Re: simple magnets question

[William Beaty <billb@ESKIMO.COM>]

On Thu, 24 Jun 1999, Michael Edmiston wrote:

> I think with William Beaty's most recent posting it has become clear
> that his question has switched from being a "simple" magnet  question
> to being a complicated magnet question.

I suspected as much.  Originally I wondered if others here had encountered
the problem before, and perhaps knew a conceptual short-cut.  Old (1970's)
papers on this subject suggest that this "simple magnet question" has no
answer, and therefor points out a flaw in modern physics (and possibly an
opportunity to do research in an unexplored area.)  Maybe the simple
magnet question is equivalent to the Ultraviolet Catastrophe question: a
simple question that causes no end of trouble for those who believe that
physics is complete.

On the other hand, if there is an answer (even a complicated one), then
modern theory has no gaping holes, at least in this region.    :)


> If two electrons are "at rest" then the only force between them is the
> electrostatic force.  If the same two electrons at the same spacing are
> both "in motion," they have a magnetic interaction as well as an
> electrostatic interaction.  But... wait a minute... there is no such
> thing as "at rest" or "in motion."

Right, and if we see that moving electrons don't fly apart as fast as the
initially-stationary ones do, then we can say that they attract each other
via magnetism, OR we can say that there is relativistic time dilation
which depends on the observer's frame of reference.  No problem there...

> I think William is questioning if this type of situation is correct...
> that is, he is describing two situations (involving relative motion)
> that intuitively seem equivalent, but they seem to yield different
> results.  Is this okay?  The answer is yes, this is normal for problems
> involving relativity.

I can't see how this is OK.  To me it is a paradox: leaping between
inertial frames can change the speed at which adjacent electrons fly
apart, but it cannot convert a curved electron trajectory into a straight
one, especially if the velocities involved can be arbitrarily low.


> However, with the proper relativistic treatment, the
> apparent problem goes away.  But the appropriate treatment is not real
> simple.

So you know the general features of this treatment?  If not, why be
certain that one exists?


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