Re: [Phys-l] local conservation (was: non-grady ...)

[Steve Highland <shighlan@uslink.net>]

> To me, conservation of energy is on exactly the same footing as
> conservation of charge.  Energy is somewhat abstract, but so is
> charge.  Energy can be viewed as "stuff" that can flow across
> the boundary, and so can charge.  Energy can be formalized as a
> completely abstract bookkeeping exercise, and so can charge.
[John Denker]

I'd like to see how electric charge could be reduced to just bookkeeping.  I
confess to being bothered (in a way I can't quite put my finger on yet)  by
your claim above.

I still want to cling to the idea that electric charge is real, tangible
'stuff' that I can hold in my hand.  Energy seems different, especially when
you can freely label any state as 'zero energy' and get the same description
a a system's behavior.  How can energy be real 'stuff' if you can
arbitrarily say how much you have to start with?

I recall that conservation of charge is a direct consequence of Maxwell's
equations, but read yesterday that energy conservation (in the first law of
thermodynamics sense) is a deep statement that contains *more* than what can
be derived from Newton's laws.


"The basic problem is that the work-energy theorem is really a dynamical
relation, derived from Newton's second law, and cannot be a truly general
energy statement. There are three independent conservation relations in
classical physics. The first is the equation of continuity or conservation
of mass. The second conservation law, that of conservation of momentum, is
the grand generalization underlying Newtonian dynamics. If the general law
of conservation of energy in classical physics could be derived from the
dynamical equations, it would be a tautology and would not constitute a
third independent condition, as it actually is. The law of conservation of
energy cannot be derived. Like the other conservation laws, it is arrived at
by induction from limited observations and is ultimately accepted because no
violations are observed."
[Arnold Arons
Development of energy concepts in introductory physics courses
American Journal of Physics, Vol. 67, No. 12, pp. 1063­1067, December 1999]


Doesn't this put energy on a very different footing from electric charge?

Steve Highland
Duluth MN