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Re: the energy

John,

Thanks for your detailed response to my message. I am glad that you can
provide a justification for the flow model for energy transfer used by
the Modelers and others. I am more impressed with the efforts of those
in Modeling Instruction to teach introductory physics than any other
group. Your discussion of the conservative flow of energy using
space-time diagrams with the y and z components suppressed reminded me
of a discussion I read in the book on general relativity by Bernard
Schutz quite a few years ago. The concept of four-dimensional space-time
would not likely be available to beginning ninth or eleventh grade
physics students. I wonder if it would be possible to visualize the flow
of energy using the classical or everyday picture of space and time.
Could one make a video of work done on spring showing some kind of fluid
flowing into the spring system corresponding to its increase in
potential energy? Perhaps more difficult, could one make a video showing
the flow of energy as a fluid in an isolated system of charged particles
(including their electric field) from the electrostatic field into the
kinetic energy of the released particles? I don't see anything in the
modeling materials that actually permits one to visualize the flow of of
a substance-like fluid in energy transfer. Their representational tools
include pie charts and bar graphs with an energy transfer (or flow)
diagram. In either case, they first choose a system. In the pie chart
representation, a sequence of pie charts is shown as something is
happening, each pie chart showing how the internal energy of the system
is apportioned among the various energy storage "containers" -- kinetic,
elastic PE, electrostatic PE, gravitational PE, thermal or dissipated
energy, etc. -- whatever applies to the situation. In the bar graph
representation, bar graphs show how the internal energy of a system is
apportioned before and after the interaction. Between the two graphs is
an energy transfer diagram which is also referred to as an energy flow
diagram. O.K. So the energy actually flows as schematized by the
diagram. The money analogy corresponds to to the amount of internal
energy in the storage "containers" at the time to which a graph (pie or
bar) corresponds. It doesn't describe very physically how the energy is
reapportioned during the interaction, and how flow is involved.
Admittedly, the money analogy is naive. Students wouldn't have been
expected to have taken Economics 600. I suppose it is more like play
money, but Feynman didn't hesitate to use Bruce's toy blocks in the
parable in Sec. 4.1 of the scripture (_Lectures_, Vol. 1) that Leigh
refers to.



John Denker wrote:


Hugh Logan wrote:

> It puts a strain on my intuition to think of





energy flowing into a system consisting of a spring as a consequence of
work done on it by an external force if the flow is like that of a
substance.




What kind of strain? What's the alternative?



Trying to visualize the flow using the ordinary concepts of space and
time such as one might expect a ninth or eleventh grade student to have.
The alternative, for a high school student, is to say that energy
flows because his bookkeeping tools such as bar graphs separated by a
energy flow diagram tell him that energy has flowed in such a way as to
tell him the mechanisms by which this happened -- unless someone can
come up with a simple (non 4-dimensional space-time) picture of how this
happened. Just saying that energy flows, if not vivifying the flow with
a picture, may be of some help if the student goes on to more advanced
physics to understand it. However, I wonder if the Piagetian goal of
making energy transfer more concrete by regarding energy as a substance
that flows, is helped unless the student can visualize the flow in the
way that the flow of water or molasses can be visualized. Can videos be
made to show the flow of energy? When a baseball is thrown, it is
difficult for me to think of something like a fluid corresponding to the
baseball's energy flowing.





However, it does not bother me to think of the energy
transfer diagrams as flow charts in which the word "flow" is not taken
too literally.




Why not 100% literally?
....






> Unfortunately, the change of mass with





change in rest energy cannot be measured except in a thought experiment,
since the change is too small to be measurable.




It is distinctly measurable in the case of nuclear reactions.



I thought of this. In particular, a mass spectrometer -- perhaps of the
Bainbridge type -- might be used to determine the mass of a proton and
also of a deuteron. Twice the mass of a proton could be compared with
that of a deuteron, for example.



As I see it, E_0=m is the conserved quantity in an isolated physical
system.




That's not wrong ... but to do physics we need a more-robust
notion of what conservation means, one that can handle a
non-isolated system. That is where the idea of conservative
flow comes in.




On 19-Oct-04 Michael D. Edmiston wrote:



>>And what exactly does E=mc2 mean? Doesn't it mean mass and energy are
>>equivalent?



No, because the equation is not valid in general. It is only
valid when the 3-momentum is zero.



Depending on how E is defined. In one of Einstein's essays, "E=MC2"
(1946) that I referred to previously, referring to "E=mc2," he wrote
that "E is the energy contained in a stationary body; m is its mass."
As Rick Tarara pointed out, Philip and Phylis Morrison wrote "E=mc2,"
on p. 91 of _The Ring of Truth_, presumably meaning rest energy by "E." The
Morrisons would prefer to write it as "E=m." I agree that E usually
means the total energy, but not always in popular literature.

Incidentally, the Morrisons state on p. 90, ""Whenever the energy
account does not quite balance it is better to look for a missing
channel into which the energy is flowing than to imagine you have
discovered an exception to the universal rule to which all experience
has thus far led us. ..." The channel sounds something like the
Modeler's energy storage container, but in most cases, I still think it
is difficult to visualize the flow of energy. The Morrisons discuss the
energy balance of a cyclist. In particular, "The wind streaming against
his face and chest is what carries away the waste heat." I suppose one
can think of energy flowing along with the wind if the system is
enlarged to include the air. But does one visualize (or feel) the flow
of air or of energy?" He might feel the cooling effect as well as the
wind itself. In this case a fluid is used to transport the energy. The
Morrisons use as a unit of energy the "JD" -- the jelly doughnut unit --
about 250 nutritional calories or 250 kilocalories -- in discussing
cycling and related sports.

Hugh Logan