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Does space have a shape?

The Big Bang, Gravity and General Relativity
The spiral galaxy M100, as seen through the Hubble telescope.
The spiral galaxy M100, as seen through the Hubble telescope.
Courtesy STScI and NASA

Three theories that are instrumental in understanding the shape of the universe are the big bang, the theory of gravity and Einstein’s theory of general relativity. Cosmologists consider all of these theories when forming hypotheses about the shape of space. But what exactly do these theories try to explain?

The big bang theory is an attempt to describe the beginning of the universe. Through observation and analysis, astronomers determined that the universe is expanding. They have also detected and studied light that originated billions of years ago back when the universe was very young. They theorized that at one time, all the matter and energy in the universe was contained in an incredibly tiny point. Then, the universe expanded suddenly. Matter and energy exploded outward at millions of light years every fraction of a second. These became the building blocks for the universe as we know it.

The theory of gravity states that every particle of matter has an attraction to every other particle of matter. Specifically, particles will attract one another with a force proportional to their masses and inversely proportional to the square of the distance between them. The equation looks like this:

F = GMm/r2.

F is the force of gravitational attraction. The M and m represent the masses of the two objects in question. The r2 is the distance between the two objects squared. So what’s the G? It’s the gravitational constant. It represents the constant proportionality between any two objects, no matter what their masses. The gravitational constant is 6.672 x 10-11 N m2 kg-2 [source: World of Physics]. That’s a very small number, and it explains why objects don’t just stick to each other all the time. It takes objects of great mass to have anything more than a negligible gravitational effect on other objects.

If the big bang theory is true, then when the universe began there must have been a huge burst of energy to push matter so far so fast. It had to overcome the gravitational attraction among all the matter in the universe. What cosmologists are trying to determine now is how much matter is actually in the universe. With enough matter, the gravitational attraction will gradually slow and then reverse the universe’s expansion. Eventually, the universe could shrink into another singularity. This is called the big crunch. But if there’s not enough matter, the gravitational attraction won’t be strong enough to stop the universe’s expansion, and it will grow indefinitely.

What about the theory of relativity? Besides explaining the relationship between energy and matter, it also leads to the conclusion that space is curved. Objects in space move in elliptical orbits not because of gravity, but because space itself is curved and therefore a straight line is actually a loop. In geometry, a straight line on a curved surface is a geodesic.

The three theories described above form the basis of the various theories about what the shape of space actually is. But there’s no actual consensus on which shape is the right one.

What are the theoretical shapes of space, and why don't we know which one is right? Find out in the next section.

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