Magnetic Test of Length Contraction
The wires contain equal amounts of positive and negative charge so they
exert no net force on each other.
Heres where LC comes into play. Because the electrons are moving, they appear to compress along their length and become closer together. Heres what the protons see:
The electrons on the other hand see themselves as still (due to identical velocities) and the protons as moving to the left. Heres what the electrons see:
LC brings the charges closer together, making the density of opposite
charges appear higher. As a result the electrons in one wire experience increased
attraction to the protons in the other wire and vice versa, leading to the wires being
attracted to each other.
The LC works well as an explanation for the magnetic force between straight wires. Lets now look at another situation: coils. Below we see a piece of wire curved into a loop. We wish to know the influence of magnetism in the middle of the loop. Initially there is no current in the wire. From the view-point of a charge at the middle of the loop it looks like this:
Now we turn on the current and the electrons flow clockwise. According to the relativistic proof of magnetism, from the viewpoint of a stationary observer, the wire should look like this:
See the problem? In order to increase charge density it was necessary to
increase the number of electrons in the wire. But this is impossible because the total
number of electrons cannot change. Special Relativity does not provide any mechanism for
creating new charges.
This would increase charge density without adding more electrons. But it would also contradict the straight wire situation where the moving electrons relocated themselves at some point along their path of travel, rather than at a point perpendicular to their motion.
Magnetism cannot be cited as a validation for relativistic length
contraction because it only predicts the correct result in some situations and not others.
 Originally shown by Edward Purcell in Electricity
Copyright © 2010 Bernard Burchell, all rights reserved.