I have kept out of this turbulent (and turbid) flow of discourse
because I think my opinion has been stated clearly before, and I
haven't been paying attention here. Basically I hold the same opinion
as Jim Green, but something John Denker said raised my hackles. I
want to record a protest now.
John said: "The flow of momentum is a more precise concept than the
flow of water. Water (in many practical situations) is very nearly
conserved, but momentum (so far as I've heard) is always strictly
conserved."
John is wrong. He cannot assert that any abstract physical quantity
is *always* strictly conserved. History teaches us that this is not
the case. Energy and momentum are good examples of abstract physical
quantities. Both were well defined toward the end of the nineteenth
century. Both were then, as now, thought to be strictly conserved.
However Nature had yet to play some tricks on smug physicists who
thought that way. The discovery of radioactivity was probably the
first indication that physicists shouldn't be so sure of the
completeness of their knowledge. Through a series of tweaks the
definitions of such quantities has evolved. These tweaks were always
made strictly for the purpose of preserving the conservation laws.
Yes John, something called momentum is always strictly conserved, but
what momentum *is* has not always been conserved, and there is no
good reason to believe that your definition of momentum will be good
for another hundred years.
Among ourselves we may speak freely of the flow of energy, etc., and
none will be confused. Think, however, of the plight of a student
approaching this concept for the very first time. How can you be
insensitive to her reluctance to believe in something she cannot
perceive? She should be introduced to the concept of energy as a
state variable, a discovery! Typically this is done through an
investigation in experiment and theory with carts rolling down
inclined planes. A miracle occurs: the roller coaster equation! There
is a state variable, the Energy, that is conserved, and it makes
reckoning easy.
If she is not thrilled by this discovery, she is not ready to learn
physics. The teacher should be aware that this should be a thrilling
moment. Perhaps a few more souls can be redirected to the path of
righteousness if due reverence is maintained at this moment in the
physics course.
Of course the roller coaster equation is a poor example of
conservation of energy. The nature of that "gravitational energy"
term is suspect, and careful laboratory experiments demonstrate to
the student that it doesn't quite work. The Energy decreases with
time. More terms will be needed to explain the roller coaster in the
real world. All of these terms are necessary to "correct" the Energy
- so that it will continue to be conserved. Einstein made the biggest
correction in 1905, and perhaps this should be pointed out very early
even though it is not yet needed.
By convincing a student that the Energy is a real thing, we have made
it more difficult for her to comprehend what the Entropy is. Rudolf
Clausius understood that well when he named the Entropy. The Entropy
is an abstract physical quantity possessing exactly the same
cognitive status as the Energy. I claim that is a very difficult
point to make once one has mistakenly reified the Energy and planted
the idea of its reality in the mind of the student!
The Energy is an abstract construct. Before it was invented it did
not exist; it certainly didn't flow. Get real; don't reify!