I looked at the video, and it seems like nonsense to me. The relativity argument relies on the charges moving at near the speed of light, but in any normal conductor they don’t. The electron drift velocity in a conductor is actually quite slow, mush slower than walking speed, so the whole relativity argument becomes nonsense.

It’s very easy to derive and understand the formula for electron drift velocity in a conductor from first principles, and easy to calculate the drift velocity using the said simple formula. An example of drift velocity calculation can be found here :-

http://resources.schoolscience.co.uk/cda/16plus/copelech2pg3.htmlThis shows that the drift velocity for a 5A current in a 0.5 mm^2 conductor is a piffling 7.35E-4 m/s, or roughly 0.1 mm/s. That’s at a respectable current density of 10A/mm^2. Even with a water-cooled conductor you are unlikely to exceed 100A/mm^2, so the highest steady drift velocity that you are likely to create is around 1mm/s, or 3.6 meters per hour.

The current density in power station alternators, xformers, transmission lines etc will generally be less than 10A/mm2, which as discussed gives an electron drift speed of 0.1mm/sec. At 50Hz powerline frequency, that means that the electrons move for a distance of only 0.01 seconds x 0.1mm/sec = 0.001mm (1 micron) before the direction is reversed. Therefore the electrons in the windings of a power station alternator will never leave the winding, much less the power station, but just jiggle back and forth by 0.001mm.

Not sure if the above alters your desire to directly measure electron drift velocity in a conductor, or influences how you might choose to do so.