Re: [Phys-l] energy is well defined

[John Denker <jsd@av8n.com>]

On 02/23/2008 08:59 PM, Jeffrey Schnick wrote:

> > Also, more importantly:  As soon as you allow a parcel to have 
> > nonzero KE,
>
> I don't.  The KE associated with the motion of the parcel relative to
>  the center of mass of the system is energy of the system, not of the
>  parcel.

At the very least, that is confusing.  It seems like a problem,
for reasons discussed below.

> If it isn't attached to the system then what you get when you sum up
> the internal energies of all the parcels and the energy due to the
> configuration of the parcels relative to each other and the (1/2)mv2
> for each parcel with v being the speed of the particle relative to
> the reference frame in question (call it O), is not the energy of the
> system. It includes a (1/2)MV2 part (where the M is the total energy
> of the system and the V is the speed of the center of mass of the
> system relative in O.  That part represents energy that might be a
> contribution to some supersystem whose center of mass is at rest in
> frame O, but it is not energy of the system.  I don't think that that
> energy is going to be useful in predicting how the parcels of the
> system interact with each other.

I'm not interested in philosophy or metaphysics;  I'm trying
to see how this applies to real-world tasks such as fluid
dynamics.  Suppose we have an airplane flying through a fluid.
It is conventional and convenient to divide the fluid into 
many parcels, and analyze things parcel by parcel, using a
reference frame comoving with the airplane.

To me, at least, this serves as a clear example of why I don't
want to focus attention on capital "The" capital "System" where
M is the mass of "The System".  I don't know M and I don't need
to know M.  For all I know, M is infinite.

We agree that MV^2 is not useful ... but so what?  I am not
required to evaluate M or MV^2.  I am not even tempted to 
evaluate such things.

I don't need to know M because all the laws of physics that I
need are *local* laws.  I can analyze each fluid parcel separately,
taking into account only that parcel and a few of its neighbors.

    FWIW as corollaries of the local laws you can prove some
    global laws, but I don't need the global laws in order to
    do practical physics.

    More generally, there are innumerable useless quantities
    that could be mentioned.  The goal should be to formulate
    physics in such a way that there is no requirement (and
    little if any temptation) to mention useless quantities.

To summarize:
 -- M is not useful.
 -- MV^2 is not useful.
 -- Focusing attention on "The System" is not useful.
 ++ Focusing attention on many local subsystems *is* useful.
 ++ A reference frame comoving with the airplane (not comoving 
  with the fluid) *is* useful.