Does space have a shape?

A diagram from the work of Copernicus showing how planets in our solar system move in relation to the sun.
Hulton Archive/Getty Images

Centuries ago, human beings looked up at the night sky and imagined that a black globe enveloped the Earth. They believed the stars were simply pinpoints of light. The sun, moon and other planets circled the Earth in a regular, perfect pattern. In their minds, the universe was small, centered on Earth and organized into perfect spheres.

­­Scien­tists like Copernicus and Galileo discovered flaws in this philosophy. It took more than a century after Galileo's discoveries for the world to accept that the Earth wasn't the center of the universe. As time passed, we began to learn more about the universe. Today, we study the cosmos through advanced telescopes, satellites and probes.


Now we have images of galaxies millions of light years away from Earth. Scientists study distant stars on a regular basis. They've even detected planets in solar systems far beyond our own.

But what about the big picture? What do we know about the universe as a whole? Is it expanding? Is it infinite? If it isn't infinite, what lies beyond the boundary of space? And what exactly does space look like?

These questions fall under the category of cosmology, the study of the universe. People have tried many different approaches to study the universe. Some concentrated on mathematics. Others preferred using physics. And quite a few took a philosophical approach.

There's no consensus among cosmologists about what space looks like, but there are plenty of theories. Part of the challenge of describing space is that it's very difficult to visualize. We're used to thinking about locations in two dimensions. For example, you can determine your location on a map using longitude and latitude. But space has four dimensions. Not only do you have to add depth to the dimensions of length and width, you also must add time. In fact, many cosmologists refer to this collection of dimensions as space-time.


What are some of the major theories that could help us figure out the shape of space? Read on to find out.


The Big Bang, Gravity and General Relativity

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.


The Shapes of Space

In this illustration you can see the three different curvature models space might have -- no curvature, positive curvature and negative curvature.
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The three main models of the universe are based on curvature: zero curvature, positive curvature and negative curvature.

A zero curvature would mean that the universe is a flat or Euclidean 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 a closed 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 universe open 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 triple torus. At first glance, the triple torus appears to be an ordinary cube. But each face of the cube is glued to 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 on Earth if you travel in a straight line, you’ll eventually come back to your starting point. You’ll just be very tired.

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Another shape is the Poincaré dodecahedral spherical shape. A dodecahedron is 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 distant galaxy that 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.


How to Measure Space

Visible, or baryonic matter
Courtesy STScI and NASA

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 the cosmic 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 the Wilkinson 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 the density 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, called dark matter.

Dark Matter
Courtesy STScI and NASA



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.

Want to learn more about space and related topics? Set a course for the links on the following page.


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More Great Links

  • Battersby, Stephen. “Fold testament: what shape is the universe?” New Scientist. Dec. 7, 2006. what-shape-is-the-universe.html
  • Castellanos, Joel. “The Shape of Space.” NonEuclid.
  • “The Geometry of the Universe.” Astronomy 162. University of Tennessee.
  • Gravitational Constant.” Eric Weinstein’s World of Physics.
  • Hawking, Stephen. “A Brief History of Time.” Bantam Books. New York. 1998.
  • Kurtus, Ron. “Newton’s Universal Gravity Equation.” School for Champions. Aug. 29, 2007. equation.htm
  • Luminet, Jean-Pierre. “The Shape of Space after WMAP data.” Brazilian Journal of Physics. Vol. 36, no. 1B. March, 2006.
  • “Torus.” Wolfram MathWorld.
  • “What is the structure of the universe?” The Official String Theory Web Site.