Re: [Phys-l] EM, is it energy

[John Denker <jsd@av8n.com>]

On 12/01/2007 07:31 PM, Craig & Margaret Lucanus wrote:

> This a helpful list.

Yes.

One thing to keep in mind is that the discussions are
sometimes contrapuntal, due to the widely varying
needs and backgrounds of the participants.  It's not
a big problem, but it bears keeping in mind.

> Attributing energy to the field rather than to an object influenced by the 
> field is something worthwhile which I can pass on to my students. So if 
> there is nothing under the influence of a field, regardless of field 
> strength, there is no energy stored in the field. Thanks JB, this is 
> something I must have missed in text books, or at least it wasn't put that 
> way. 

There are two ways of looking at this.  I'm not going to
argue for either extreme, but rather to point out the 
contrast:

 1a) If you are hooking up a light bulb to a battery using
  clip-leads, then you say Kirchhoff rules, and fields are 
  an unhelpful distraction.

 1b) If you are hooking up some 10 GHz vFETs along a bit
  of stripline, then you say the fields are all that 
  matter, and Kirchhoff was severely deluded.

 2a) If you are playing catch with a ball, the earth is for all 
  practical purposes immovable, and there is a one-to-one 
  correspondence between the energy of the system and the
  state of the ball.  It makes sense to associate the energy
  with the ball.  Energy is a state function if you do that,
  and not otherwise.

 2b) If you are doing cosmology, treating the earth as immovable
  doesn't work so well.

I'm not saying that (a) is better than (b) or vice versa.  I can 
do cosmology, but I can also play catch.  Something that is a good 
approximation in one situation might be a lousy approximation in 
another situation.

  b) A description in terms of fields is absolutely necessary in
   principle.  Otherwise there is no hope of being relativistically
   correct i.e. Lorentz invariant.

  a) There is such a thing as "too much principle".  A lot of 
   the time in the real world, the nonrelativistic approximation
   works just fine.

Bottom line:  It doesn't pay to get too dogmatic about who "has"
the energy.