« Quarter Million Year Canon of Solar System Transits | Main | FORTRAN Double Precision Constant Gotcha »

Sunday, November 28, 2004

Yotta Yotta Universe

As you probably know, the SI unit prefixes which used to stop at "exa" (1018) and "atto" (10-18) have been expanded to include "zetta" (1021), "yotta" (1024), and on the small side "zepto" (10-21) and "yocto" (10-24). Excuse me if I think of the Marx brothers.

I thought it would be interesting to work out the size of the universe in terms of Planck lengths (the smallest meaningful length based on dimensional analysis of the fundamental constants; the length scale at which quantum gravity is believed to be fully manifest). The "size of the universe" in any units depends on a large number of assumptions; I'll use the Hubble age of the universe, about 13.7×109 years times the speed of light here (most topological models of the universe yield a larger size, so consider this conservative). The Hubble time is 4.32×1017 seconds which, converted to distance by multiplying by the speed of light, is about 1.30×1026 metres. Now the Planck distance ((Gℏ)/c³)½ is about 1.6×10-35 metres, so the radius of the universe is about 8×1060 Planck lengths. Given the uncertainty in the age of the universe and what expressing it in length means, we might as well round this off to 1060 Planck lengths. So how big is the universe in Planck lengths? Mega, mega, yotta, yotta big!

Posted at November 28, 2004 22:48