Lorentz Force: Does Velocity Still Matter?

[Phrak]

The electron mass also goes to infinity, Dick.

 

[Dick]

The electron mass also goes to infinity, Dick.

Sure, Phrak. I'm just saying nothing here says you can't do the analysis in the beam rest frame and then translate to the lab frame. I had originally thought Bob S was saying in the 'highly relativistic' case the magnetic force would exceed or balance the Coulomb force. I don't think that's what being said.

 

[Phrak]

You know. This is something I asked in my freshman year. I was very disappointed to hear that it was due to both an increase in mass and a decrease in force. It seemed to messy. Acceleration of the beams (divergence) goes to zero in two ways.

Unless I'm missing some subte point, I think I know what you're asking. Not only are mass, length and time Lorentz tranformed, but force also transforms; the[/PLAIN] Faraday tensor is also transformed.

 

[Dick]

Yes, force is a messy concept in SR. And yes, everything else transforms as well. That's why it pays to find the right frame to express your question and then transform to another frame if you have to. You really can draw correct conclusions by just working in the beam frame. I'm not really asking anything. I'm just saying that the conclusion that opposite charges in the rest frame of the charges will repel is true, no matter how much you try to complicate it by frame change.

 

[Phrak]

OK. But we could despense with the force and just use the vector potential and Dirac equation for the vector potential's action on a charged particle. Now everything is nicely expressed in 4 dimensional tensors as it should be, and the result is the same.

 

[Dick]

Sure you could. Or you could just find a simple frame. I'm glad everyone agrees.