Re: [Phys-l] Charged particles moving along parallel paths

[John Denker <jsd@av8n.com>]

On 12/03/2011 03:44 PM, I wrote:
> This is easy to visualize, easy to explain, and easy to
> understand in four dimensions ... and not otherwise ...
> as far as I can tell.  The pictures can be found here:
>  http://www.av8n.com/physics/magnet-relativity.htm
> and the equations can be found here:
>  http://www.av8n.com/physics/straight-wire.htm


I spoke of "pictures".  For email and for web pages, that's
the right thing.

For classroom use, you should make a cardboard model.  
Use three different colors of cardboard.  Tape them
together to represent three bivectors such that A+B=C, 
showing how bivectors add edge-to-edge (just as vectors 
add tip-to-tail).

The story goes like this:  This hypotenuse here is the 
electromagnetic field bivector in the lab frame.   It's
purely horizontal, i.e. purely magnetic.  If we rotate 
it a little bit ... or (better!) leave it alone and rotate
our point of view! ... then it is tilted like this, and 
then we can resolve it into a magnetic component plus a 
small electric component, as you see here.......

If we rotate something in the XY plane, the tangent of
the rotation angle is called slope, dY/dX.

If we rotate something in the TX plane, the hyperbolic
tangent of the rotation angle is called velocity, dX/dT.

Special relativity is not weird or paradoxical.  It is
just the geometry and trigonometry of spacetime.

The bivector formulation of electromagnetism is explained
in more detail at
  http://www.av8n.com/physics/maxwell-ga.htm

Make the cardboard model already.  Keep it around.  If
you untape one of the three edges it folds flat for easy
storage.  The same model is used to explain gyroscopic 
precession.
  http://www.av8n.com/how/htm/motion.html#sec-gyro-rule