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The universe may be revealing its shape, new findings suggest

Oct. 6, 2004
Special to World Science

For centuries, scientists, philosophers and ordinary people have wondered whether the universe is infinite, and what its shape might be. In two recent studies, scientists say signals from the explosion that gave rise to the universe may be leading them to answers to both questions.

Some researchers say the universe may be shaped like a dodecahedron, in which objects that go out one side come back in the opposite.  (Image courtesy Paris Observatory)

As for whether the universe is infinite, these signals point to “no,” the researchers say. 

As for its shape, if ever a shape could be at once hauntingly beautiful, yet impossible to draw or visualize exactly, this one might be it. But roughly, it would resemble a dodecahedron, a 12-sided box similar to some dice used in the popular role-playing game Dungeons & Dragons.

Some researchers disagree with the findings. “I’d be happy to wager a bottle of scotch against the dodecahedral universe,” wrote cosmologist Ned Wright, of the University of California at Los Angeles, in a recent email.

The dodecahedral universe claims are based on observations of the furthest reaches of our universe. Since light takes time to travel, the further we peer out into space with telescopes, the further back in time we see. If we look far enough, we can see the aftermath of the “Big Bang,” a tremendous explosion that astronomers believe created our universe.

The radiation from this explosion tells us some things about the early universe. In particular, it reveals the approximate density of different areas of the universe during that early time. Slight variations in the density of different parts of the early universe result in corresponding variations in the radiation’s temperature.

These variations follow patterns in space that, mathematically, are identical to the vibration patterns of a musical instrument as it’s being played.

Such vibrations that they normally come at many size scales, depending on the size of the instrument. When a bell rings, there are large ripples that span its whole surface, and tiny ones, but none bigger than the bell itself. The size of the largest ripples would reveal the size of the bell. The universe is thought to work similarly: the size of the biggest ripples could give astronomers some idea of the size of the universe.

In the case of the universe, ripples could conceivably be found in a very wide range of sizes. But they’re not found in all these sizes; ripples larger than a certain size aren’t seen. The most natural explanation of this seems to be that space is finite, say Jean-Pierre Luminet of the Paris Observatory, France, and colleagues. This is because only a universe of limited size could easily explain why the ripples are also limited in size. “Just as the vibrations of a bell cannot be larger than the bell itself, the density fluctuations in space cannot be larger than space itself,” he wrote in the research journal Nature last fall.

This leftover light from the Big Bang – called the cosmic microwave background – may also reveal the shape of the universe, Luminet and colleagues argue. They claim that the details of the ripples point to a universe with a dodecahedral form described by the 19th- and early 20th- century French mathematician Henri Poincaré.

A peculiar aspect of this structure is that if we look out to one side of the dodecahedron, we see not a boundary, but our own universe all over again, as seen from the other side. It’s like a hall of mirrors, except that instead of seeing your face, you see the back of your head. In addition, you would see the images partially rotated.

In the September 2004 issue of the research journal Astronomy & Astrophysics, a group of researchers write that they has found “hints” of the structure Luminet described. If space is structured this way, researchers believe that the cosmic microwave background should exhibit a specific pattern called “matched circles.” This means that as we peer into space, certain areas of the radiation should look the same as other areas.

In the paper, Boudewijn F. Roukema of Copernicus University, Torun, Poland, and colleagues wrote that the patterns they found “correlate unusually well” with the matched-circles pattern required by Luminet’s theory. However, at present it’s hard to prove that this is not a coincidence, they wrote.

Wright is skeptical. The researchers “presented no evidence that this result was statistically significant,” he points out on his website. Luminet agrees: “Their result has to be confirmed by further statistical analysis,” he writes in an email. “The question remains open.”

If the findings turn out to be correct, professors may be kept busy for years explaining the shape of the universe to students. This is because the dodecahedron picture is an oversimplification. The actual theory has several strange twists.

In some video games, you can fly your spaceship off the edge of the screen and it comes back in from the opposite edge. A creature dwelling in the world of the video game would have the illusion of living in an infinite space, at least until it started moving around and realizing that things were repeating themselves everywhere.

In the same way, we may have the illusion of living in a much bigger universe than the real one, Luminet argues. This is because as we look far enough out with our telescopes, we begin to see the same objects repeatedly. However, we would see them partially rotated each time.

The reason for this rotation is that it allows our dodecahedral universe to fit into a bizarre mathematical creation called a hypersphere – a concept that requires some explanation.

Most people would consider a circle two-dimensional, and a ball three-dimensional. In fact, a ball is sort of a three-dimensional version of a circle. In the same way, mathematicians have invented “balls” that exist in four or more dimensions. These objects are impossible to picture, but they are perfectly real in a mathematical sense; in other words, one can do calculations with them, just as with a circle and a ball.

Now, the surface of a normal ball, or sphere, is two-dimensional. Thus it makes sense that the “surface” of a four-dimensional ball would be three-dimensional. This surface of a four-dimensional ball is just as impossible to visualize as the four-dimensional ball itself, but nonetheless, mathematicians have given a name to this type of surface: a hypersphere.

“A hypersphere is the 3-dimensional surface of a 4-dimensional ball,” wrote Luminet. Nineteenth-century mathematicians first devised the hypersphere as a possible shape of the universe. This served as a way to explain how space might be finite, yet have no boundary – just as the surface of a sphere has no boundary, yet doesn’t go on forever.

Understanding the hypersphere is first step toward understanding what, according to some researchers, is the shape of the universe. There is also another step or two.

Consider a soccer ball (or as non-Americans call it, a football). Its surface is covered with five-sided shapes, colored black and white. These shapes are basically pentagons, but not quite normal pentagons. Their edges are slightly bent, and their corner angles slightly different, compared to regular pentagons. These alterations allow these “modified pentagons” to fit snugly together on the surface of a ball. Otherwise, it couldn’t be a ball, but a shape like that of 12-sided die.

Now, return to the concept of a hypersphere. Remember, a hypersphere is the three-dimensional “surface” of a four-dimensional ball. If pentagons – which are basically two-dimensional – tile a three-dimensional soccer ball, it makes sense that some sort of three-dimensional objects can be said to tile the surface of a four-dimensional ball. It also makes sense that these would be three-dimensional versions of the “modified pentagons” described above.

These bizarre new objects are modified dodecahedrons: in other words, that 12-sided die shape again, but with slightly “bent edges.” It takes 120 of them to fill a hypersphere, the same way it takes 12 modified pentagons to cover a soccer ball. In the case of the universe, however, 119 of these dodecahedrons would be illusory, because they are all repeating images of a single one. Nonetheless, the hypersphere containing them is real – real enough to serve as a framework that determines the details of the shape and angles of the dodecahedron.

One outcome of the hypersphere framework is that objects leaving one face of the dodecahedron come back in the opposite face, but rotated partially. To be exact, the amount of the rotation is 36 degrees, which also happens to be the angle by which your direction would change if you turned a corner while walking along the edge of a pentagon. 

Luminet admits that the accuracy of this whole theory remains to be confirmed. The claim that the universe is finite remains unproven, he says; its confirmation will require a more precise measurement of the density of the universe today. If the density is above a critical level, it will prove the universe is finite, he says. A better measurement of the density could come from the Planck Surveyor, a European spacecraft planned for launch in 2007 to study the birth of the universe.

“Since antiquity humans have wondered whether our universe is finite or infinite,” Luminet writes. “Now, after more than two millennia of speculation, observational data might finally settle this ancient question once and for all.”

EJL

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