## Comment Re:Question for the Physicists. (Score 3, Interesting) 79

*Here is a really cool fact that you can use to impress chicks at cocktail parties: A magnetic force and an electrical force are the SAME THING. The only difference is your inertial frame of reference. Let's say you have two parallel copper wires with current flowing through them. The negative charge in the electrons and the positive charge in the copper nuclei should cancel each other out, and there should be no force between them. BUT THERE IS. This is magnetism. But it is really just plain only electrical attraction because the electrons are moving, so their inertial reference frame is different from the reference frame of the copper nuclei. A moving reference frame has a Lorentz contraction, so the copper nuclei "see" more electrons per length of wire, resulting in an attraction.*

No. Magnetic and electrical force and energy aren't exactly "the same thing". The magnetic and electric field are both components of the second rank field strength tensor, the Lorentz force in electromagnetic theory is not just the Lorentz transform of the Coulomb force, and magnetic and electric field energies are independently summed when assembling the total electromagnetic field energy density. Finally, good luck describing electron spin and the resultant intrinsic magnetic dipole moment in terms of a Lorentz transformation of the bare Coulomb field of the (point) charge -- there is no rotating frame or mass moving around mass.

There are basically two different ways to discuss them. One way is to stop talking about electric and magnetic fields independently at all and only work with the electromagnetic field (strength tensor) where the electric and magnetic components are NOT THE SAME and do NOT HAVE THE SAME SYMMETRY. The other way is to pretend (as most intro books do, because usually it works pretty well if you're considering low velocities and coarse-grain-averaged "smooth" charge/current densities) that E and B are ordinary vectors and write down Maxwell's equations. There are FOUR of them -- two if you go with the covariant field strength tensor formulation, and you cannot write them all down in terms of a single vector field (or the resultant force).

F_e = qE (F, E vectors)

F_b = q v x B (F, v, B vectors)

The electrostatic force obeys Newton's third law. The magnetic force (with the cross product) does not,. and one has to work very hard indeed to find the missing energy and momentum in the electromagnetic field when two charged particles interact in the general case.

Sadly, I haven't found that knowing graduate level electrodynamics well enough to teach it impresses chicks at cocktail parties.