Comment by pak | Hacker News Reader

Comment by pak | Hacker News Reader

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I would refine your explanation a bit--you were 90% there but you got the direction of the magnetic force wrong, and the way I learned it involved special relativity. So when you are sitting on an electron in one wire and you see the protons zipping backwards in the other wire and the electrons twice as fast as that, the phenomenon of "length contraction" (http://en.wikipedia.org/wiki/Length_contraction) occurs because all these particles are moving close to the speed of light. Since from your reference frame the electrons are moving faster than the protons, they are length contracted to a greater degree, so they appear to have a higher charge density than the protons. Therefore the repulsive electric force between your electron and the charge density of the electrons is greater than the attractive force between your electron and the charge density of the protons, so your electron is repelled (and we observe this as the magnetic force).

Laughable ASCII diagram (just note that within each wire, the opposite charges are intermingled, not separated like shown):

          Lab reference frame     Reference frame of e- on wire 1           
                                               V
              - - - - - - - ==>          -  -  -  -  - 
  wire 1      +  +  +  +  +          <== + + + + + + +

          <== - - - - - - -        <==== -------------
  wire 2      +  +  +  +  +          <== + + + + + + +

                                  charge density of e-'s in other 
                                  wire is greater than that of p+'s

So, two wires with current in opposite directions repel each other, not attract. You can do the above exercise with the currents in the same direction to see that relativity would then postulate that the protons in the other wire have greater apparent charge density than the electrons, causing a net attractive electric force observed as magnetism.

Interesting footnote to this: when Maxwell first derived the relationship between electric current and magnetism he postulated the existence of a fixed medium, aether, through which light travels at a constant speed. For a while measuring the Earth's relative velocity to the aether proved challenging. Einstein eventually did away with the concept of aether and asserted that light moves at the same speed in all reference frames, thus reconciling mechanics and electromagnetism.

Einstein didn't do away with the concept, Michelson and Morley did.

http://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experi...

Einstein filled the hole they left. It is worth mentioning because Morley was the first American to win the Nobel in Physics. That experiment changed business as usual.

The free electrons in a conductor move at nothing near the speed of light, though.

Even though the speed of the electrons is nowhere near the speed of light, electromagnetism is so strong that the tiny length contraction at those speeds is enough to produce the magnetic force.

Yes, this is the correct answer. It's a relativistic effect that is nonetheless observable at velocities not usually considered to be relativistic.

I think this is extremely cool, BTW: any ordinary refrigerator magnet serves to demonstrate the truth of special relativity. Indeed, since the propagation of a photon involves oscillating electric and magnetic fields, the very existence of light itself depends on relativity.

So in a strange and unexpected way, one could say that when Michelson and Morley went searching for the ether, they actually found it. The fact that the speed of light is the same in every inertial reference frame is precisely what allows it to propagate at all.

I may be confusing propagation speed and drift velocity--it's been a while since I learned this, and I think there is some way to rationalize that the net current is really moving close to the speed of light when you add/subtract the motions of all the individual particles, even if none of them in isolation are moving anywhere close to that speed.

In any case, this article explains the whole matter a lot better than I could.

http://en.wikipedia.org/wiki/Relativistic_electromagnetism

The drift speed of electrons in an conductor is slow. The actual velocity they travel at is much faster. Though the actual range defies me at this point, so I have no idea if relativistic effects are noticeable.

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