Re: corrupting the youth

["John S. Denker" <jsd@MONMOUTH.COM>]

Bob Sciamanda wrote:
> |  . . . The field F is still
> | a bivector.  The electric component is a bivector.  The
> | magnetic component is a bivector.  Always was.  Always
> | will be.
>
> This is a hard saying  ;>)
> Is the irrotational, zero curl, conservative electric field also a
> circulation (bivector) in this scheme?

1) [important] The old-fashioned electric field "vector"
should be thought of as a _slice_ through the more-fundamental
electric field bivector.  The bivector extends in the TX
plane.  In a given frame,  you can project out the spacelike
piece by dotting F with a unit vector in the timelike (g_0)
direction.

Since you can't freely travel back and forth in the T
direction, you can't freely circumnavigate the electric-field
bivector.

Also note that CIRCULation may not be exactly the right
word to apply to timelike bivectors.  A spacelike bivector
is associated with a rotation, and if you iterate this
rotation you will go around in circles, as described by
circular-trig functions (sine and cosine).  In contrast, a
timelike bivector is associated with a boost, and if you
iterate that you will generate hyperbolic-trig functions
(sinh and cosh).  For details see
  http://www.monmouth.com/~jsd/physics/rotations.htm#eq-exp-expanded

I don't have a better word.  Maybe hyperbulation????

2) [possibly less important] It might be true, for a certain
observer Alice, that a certain old-fashioned E-field "vector"
is irrotational i.e. curl-free i.e. conservative, but
 2a) That can only happen for electroSTATICS, i.e. if
     the field is independent of time, and
 2b) Time-independence can only happen for one very
     particular velocity of observer-frame (unless the
     field is independent of space, also -- a considerably
     less-than-general case).