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Re: ENERGY WITH Q



Regarding Robert Cohen's comment (in response to Jim Green):

I ask these questions because I want to know the proper vocabulary
to use. A couple more annoying questions...

Is kinetic energy the only "non-pretend" energy (i.e., energy that
does not include the likes of PE)?

If not, what are some other "non-pretend" energies?

Is energy conserved (i.e., energy that does not include "pretend"
energies like PE)?

I suspect that "'non-pretend' energy" and "'pretend' energies" are
not "proper vocabulary". In fact, the practice of distingishing PE
from KE by calling one of them "pretend" and the other "non-pretend"
is *very* misleading. If you must find some way of distinguishing
them maybe you ought to call PE the energy something has by virtue of
the configuration (i.e. position, orientation, etc.) in space of each
of its dynamical degrees of freedom (including its overall center of
mass and overall orientation esp. in relation to other physical
objects). Essentially, the PE is the contribution to the object's
energy due to the energy's dependence on the values of each of its
configurational degrees of freedom. But KE is the energy something
has by virtue of its motion and the motions of its parts in that it
is the contribution to the object's energy due to the nonzero values
for all the momenta associated with the system's (micro)state
(including the overall total momentum of the center of mass and the
total overall angular momentum).

In a relativistic context the total energy of an object is typically
not a simple sum of purely KE and PE (and rest energy) contributions.
Also, objects can interact with each other via an interaction energy
that is not purely 'kinetic' nor 'potential' in character (esp. in
field theoretic circumstances). In such a situation it is not very
useful to try to partition the total energy into a simple sum of KE,
PE and RE parts because the functional form of the total energy is
not in terms of a simple sum of a purely momentum-dependent part and
a purely configurational part. Often there are terms that depend on
complicated functions of both the momentum and the configurational
degrees of freedom. A GR example of this is the total energy (w.r.t.
a convenient standard set of coordinates) for a freely falling
particle in the fixed background spacetime of a black hole.

In general, the energy of a system is the value of the system's
Hamiltonian. And the Hamiltonian is the quantity that generates the
virtual transformation of the system's microstate that
infinitesimally translates that state in time (as defined in some
particular reference frame or coordinate system). Whether or not it
is useful to attempt to partition the energy into a PE part and a KE
part depends on the particular problem at hand an on its particular
functional form for the Hamiltonian.

David Bowman
David_Bowman@georgetowncollege.edu