Re: Park City Paradox ?

[John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>]

On Tue, 8 Jan 2002, Robert Cohen wrote:

> ...
>
> Are you saying that you *don't* view it my way or that one *can't*
> view it my way?  If it is just that you *don't* view it my way
> then could it be that my way provides the same results if applied
> in a more rigorous manner?

I'm only saying I don't.  I can imagine making the "information
can't keep up" (or "is delayed") viewpoint more rigorous.  I'm not
sure I'd find it less distasteful, but I will withhold judgment!

> ...
>
> P.S. I'm going to get into trouble for this, but how's this for an
> analysis for v<c?  Can we say that if the magnetic force is
>      k(q)(q)/r^2 when v=c
> then perhaps the magnetic force is
>      k(qv/c)(qv/c)/r^2 when v<c
> in which case the magnetic force is
>      (k/c^2) (qv)(qv)/r^2.
> At least it gives the correct constant. I admit it isn't rigorous.

Almost.  You are just missing a factor of gamma.  The Lorentz
transformation shows that the electric force in the lab frame is

  F_E = gamma*(kq^2/r^2), away from the other charge

and the magnetic force is

  F_B = gamma*(v/c)^2*(kq^2/r^2), toward the other charge

Thus, the net force is

  F_net = (1/gamma)*(kq^2/r^2), away from the other charge

Note that both the electric and magnetic forces increase without
bound as v approaches c but that the net force goes to zero.

John Mallinckrodt      mailto:ajm@csupomona.edu
Cal Poly Pomona          http://www.csupomona.edu/~ajm