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Union University Department of Physics

The Science Guys

Science Guys >September 2000

September 2000

The news media has reported extensively about new evidence that the universe is "flat." What does "flat" mean and does that refute Einstein’s contention that the universe is "curved"?

One of the consequences of Einstein’s theory of general relativity is that space may be curved or flat depending upon a number we will call omega. Omega is related to the density of the universe, which is mass per unit volume of space. If omega is less than one, the universe has negatively curved (hyperbolic) geometry; if omega is greater than one, the universe has positively curved (spherical) geometry; and if omega is one, the universe has Euclidean (flat) geometry.

The Earth has essentially a spherical geometry rather than a flat one- that is, the shortest distance between two points on the Earth’s surface is not a straight line; it is a curved path (circle) called a geodesic. To us the Earth appears to be locally flat, but we know full well that it is not a sheet but a sphere. Suppose you start walking due east on the equator. Keep walking and eventually you will wind up where you started. This cannot happen on a flat sheet. Keep walking straight forever on an infinite flat sheet and you’ll never return to your starting place.

Now the question moves to the universe. We can view it only locally, but if we could somehow get "outside" of it, what would we see? What would the geometry be? Einstein said that it was possible that the fabric of the universe was curved. He showed that space is warped or curved around matter- an effect that has been experimentally verified. But is the geometry of the whole universe intrinsically curved or flat? If curved, you could start anywhere in the universe, move in a straight line and return to where you started after a long enough time.

The current scientific consensus is that the universe (space) is expanding as a result of a tremendous "explosion" at the birth of our universe- the Big Bang. The Universe’s curvature has important implications for its future. One curvature implies an expansion for all time (open), another implies that the expansion will someday cease and a collapse (a Big Crunch) will occur (closed).

The Big Bang left behind a telltale sign - radiation waves that fill the universe [called the Cosmic Microwave Background (CMB)]. Studying the CMB is a way of exploring the birth of the universe as well as its geometry. Until recently, the CMB had not been mapped with detail sufficient to infer the universe’s geometry. In 1998 a collaboration of physicists from around the world performed the "Boomerang" and "Maxima" experiments, which provided this detailed map. Two independent research teams sent microwave telescopes aloft on high-altitude balloons and performed the most precise measurements of the CMB to date.

While the experiments only looked at 3% of the universe, the central result is an indication that the universe is not curved, but flat. This implies the universe will expand forever (unless our Creator intervenes.) There will be no Big Crunch and the shortest distance between two points is not some sort of geodesic, but it is a straight line. To be sure, the full consequences of the data gathered by Boomerang and Maxima will require further analysis, but the discovery that a Big Crunch is unlikely is one of the most monumental in the history of physics.

Errata: In the sixth paragraph of the August column a digit was missing. The last sentence of that paragraph should read "Therefore, gold weighs 19.3 times as much or (19.3 x 8.3 lb) about 160 pounds per gallon." We apologize for any confusion.