Jan 15 2011

## Permittivity of Free Space

It is interesting, to say the least, the way some of the constants of physics mix and match. There are lots of examples of this in text books and on web sites, including this one, so there is no point in reiterating any now which do not relate specifically to this entry.

Some constants, nevertheless, turn out not to be constants, including the permittivity of free space, termed ε_{0}. At the surface of the earth, and at any point not far enough away to discern a difference, we have ε_{0} = 8.85 x 10^{-12} C^{2}/(N-m^{2}) when measured in a vacuum. One of the ways in which the permittivity of free space relates to other physical entities is in the makeup of the Coulomb constant, k = 1/(4πε_{0}), which is then also not really a constant in all locations, the difference relating to the local density of gravitons.

The speed of light in a vacuum can be written as: c = sqrt(k/k_{m}) = 1/sqrt(ε_{0} µ_{0}) = 2.998 x 10^{8} m/s, which is a constant throughout the universe. One may be tempted to say then that µ_{0} is an inverse function to ε_{0} when evaluated at a given point, except that this is so unlikely with present understanding so as to be unimaginable. Along with the constancy of the speed of light in a vacuum in any reference frame, the fact that it equals 1/sqrt(ε_{0} µ_{0}) in our locale can remain somewhat of a mystery.