Re: Park City Paradox ?

[Jack Uretsky <jlu@HEP.ANL.GOV>]

Hi all-
        This relativistic effect has come up twice in my life.  Once was
in my Ph D oral exam (I answered correctly), the second was in a patent
application I wrote in the early '80's.  The patent was granted to Norman
Rostoker (as I recall), if anyone wants to look it up, and had to do with
injection of beams into accelerators.
                                        Regards,
                                                Jack


On Tue, 8 Jan 2002, John Mallinckrodt wrote:

> On Mon, 7 Jan 2002, Robert Cohen wrote:
>
> > I guess I had the same misconception as Ludwik...
> >
> > Isn't the magnetic force proportional to (q_1v_1)(q_2v_2)/r^2?
> > If both charges are moving with speed c in our reference frame, wouldn't
> > this give rise to a magnetic attraction?
>
> The electrons don't need to move (and, indeed, *can't* move) with
> speed c in our reference frame for there to be a magnetic
> attraction.  But all I am saying is that, since the two electrons
> *do* move apart in their own frame, they will do the same in every
> frame and that fact will be properly accounted for by a net
> repulsive force.
>
>
> Here is a sketch showing the fields in both frames at the position
> of one of the electrons as obtained from the Lorentz
> transformation:
>
>                            v
>       e          :         e--->
>                  :
>                  :         ^
>       ^          :         |
>       | E        :         |E_lab = (gamma)E
>       |          :         |
>       e          :         e--->
>                            * B_lab = (gamma*v/c^2)E, outward
>
>  electron frame        lab frame
>
> You can see that the electric force is larger (more repulsive) in
> the lab frame than in the electron frame, but that the attractive
> force, due to the magnetic field that arises in the lab frame,
> more than compensates for the increase in the electric force.
> The bottom line is that the Lorentz force on either electron in
> the lab frame will be reduced by a factor of gamma from what it
> was in the electron frame.
>
> So it is true that as gamma goes to infinity the force goes to
> zero and *if* gamma could *equal* infinity the force would *be*
> zero.  However, I think of this as mostly being an effect of time
> dilation. The separation that takes place in the electron frame
> takes place by *their* clocks.  Since we see their clocks running
> slow by a factor of gamma, we observe the separation process
> running slow by the same factor.  We interpret that observation in
> terms of a reduced lateral force.  Since "time stops" for v = c,
> no separation would be observed.
>
> John Mallinckrodt      mailto:ajm@csupomona.edu
> Cal Poly Pomona          http://www.csupomona.edu/~ajm

--
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you, because that is what I must do.  Tonight it is only you and me, fish.
It is your strength against my intelligence.  It is a veritable potpourri
of metaphor, every nuance of which is fraught with meaning."
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                     <The 5-MINUTE ILIAD and Other Classics>