M S La Moreaux

Does anyone really need a diagram of a straight current-carrying wire? Length contraction applies not only to moving objects but also to the spaces between those moving with the same velocity.

Copper contains 10^22 free electrons per cubic centimeter. A paradox within special relativity may be impossible, but that is not the situation I am describing. It is instead a discrepancy between what special relativity predicts and what is actually observed. A magnetic field affects a moving charge, not a stationary one. The effect the I am describing would affect a stationary charge external to the wire.

There is no cutoff velocity of relativistic effect. Although the drift velocity of the electrons is minuscule, the relativistic increase in their density multiplied by the huge number of free electrons is palpable, on a par with magnetism. I do not see that the ladder paradox applies. In the ladder paradox, the paradox involves the discrepancy between the views of two different reference frames. The relativistic length contraction of the ladder, and thus the increased density, as it were, of the rungs in the barn's frame is not denied.

This really should not be this difficult. I assume a straight side to avoid acceleration so special relativity will apply. The circuit is stationary. The only things moving are the free electrons. Their charge density appears greater while the charge density of the protons remains unchanged, thus resulting in a net negative charge for the segment of the circuit under discussion. This should be observed by someone in the frame of reference of the circuit, but is not.

Consider a current carrying circuit with a straight side. Because of length contraction, in the straight side the moving electrons will appear closer together than they would be if there were no current. This gives a greater charge density, so the straight side should have a negative charge. But this is not observed. How come?