[Phys-L] representation +- reification

[John Denker <jsd@AV8N.COM>]

Spagna Jr., George wrote:
> Part of the challenge with finding ways to draw the field lines is that
> the lines do not exist!  We have heard myriad warnings not to reify
> concepts like energy ... let's not reify "lines of force" either.

I've also heard myriad warnings that the sky is falling.  Words
fail to express how much I don't worry about it.

Saying "reify" or "don't reify" is almost entirely the wrong
question.  It would be better to ask about representation.
   http://www.av8n.com/physics/reality-reductionism.htm

A very great deal of physics -- and especially physics teaching --
is representational.  We build models that _represent_ the physics.
Sometimes we represent things with equations;  sometimes we
represent them with pictures, or mechanical models, or whatever.

The question is not whether or not to build models;  we *are*
going to build models.  The only question is which models are
more (or less) faithful representations of the underlying reality.

Electric field /lines/ are neither perfectly good nor perfectly
bad representations of the electric field vector.

What's more interesting is that the electric field /vector/ is
not even the best available representation of the field!  The
E-vector is notoriously not relativistically covariant.  It
is not even _part_ of any useful 4-vector.

The clever way to represent the electromagnetic field is as
a *bivector*.  This bivector is relativistically covariant,
which means that if you draw a picture of it, everybody (in
every reference frame) agrees the picture is correct.  This
is in dramatic contrast to electric field lines, which different
observers would draw differently.
  -- In the special case where the EM field looks like an electric
   field in the x direction in our reference frame, the corresponding
   bivector has one edge in the x direction and one in the t direction.
  -- In the special case where the EM field looks like a magnetic
   field in the x direction in our reference frame, the corresponding
   bivector has one edge in the y direction and one in the z direction.

In non-relativistic situations, E-vectors and field lines aren't too
bad.  Even in relativistic situations, almost all the usual objections
to "field lines" can be removed by drawing the bivector instead.
Yeah, I know drawing bivector fields is harder than drawing lines,
but it's not impossible.  A number of good examples can be found in
Misner,Thorne,Wheeler _Gravitation_.  See also
   http://www.av8n.com/physics/magnet-relativity.htm
and references therein.
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