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Re: the energy

I'm sorry to be so slow in my own discussion. I do appreciate all the
comments that are being made. They will inform my thinking, I'm sure.

To my note:

The orthodox view, which I hold to be correct: The energy is not
substantial; it is not a real entity. The energy is an abstraction.
The
energy did not exist before it was invented. The energy is a state
function, a quantity which may be calculated for any isolated physical
system from the values of all the parameters that characterize its
state.

John Clement replied:

Yes, but is this how energy should be taught? The Modeling people
firmly
come down against this view as one that should be taught in the intro.
course. They model energy as something which can be transferred sort
of
like a fluid. Now this may be called heresy, but remember the essence
of a
model is that it is a picture or concept that you can use to help
understand
and explain. Such a picture can and will then be modified as
understanding
increases. Their point of view is one which is based upon their
observations and testing of students.

Perhaps the modelers are correct if the goal in teaching this is merely
to
get the students to apply conservation of energy correctly. My goal in
teaching the few students who want to go farther in physics looks to the
future, when I get to introduce them to the entropy. I am fully aware
that
these students are a minority, but another of my aims is to increase the
size of that minority by making the learning of physics attractive to
those students who are capable of appreciating it.

My other goal here, in this group, is the discussion of the physics
itself
with my colleagues, all of whom have qualified already as members of
that
minority. I assume that we are all true believers, though of course
there
will be differences in opinions expressed, as one finds in any
theological
discourse. Since I have never found anything with which I could disagree
in *The Feynman Lectures on Physics*, and since Feynman chose to write a
parable about energy which emphasizes this point, I refer to Feynman as
scripture.

Essentially the students need at first a concrete picture which helps
them
to be able to correctly predict what happens in a variety of
situations. If
the student manages to arrive at the "theoretical level" of thinking,
then
the orthodox view is natural and understandable. As such, treating
energy
like a substance allows them to understand that when it increases in
one
place it must decrease by the same amount somewhere else.

Agreed. It is a satisfactory *description* of Nature to a fairly deep
level, but as I and some others (e.g. Jim Green, I think) see it, there
is a tendency to forget that the energy is an abstraction. Since we all
pay for gasoline at the pump such a lapse is understandable, but there
is
good reason to go back to fundamentals frequently so one does not become
sloppy (some examples will follow if I get to them) in application or
thinking about conservation of energy.

One way to use conservation of energy is to apply it to novel physical
processes as a test. One may find that there appears to be an anomaly,
as
Einstein did, leading him to conclude that another term had to be added
to the canonical energy function to preserve the conservation law. The
conservation law is more fundamental than energy itself. As I understand
it, Noether's theorem says that there must be some conserved dynamical
property of isolated physical systems evolving according to time
invariant
physical laws. We call that quantity the energy, and we carefully
account
for all of its parts in any valid description of Nature.

I would propose that to a certain extent student understanding has to
proceed through various stages, and some stages will of necessity not
be
consonant with current theory, but may actually be similar to earlier
historical understanding. This is fairly similar to the Piagetian
stage
theory which says that individuals progress through all of the lower
stages
before they can arrive at the higher levels. I would say that it is
often
impossible to skip stages of physics understanding, just as it is
impossible
to skip the Piagetian stages.

In addition, attempts to skip stages may block progress to the next
necessary stage, and will always prove to be fruitless. An example
from
Piaget is quite revealing. Children always go through a stage where
they
equate the amount of something with how it is spread out rather than
the
number of items, before they comprehend that the amount depends on the
number of items. They always go through the stage of thinking a
heavier
ball pushes up water more than an identical size lighter ball when both
balls sink. Some individuals never come to an understanding of this
task.

I would propose the energy as a "fluid like substance" is a necessary
bridge
to more abstract models of energy. It is also probably the only way in
which students below the formal operational level can have any
understanding
of energy. The orthodox model requires the highest or "theoretical
level"
(as proposed by Anton Lawson). Since only 20% of HS graduates are at
the
"formal operational" level and probably only 20% or fewer of college
graduates are at the "theoretical" level, the orthodox model is a tall
order
to try to teach.

I accept the argument that the bridge is helpful in teaching the concept
to all students, even those few who have progressed to Piaget's highest
level. What I am suggesting is that it not constitute the sole
description
with which we leave them. We don't expect our students to learn
everything
we teach them; indeed in our country there is a strange "50% pass" myth
that students bring in from high school. I'm perfectly prepared to
accept
what I can't change. What I argue is that a student should not be told
the true ontological status of the energy for the very first time when
he
or she hits the junior level thermodynamics course. I have trouble
enough
convincing students that entropy is not "a measure of the disorder of a
system" when I introduce the topic either statistically or classically.
Somehow that half truth, learned in high school, seems to have stuck.

Incidentally our notions of reality are based on our senses which
measure
certain things. Would a being who has senses that directly measure
energy
say that energy is a substance, and that our notions are wrong?

You have anticipated the ontological direction of my essay, John. More
later, but can you think of any physical instrument that directly
detects
the energy?

Leigh