Originally Posted by **Woody** What are permeability and permittivity?
What sets the properties of "empty" space such that its permeability and permittivity are these specific values? |

The permittivity is a property of materials in an electric field. Probably the best introduction to this is a parallel plate capacitor. The formula for the capacitance is $\displaystyle C = \epsilon \dfrac{A}{d}$. (This is actually something of an idealization, but it works.) $\displaystyle \epsilon$ is the (electric) permittivity. If the capacitor is "empty" then $\displaystyle \epsilon$ is a measure of the permittivity of air, which is going to be very close to that of empty space. (And, of course, you could put the capacitor in a vacuum if you like.)

The (magnetic) permeability is somewhat more complicated. So far as I know there is no such thing as a magnetic capacitor. But we define $\displaystyle \vec{H} = \mu \vec{B}$ where H is the magnetic field and B the magnetic induction. The best idea that I have here is an inductor (or perhaps an electromagnet with an inner core.) H represents the field inside the inductor and B the field outside the conductor. For the free space $\displaystyle \mu _0$ can be got by using an inductor (or electromagnet) with no core.

ln the derivation of the EM wave equation we get that the speed of light in a material is $\displaystyle v = \dfrac{1}{\sqrt{ \epsilon \mu }}$. Obviously in empty space we use $\displaystyle \epsilon _0$ and $\displaystyle \mu _0$.

-Dan