Re: [Phys-l] non-conservative --> non-grady ???

[Steve Highland <shighlan@uslink.net>]

Now I am beginning to catch on to how our usages of the term "conservative
system" differ.  I am calling a system conservative if there is a way to
define a total energy for the system that stays constant as the system
evolves.

You seem to be calling a system conservative if there's a way to track the
energy flowing across the system boundary and matching it with the change in
energy inside the system.

> "In this
system, energy is conserved, but the energy of the system is
> not
constant.  Energy is transferred across the boundary of the system.


> Conservation of XX means that XX is constant _except_
  insofar as XX flows
> across the boundary of the system."  [John Denker]

I understand the idea of local conservation just fine when dealing with
conservation of electric charge.  Charge strikes me as real 'stuff' that
moves from place to place, so it can't just pop out of existence in one
place and appear someplace else.

Energy does not seem the same to me.  I tend to go back and forth on whether
energy is 'real' or just bookkeeping, but right now I'm going the
bookkeeping route.

Going back to the example of a ball falling in a gravitational field, how do
you locate the energy flow into the system of just the ball?  I don't see
how to identify an energy flux across any boundary.  If there is one I would
think that the flow must get denser near the ball, because a mathematical
surface enclosing the ball close to the ball's surface has a smaller area
than one enclosing the ball along with some air around it.

Unless there's some way of creating something along the lines of a Poynting
vector for gravitational fields I'm lost here.

Steve Highland
Duluth MN