Since I don't remember contributing to the previous perennial
incarnations of the 'does energy flow?' controversy, I would like to
spout off on the subject with my 2 cents.
I agree *partially* with both sides. I agree that energy, mass,
temperature, volume, x component of momentum, etc. are properties, and
that properties being descriptive quantities do not exist in the absence
of a system or object to describe. I thus agree that we ought not reify
energy by considering it as a form of matter or 'stuff' in its own
right. I cringe when I here people glibly talking about something
called 'pure energy' (when they are discussing pair creation and
annihilation or some other such topic).
But that being said, John still has a point. Just because a property
doesn't exist without some antecedent substance or system to describe is
not sufficient reason to say that it does not flow. I don't think that
only fluids of ordinary matter are essentially the only things that
flow. I would (along with John) consider the concept of flowing to
extend to any locally conserved infinitely divisible extensive quantity.
Even a purely mathematical concept such as probability can be made to
flow using such a definition. Therefore I have no problem with
properties such as energy, mass, charge, y-component of angular
momentum, Poynting flux, DeBroglie probability--even the probability in
the distribution of microstates in classical Poincare phase space, etc.
being afforded the right to be considered as flowing.
The way I see it (TWISI) in order for a quantity to be eligible for
flowing it needs to be locally conserved *and* continuously extensive in
the sense that it is a spatial integral of a density of that quantity
where the smallest pieces of the quantity are considered as so small
that the quantity is thought of as being infinitely divisible (whether
it actually is so or not on a sufficiently fine length scale). Thus,
whether or not a particular kind of quantity can flow, is somewhat
dependent on the particular model used for the system because different
models will have different ways of assigning the attributive properties.
For instance if our model system is a field theory model where the
Hamiltonian function can be written as a spatial integral of some local
energy density function (such as in the case of classical
magnetohydrodynamics, or for the Hamiltonian density made of the Maxwell
and Dirac fields of QED), then the energy of such a system can be said
to flow. (Of course for a quantized system we must be careful and
consider the flow to be in the constituent relevant operator-valued
distributions as described in the Heisenberg Picture of QM.)
*But* if the model has the property being evaluated in a non-local
manner, or if it is not continuously extensive, then that property does
*not* flow for that particular model. An example of such a model is for
a classical system of N classical Newtonian particles (e.g. a planetary
system or a galactic cluster) interacting via only their mutual
Newtonian gravitation. In such a system the potential energy is
non-local and scales quadratically in N. There is no convenient energy
density that has the property that the total energy of the whole is the
sum of the energies of the separate parts. Indeed, any particular
subsystem does not even *have* its own individual energy because part of
a subsystem's energy is an interaction energy between it and the rest of
the whole system external to the subsystem, and that interaction energy
depends on the state of the whole external part of the overall system as
well as the internal state of the subsystem. For such a system the
system's energy does *not* flow in any useful sense of the word.
So, in a nutshell, whether or not energy flows depends on just what the
system is and how it is modeled.