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## Sunday, November 28, 2004

### Yotta Yotta Universe

As you probably know, the SI unit prefixes which used to stop at "exa" (10^{18}) and "atto" (10

^{-18}) have been expanded to include "zetta" (10

^{21}), "yotta" (10

^{24}), 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 13.7×10^{9} 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 4.32×10^{17} seconds which, converted to distance by multiplying by the speed of light, is about 1.30×10^{26} metres. Now the Planck distance ((Gℏ)/c³)^{½} is about 1.6×10^{-35} metres, so the radius of the universe is about 8×10^{60} 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 10^{60} Planck lengths. So how big is the universe in Planck lengths? *Mega, mega, yotta, yotta big!*

Posted at November 28, 2004 22:48