Does space have a shape?

Three theories that are instrumental in understanding the shape of the universe are thebig bang,theory of gravityandEinstein’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 studiedlightthat 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 oflight yearsevery 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 r²is the distance between the two objects squared. So what’s the G? It’s thegravitational constant. It represents the constant proportionality between any two objects, no matter what their masses. The gravitational constant is 6.672 x 10^-11N m²kg^-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 thebig 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 iscurved. 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 ageodesic.

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.

The three main models of the universe are based on curvature:zero curvature,positive curvatureandnegative curvature.

A zero curvature would mean that the universe is aflatorEuclidean universe(Euclidean geometry deals with non-curved surfaces). Imagine space as a two dimensional structure -- a Euclidian universe would look like a flat plane. Parallel lines are only possible on a flat plane. In a flat universe, there is just enough matter so that the universe expands indefinitely without reversing into a collapse, though the rate of expansion decreases over time.

If the universe has a positive curvature, it’s aclosed universe. A two-dimensional model of such a universe would look like a sphere. It’s impossible to have parallel geodesics (straight lines on a curved surface) -- the two lines will cross at some point. In a closed universe, there is enough matter to reverse expansion. Eventually, such a universe will collapse on itself. A closed universe is a finite universe -- it will only expand to a certain size before collapsing.

Negative curvature is a little trickier to visualize. The most common description is a saddle. In a negative curvature model, two lines that would be parallel on a flat plane will extend away from each other. Cosmologists call negative curvature models of the universeopen universes. In these universes, there’s not enough matter to reverse or slow expansion, and so the universe continues to expand indefinitely.

Does this mean space is shaped like a flat plane, a sphere or a saddle? Not necessarily. Remember that space-time is measured in four dimensions, which reduces the usefulness of two-dimensional examples. And there are many competing theories about what the ultimate shape of the universe actually is.

One possible shape is the三重环. At first glance, the triple torus appears to be an ordinary cube. But each face of the cube isgluedto the face on the opposite side. Imagine that you’re in a spaceship that’s flying inside a large cube. You head toward the top of the cube. You wouldn’t smash yourself flat once you made contact. Instead, you’d appear in a corresponding spot at the base of the cube. In other words, you’ve gone up through the top and came back in through the bottom. If you traveled far enough in any direction, you’d eventually come back to where you started. This isn’t that foreign of a concept, since onEarthif you travel in a straight line, you’ll eventually come back to your starting point. You’ll just be very tired.

Another shape is thePoincaré dodecahedral spherical shape. Adodecahedronis a 12-sided object. The Poincaré variation has surfaces that curve outward slightly. What’s puzzling is that the projected size of this universe is smaller than the area we can actually observe. In other words, our visibility exceeds the boundaries of the universe. No problem, say the cosmologists. When you look at a distantgalaxythat would seem to lie beyond the boundaries of space, you’re actually experiencing the wrap around effect described above. The galaxy in question would really be behind you, but you’re looking through one face of the dodecahedron as if it were a window. If you could see far enough, you’d be looking at the back of your own head.

Dizzy yet? There are many other theoretical shapes the universe could take, but most don’t fit the evidence we have so far. What is that evidence, and how do we gather it? Find out in the next section.

Optical telescopes let us examine objects within the visible light spectrum but are relatively weak tools. That’s because the light from distant galaxies can intercept clouds of particles and other bodies before reaching Earth. Other devices can measure wavelengths that fall well outside the visible spectrum. Many of the recent studies in cosmology focus on thecosmic microwave background(CMB). The CMB is radiation that the universe generated when it was only 380,000 years old [source:Luminet]. By studying this radiation, cosmologists can draw conclusions about what the universe was like shortly after it began.

Using theWilkinson Microwave Anisotropy Probe(WMAP), scientists made an interesting discovery about the CMB. They found that the variation in radiation wavelengths of the CMB stops at a certain point. In an infinite, unbounded universe, there would be no limit to the size of wavelengths. We would expect to see variation and frequencies at all sizes. It’s only in a finite universe or a very specialized infinite one that we’d expect to see a definitive cap on wavelengths.

As for expansion, cosmologists call the ratio of the amount of matter in the universe and the amount needed to stop expansion thedensity parameter. A density parameter greater than 1 would mean a closed universe -- there is more mass in the universe that would be needed to reverse expansion. A density parameter of 1 would mean a flat universe in which expansion slows but never truly stops. And a density parameter between 0 and 1 would mean an open universe that would continue expanding forever.

But we don’t know how much matter really is in the universe. The amount we can detect is relatively small -- 5 percent of the matter needed to reverse expansion. But there appears to be matter that we can’t see at all. Cosmologists have noticed that stars move in an odd way -- they behave as if there is more matter exerting a gravitational influence on them than we can detect. Some cosmologists theorize that this means there is a kind of matter we can’t see at all, calleddark matter.

But is there enough dark matter to cause a big crunch? That is, is there enough matter in the universe to make up the balance and push the ratio to a 1 or higher? While cosmologists believe there is far more dark matter in the universe than observable matter, they estimate the combination of both visible and dark matter still only comes to about 30 percent of the amount needed to reverse expansion [Source: String Theory Web Site].

While we don’t know what the definitive shape of space is right now, research continues to bring us new information every day. And if space has boundaries, what lies beyond them? We don’t know, and we may not be capable of knowing.

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