Re: Fields can be nonlinear

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

Hi Folks --

Jim Green asked:
> Does it make any sense to say something like one electric field
> interacts with another?

Several people including L.K. have correctly made the point that
> in classical physics, electric fields do not interact.

I would like to supplement this by pointing out that if we don't limit
ourselves to *classical* physics, it is possible to have quite interesting
nonlinear interactions between electromagnetic fields.  The buzzword is
"light-by-light scattering".

One way to come to grips with this is as follows:
  1) Imagine that the vacuum is populated by innumerable *evanescent*
electron-positron pairs.  That's the only vacuum we've got.
  2) Using a reeeeeally bright laser, create an electric field so strong
that you can materialize one of these pairs.  This is sort of like the
Hawking radiation, but using light rather than gravity to do the work.
  3) Some light will scatter off the electron and/or positron.
  4a) You can let the electron and positron annihilate each other, leaving
you with nothing but light which (from the black-box point of view) was
scattered by light.
  4b) Or if you prefer, let the electron and positron hang around,
representing matter created from pure light.

A version of this has been done;  a cloyingly cute popular account can be
found at:
  http://www.slac.stanford.edu/exp/e144/e144.html

Bottom line:  in the classical approximation, the Maxwell field is linear.
Linearity implies superposition, which implies no interaction.  But (!)
when you consider the real world of *quantum* electrodynamics, nonlinear
things can and do happen.

Other fields (sound, gravity, ...) are also nonlinear.

Cheers --- jsd