TCS Daily

Living in a Finite Universe?

By Kenneth Silber - October 22, 2003 12:00 AM

Scientists publishing in the journal Nature recently proposed that the universe has "dodecahedral space topology" -- an assertion that gave rise to a flurry of headlines that the universe is "soccer-ball shaped." This was followed by denials from other scientists that the universe is shaped like a soccer ball (or a "football" in European terms).


What is remarkable here is not that scientists disagree, but rather that there is something tangible for them to argue about. An ancient philosophical question has begun to yield to scientific observation and explanation, and data arriving from space probes may even settle the matter in the next few years. The question is whether the universe is finite or infinite -- or, put another way, whether space curves in on itself or stretches out forever.


The philosopher Immanuel Kant (1724-1804) regarded the question of a finite versus infinite universe as an "antinomy of reason," a limit on human ability to understand the world. But half a century after Kant's death, mathematician Bernhard Riemann proposed curved geometries, and in the early 20th century Albert Einstein's general theory of relativity explained gravitation as a curvature of space, which raised the possibility of a finite universe.


However, relativity did not settle the issue, as it addressed space's local geometry rather than its overall shape, or topology. In recent years, scientific opinion has swung toward the view that the universe is infinite. This view has gained support from astronomical data indicating that there is not enough matter in the observable universe to curve space into a closed shape. In addition, an open universe is more compatible with cosmic inflation, a theory that the universe expanded extremely rapidly in its earliest moments.


Yet the case for a finite universe persists, and has gained some support from data that space probes have collected about the cosmic microwave background, a pervasive low-level radiation believed to be a residue of the Big Bang. The microwave background contains fluctuations that give clues to the universe's topology. In an infinite universe, fluctuations would be random, coming in various shapes and sizes. A finite universe, however, would produce certain patterns in the microwave background. The fluctuations would reflect the universe's shape, and their intensity would be limited by the universe's size (much as your bathtub is too small for huge tides to form in it).


Cosmic microwave fluctuations were first observed by NASA's Cosmic Background Explorer (COBE) space probe in 1992. NASA's Wilkinson Microwave Anisotropy Probe (WMAP), launched in 2001, now collects higher-resolution data on the microwave background while orbiting the sun at a point about 1 million miles from Earth. The European Space Agency has postponed the launch of its own microwave background surveyor, called Planck, from 2003 to 2007.


Observations from the WMAP spacecraft are compatible with the idea of a dodecahedral topology similar to a soccer ball, as was pointed out in the October 9, 2003 issue of Nature by scientists based in France and the U.S. (An abstract of their paper can be accessed here and a PDF file of a longer version is here.) However, the data analyzed so far are compatible with other shapes as well, and are not sufficient to settle the question of whether the universe is infinite or finite.


Both types of universe raise strange possibilities. A spacecraft moving through a finite universe eventually could return to its starting point, like an ant crawling on a soccer ball. Janna Levin, a cosmologist at Cambridge University, notes that in a finite universe, far-flung objects in the sky could actually be the same thing -- and it would be possible in principle for astronomers to take pictures of events in Earth's own past. Levin's book How the Universe Got Its Spots: Diary of a Finite Time in a Finite Space (Anchor Books) is an engaging combination of such cosmic topology and more personal reflections.


An infinite universe may be even stranger. Such a universe might include not just multiple images of all its objects but actual copies of them, indeed an infinite number of copies. There have been various speculations about other Earths containing exact duplicates of ourselves, or about events somewhere playing out in every possible way (for example, this article being published in Mad magazine rather than Tech Central Station). Such unending duplication is implied by the mathematics of infinity, but whether it would actually take place in the physical world is unclear.


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