I would like to simulate what happens if you move electric circuits at relativistic speeds. At first, I would like to check the resistor.
If I move a wire in the simplest case with speed $v$ along its axis $\vec{e_z}$, I get as transformation the following expression $R' = \frac{l'}{\sigma'A} = \frac{l'm'}{e^2n'\tau'A}$ where $\sigma$ is the conductivity depending on mass, charge, spatial density and relaxation time $\tau$.
Inserting the correct transformations for mass, length, density and time I would expect $R' = R$. But it seems to me that the relaxation time is not a time transformed as usual.
Has anyone an idea how to deal with it? Otherwise, if I transform Ohm's law directly, it gets much more complicated due to the transformation of the relative speed of the electrons.
