Time dilation and thermodynamics

[Dale]

Okay then, let's not ignore any current, but let's divide the confusing current into two components:

1: the current that goes through the wire, carried by slowly flowing electron gas.
2: the current that goes through empty space, carried by fast moving charged wire.

Then we consider the two currents separately. No current gets ignored, and hopefully we don't get confused.

Sure, you could do that. In the end, that would amount to transforming to the rest frame and doing standard circuit analysis in the rest frame.

 

[Dale]

Of course Kirchhoff circuit theory is not Lorentz covariant since it's an application of the quasi-stationary approximation, i.e., Maxwell's displacement current is ignored, and this violates Lorentz covariance.

Yes, that is clear and concise. Well said.