The Geometry of the Universe

Most recent answer: 08/01/2012

Are the three spatial dimensions orthogonal and infinite? If so, how can the universe have a limited size (as postulated by the big bang theory)? If the dimensions are not infinite, what are they? Are they circular? Do "infinite" "orthogonal" "straight" lines intersect more than once?
- Eamon Moloney (age 23)
Co. Meath, Ireland
We don't know whether the three spatial dimensions are infinite or finite. The general form of the big bang picture is consistent with either a spatially finite or infinite universe. If the dimensions aren't infinite they are indeed most likely close to having uniform curvature of a large scale, so I guess you could call that circular.

In discussing geometry on a large scale, you need to include the time dimension as well. I'll rephrase your last question as "can two things traveling in straight lines (geodesics) from the same point ever bump into each other again?" The answer to the last question is yes if you include local gravitational effects, but let's ignore those small-scale curves. On a large scale, we don't know. It's another way of asking your starting question about whether the universe is finite or infinite.

Mike W.

(published on 08/01/2012)