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Re: [Phys-l] energy is well defined

See comments inserted below.

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of John Denker
Sent: Saturday, February 23, 2008 11:53 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] energy is well defined

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.

How so?

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.

There would be no change in how you calculate observables.


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.


Because the interaction of the plane with the air only depends on the
relative velocity between the plane and the air I suspect that you might
be working in the center of mass frame of the relevant system--perhaps
your model involves a plane of infinite mass or because the plane is
only interacting with a small number of parcels at any instant the
relevant system is much smaller than you think. But even if that is
wrong and center of mass of the relevant system involving the plane and
the air has a huge velocity relative to the frame in which you are
working, the energy-is-mass viewpoint still works. It is just that the
(1/2)MV^2 associated with the center of mass motion of the system
relative to your reference frame is not energy of the system. You could
call it external energy. It represents energy that is part of the total
energy of a supersystem whose center of mass is at rest in your
coordinate system. But there is no requirement that you identify that
supersystem.



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".

There's no call for doing that.


When it comes down to choosing between two competing models by means of
Occam's razor, we are employing metaphysics. That's all we're doing
here.

Which is simpler, A or B?

A. Energy is defined recursively.
B. Energy is mass. The total energy of a system is a measure of its
inertia. The gravitational field of a system is determined by how much
energy the system has and how that energy is distributed.

A. (1) Some kinetic energy can be part of the mass of a system, e.g. the
two proton system discussed in my last post (in which the total energy
should have included potential energy). Both the inertia of the overall
system and the gravitational mass of the entire system is different for
the case of two protons closing in on each other at a large fraction of
the speed of light than they are for the case of the two protons at the
same separation but having zero relative velocity. (2) Some kinetic
energy, that calculated relative to an arbitrary reference frame, is not
mass.
B. All energy is the mass of some system.

A. Energy can be classified in two broad categories: internal energy and
external energy.
B. All energy is internal to some system. In much the same way that
external forces on one system are internal forces within a larger
system, external energy of one system is the internal energy of a larger
system.

A. In the rest frame of a system, the potential energy of the system
belongs to the system as a whole, but the kinetic energy belongs to the
individual constituents of the system.
B. In the rest frame of a system, both the potential energy and the
kinetic energy are energies of the system, not of the individual
constituents of the system.