. Only the third Friedmann model corresponds to a universe whose large-scale geometry is flat (though space is still curved, or warped, in the vicinity of massive objects).
Which Friedmann model describes our universe? Will the universe eventually stop expanding and start contracting, or will it expand forever?
It turns out the answer to this question is more complicated than scientists first thought. The most basic analysis depends on two things: the present rate of expansion of the universe, and its present average density (the amount of matter in a given volume of space). The faster the current rate of expansion, the greater the gravitational force required to stop it, and thus the greater the density of matter needed. If the average density is greater than a certain critical value (determined by the rate of expansion), the gravitational attraction of the matter in the universe will succeed in halting its expansion and cause it to collapse—corresponding to the first Friedmann model. If the average density is less than the critical value, there is not enough gravitational pull to stop the expansion, and the universe will expand forever— corresponding to Friedmann’s second model. And if the average density of the universe is exactly the critical number, then the universe will forever slow its expansion, ever more gradually approaching, but not ever reaching, a static size. This corresponds to the third Friedmann model.
So which is it? We can determine the present rate of expansion by measuring the velocities at which other
The Expanding Balloon Universe
As a result of the expansion of the universe, all galaxies are moving directly away from each other Over time, like spots on an inflating balloon, galaxies that are farther apart increase their separation more than nearer galaxies Hence, to an observer in any given galaxy, the more distant a galaxy is, the faster it appears to be moving
Friedmann derived only one model of the universe. But if his assumptions are correct, there are actually three possible types of solutions to Einstein’s equations, that is, three different kinds of Friedmann models—and three different ways the universe can behave.
In the first kind of solution (which Friedmann found), the universe is expanding sufficiently slowly that the gravitational attraction between the different galaxies causes the expansion to slow down and eventually to stop. The galaxies then start to move toward each other, and the universe contracts. 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. Finally, there is a third kind of solution, in which the universe is expanding only just fast enough to avoid collapse. The speed at which the galaxies are moving apart gets smaller and smaller, but it never quite reaches zero.
A remarkable feature of the first kind of Friedmann model is that in it 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. This is rather like the surface of the earth, which is finite but has no boundary. If you keep traveling in a certain direction on the surface of the earth, you never come up against an impassable barrier or fall over the edge, and you eventually come back to where you started. In this model, space is just like this, but with three dimensions instead of two for the earth’s surface. The idea that you could go right round the universe and end up where you started makes good science fiction, but it doesn’t have much practical significance, because it can be shown that the universe would collapse to zero size before you could get around. It is so large, 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! Space is also curved in the second Friedmann model, though in a different way. Only the third Friedmann model corresponds to a universe whose large-scale geometry is flat (though space is still curved, or warped, in the vicinity of massive objects).
Which Friedmann model describes our universe? Will the universe eventually stop expanding and start contracting, or will it expand forever?
It turns out the answer to this question is more complicated than scientists first thought. The most basic analysis depends on two things: the present rate of expansion of the universe, and its present average density (the amount of matter in a given volume of space). The faster the current rate of expansion, the greater the gravitational force required to stop it, and thus the greater the density of matter needed. If the average density is greater than a certain critical value (determined by the rate of expansion), the gravitational attraction of the matter in the universe will succeed in halting its expansion and cause it to collapse—corresponding to the first Friedmann model. If the average density is less than the critical value, there is not enough gravitational pull to stop the expansion, and the universe will expand forever— corresponding to Friedmann’s second model. And if the average density of the universe is exactly the critical number, then the universe will forever slow its expansion, ever more gradually approaching, but not ever reaching, a static size. This corresponds to the third Friedmann model.
So which is it? We can determine the present rate of expansion by measuring the velocities at which other
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