Re: "non-transfer" of energy

[David Bowman <dbowman@TIGER.GEORGETOWNCOLLEGE.EDU>]

Regarding BC's comment:

> I finally (think I) realize the essential difference between the Greens and the
> Denkers, et al.
>
> The Greens define flow as the movement of substance while the others define
> flow as the movement of anything that appears to move obeying certain
> conservation laws, et cet. whether it's the same thing before and after the
> movement or not.
>
> "The essential property of "flow" is that a
> decrease of something in one region is accompanied
> by a simultaneous increase of that thing in a
> neighboring region."
>
> I don't call PE and KE, for example, the same thing.

Although I think you have given a fair characterization of the main
difference, let me clarify my particular version of the non-Greenian
view, i.e. if it mathematically acts like it flows, then it *does*
flow.  The criterion for flow is simply a mathematical application
of the 'duck test'.

The above quote from John D. does indeed give the essential property
of the concept of flow in that it is characterized by a continuity
equation (with or without a source/sink term, depending on whether or
not the 'stuff' that is to be flowing is strictly locally conserved
or not).  I would only add that in order for such a local continuity
to exist (so that a continuity equation can describe it) a few other
properties need to be satisfied first.

Being able to flow seems to require about 4 prior conditions, and
none of them necessarily have anything to do with the 'fluid' being
any kind of actual substance.  First, the prospective quantity needs
to be effectively infinitely divisible in space at the macroscopic
level (so that macroscopic differential relationships can apply to
macroscopically infinitesimal-sized regions that are themselves
effectively so large in size on a microscopic level that they are
already in the thermodynamic limit.  Second, the quantity needs to be
*extensive* at the level of the macroscopically infinitesimal regions
defined in the first point.  Third, the value of the quantity has to
be capable of changing from place to place from time to time.  And
the fourth condition is what I call a 'locality of causation'
condition.  IOW the net value of the quantity in some region of space
needs to be determined solely by the conditions that exist in *that*
region of space, and any *changes* that happen in the local value of
the quantity in any infinitesimal region of space need to be
determined solely by the conditions in *that* region *and* on the
*immediately adjacent* regions on the boundary of that region via
some sort of short ranged causality principle or interaction that
reaches across the boundaries of the local region to its immediately
neighboring regions.

When these conditions are met it becomes possible to define a local
density field and a local flux current density field for the
quantity.  The net amount of the 'fluid' in any region of space is
then the integral of the density of the 'fluid' over the volume of
that region, and the net current of the 'fluid' across any given
surface is the integral over the surface of the component of the flux
current density normal to the surface.  Any quantity that satisfies
these conditions may be said to be able to 'flow' and *how* it flows
is described in terms of a local continuity equation (possibly with a
source or sink term). *If*, in addition, the quantity also is a
locally *conserved* quantity, then its continuity equation has *no*
sources nor sinks.  In this latter case the only way the quantity can
change in some region is for it to 'flow' into or out of the region
across the region's boundaries (separating the region from its
surroundings).  All that this 'flow' process really means in practice
is that the rate of change of the total amount of the quantity in the
region of interest is the net current of that quantity across the
boundaries of the region into the region.  There is not necessarily
supposed to be any sort of connotation of this 'fluid' quantity being
an actual ontological substance of some kind.  Some of the kinds of
quantities that satisfy the above conditions and can be said to flow
are energy, entropy, mass, momentum, angular momentum, strangeness,
electric charge, hypercharge, probability, etc. (as well as numbers
of atoms or other particles of so-called substance).

David Bowman