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Finite Universe: The Torus Shape
http://www.ams.org/new-in-math/mathnews/universe.html
What is the shape of the universe? Is it finite? These are two of the most important questions in cosmology today. Mathematics is providing striking new insights into deducing the shape of the universe from observational data. These insights, which will be put to the test in the coming decade as scientists receive data from a new space probe, have the potential to transform our view of cosmology. Gazing out into the night sky, one easily gets the impression that the universe continues forever in all directions. However; this impression is akin to thinking that the Earth is flat and continues forever in all directions because that is how it appears when one scans the horizon. Fairly sensitive measurements are needed to detect the curvature of the Earth. The same is true for detecting the shape of the universe. One possible shape the universe might have is analogous to the surface of a doughnut. Mathematicians call this shape a torus, and it is a fundamental object of study in the areas of geometry and topology. The torus model has a weird property: For every object we observe in the universe, we would see not one but multiple images of the object. These images correspond to light emitted by the object at different points in time and at different angles. In fact, mixed in with all the observational data cosmologists collect would be multiple images of our very own galaxy. Taken together, these images would provide information about some fundamental properties of the shape of the universe. The problem is that we cannot recognize these images of our own galaxy; we do not even know what it looks like from the "outside". However, the Cosmic Microwave Background radiation---the after-glow of the Big Bang that permeates the universe---may provide some clues. For this approach to work, more detailed data of the CMB is needed. By 2002, NASA's Microwave Anisotropy Probe will have furnished more accurate data with much better resolution than is available today. These ideas are explored in the article "Measuring the Shape of the Universe" by Neil J. Cornish and Jeffrey R. Weeks, which appeared in the December 1998 issue of theNotices of the AMS. |
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