This is perhaps getting to close to arguing semantics, but here it goes
none-the-less
|
| The idea of putting energy into a system, is certainly valid,
| but this is very abstract and is not understood well by
| beginning students.
Actually I find and found as a student, and witness my students finding
the field concept to be quite abstract, more so than a system of
interacting particles model.
|The field does not have to be
| mathematically defined, but can be invoked as the connection
| between objects.
If its not defined, than it is going to be exceedingly abstract and one
might as well talk about an interaction between particles.
|It becomes the "container" in which the
| energy resides. Students have not trouble with understanding
| that energy is in a spring or rubber band.
|
They have no trouble with springs, as they are actual objects. Though
one would more properly refer to a wall and mass interacting through the
mechanism of the spring. The spring by itself in some sense is a poor
container for the energy as well, because it always requires something
else in order for it to store PE (not worrying about gauge invariance
here, i.e. lets agree that a relaxed spring has zero PE). There has to
be two something elses interacting via the spring.
| Notice that in doing this the field is simply the name for
| the mechanism that pulls the ball to the Earth, and the Earth
| to the ball.
We already have a name for that. Why subtly change the meaning of
"field". It strikes me as using the name "field" when you can just as
easily say "force of gravity" or better yet, the "gravitational
interaction"; its making the words synonymous, when they shouldn't be;
the idea of interaction serves just as well for providing a connection.
I.e. simply say that the PE energy resides in the interaction between
the objects. Then you can very easily calculate the PE of a three
particle configuration. Something that the field model would have a lot
of difficulty doing for the beginning student. (see below)
| Now with kinetic energy, the energy is in the object. With
| thermal energy, the energy is in various physical places such
| as the two objects that are rubbing against each other...
|
See Dan MacIsaac's comment
| Unfortunately the idea of energy in a system looks like
| handwaving to lower level intro. students, but it might be
| more appealing to the higher level thinkers than a mysterious
| field. So when one talks about it, both ideas can be
| mentioned.
Except my experience has been that fields seem like a lot of hand waving
to lower level students as well. The idea of the field as an
intermediary to the interaction is an exceedingly abstract idea. More
so than the idea of interaction itself. I'm guessing that what is
happening is that the word "field" is being operationally redefined to
be what one ordinarily means by interaction.
|In either case the field implies a system, so it
| provides a mental connection between the objects, and helps
| the students understand the idea of system.
|
The field concept is really designed to logically separate the "cause"
(source) from the "effect" (the object being acted on). It is a concept
that is designed to allow one to handle the problem by getting around
the idea of a system.
The system idea is that particle one interacts with particle 2
The field idea is that we may ignore particle 2, view particle one as
producing a field. No reference to particle 2! If we care about what
happens to particle 2 we may then, later, calculate the effects that the
field has on particle 2.
I.e. is the field implies no particle system.
| The idea that you just present the math is what most
| traditional courses have done, and the research shows that it
| loses most of the students. They are adrift with no mental
| model.
I'll just say that IMO the field concept is more abstract than the
interaction concept; and I hold that the interaction concept (no math
here) leads to a model that is more easily translatable into calculating
the PE of a configuration than the field concept (for beginning
students);
Consider three point charges at the corners of a triangle, do you think
a student (or even a professor) will have an easier time calculating the
PE using a field concept or an interaction concept?
This is being written quickly and probably is a bit muddled, but
hopefully it provides some food for discussion (or fuel for the
conflagration).
_____________________________
Do not infer from the above that I don't fields exceedingly useful; I do
for all the local conservation of energy reasons (not to mention
photons) that John D. has mentioned. My comments above are restricted
to the field concept versus an interaction concept in understanding PE
at an introductory level.