where $\eta = \sqrt{\frac{\mu}{\epsilon}}$. This may be written in a form that more closely mimics the tradition relations via

$\star(v d t\wedge E) = \frac{1}{\epsilon} D\quad\text{and}\quad\star B = \mu H\wedge v d t
\,,$

where $v = \frac{1}{\sqrt{\mu\epsilon}}$ (Note: $v = c$ in vacuum).

What this means is the the electromagnetic properties of matter can be interpreted geometrically and are encoded in the Hodge star operator. Conversely, it means that geometrical properties of matter can be interpreted electromagnetically.