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Re: IONS in metals

To Ludwig and Bob,
As a freshman physics student, I agree with Bob on this pedagogical
issue. The reason we (or more accurately you, the instructors) have
been forced into the difficult situation of explaining a non-classical
effect to a student in an introductory physics course is that the
student saw the inconsistency in classical theory. If a student is
comfortable enough with a concept to notice points where it seems to
fail, it seems time for the more advanced concept to be introduced, if
only in some basic form. In a few cases in my two high school physics
courses I was exactly this questioning student. Two or more of the
generalizations that are, and must be, taught in introductory physics,
stuck in my head as mutually exclusive.

Perhaps the most basic example from my first kinematics and mechanics
course is this: F=ma, v(final)=v(original)+a*t. I had also heard
that nothing could exceed the speed of light. It seemed simple that
applying a force to an object with an original velocity slightly lower
than the speed of light for some easily determined length of time
would yield an final velocity greater than the speed of light. When I
asked my teacher about this dilemma after class, he didn't explain the
whole, or even much of the basics of the special theory of relativity
to me. He did take the time to tell me that certain properties of
space and time are not constant, but change with relative velocity,
and that the some of the functions that describe these changes are
asymptotal at v=c and that for v<<c the changes are inconsequential.
This very basic idea was enough for me to understand why F=ma was
neither invalid, nor completely absolute.

I do not think that a student will be confused by the introduction of
a more advanced concept if he has already seen through the
simplification that has been presented.

Best,
Zach Wolff
freshman, physics
University of Arizona
zachary_wolff@yahoo.com



---Bob Sciamanda <trebor@velocity.net> wrote:

Hi Ludwig,

Even within classical mechanics the force concept can be subsumed
within
the use of a Lagrangian or Hamiltonian function. True, the force
concept
told us how to construct these functions, but they can then be used as
the basis of speculations based on variations of these functions -
possibly resulting in new systems and behaviors not intuitively
amenable
to simply an inter-particle "force" description (fields might then be
endowed with particle properties, to "save" the model).

Simple example (not a speculation) : within classical theory, two
interacting charged particles will not in general conserve momentum
and
energy (between themselves) and their motions will not exactly
follow the
dictates of a two-particle "Lorentz" force - hence we invent some
"particle properties" for the fields (ie; we read them into the
Lagrangian/Hamiltonian which works!). I don't think that it is
possible
to exactly describe the (classically predicted) motion of two
electrons
shot past each other in terms only of forces between the two particles
(even if you want to dream up forces of the particles on the
fields!).
The fields carry momentum and energy, but they are not "acceleratable
masses"; F=ma does not apply, even in concept.

We are now so used to including these fields (first introduced as
purely
mathematical entities) as "quasi-substantive" participants that we
miss
the stretching effect which these notions had on the original
Newtonian
force concept and the selective particle properties which it slyly
attaches to the fields (presaging the photon?).

The quantum mechanical particle state (and its time development) is a
completely different conceptual and physical entity. You are
correct in
asserting that in the Shroedinger representation the potential energy
V(r) enters into the Hamiltonian. It contributes to the
specification of
the eigenstates of energy available to the particle. At this point,
there emerges the existence of impossible particle states, and this is
not attributable to any new Newtonian force in any simple intuitive
sense. The force concept has really been subsumed and will re-emerge
only if one goes to a situation where a classical limit applies, and
considers the behavior of the average values of observables
(Ehrenfest's
equations).

I don't think the answer to your pedagogical problem lies in seeking a
Newtonian type force to account for these phenomena of "particle
trapping"; there isn't any. More important is the Pauli principle
and
the "quantization of states" dictated by boundary conditions;
classically
possible states may be forbidden. An electric force field applied
to an
insulator will not accelerate an electron because there is no
unoccupied,
appropriate state available to it, etc.

I think that you need to sell your students the denial of classical
force
effects which Bohr asserted in 1913. Tell them about the Bohr atom,
its
restricted set of orbits and the impossibility of classically
permissible
motion out of an orbit until enough energy is available to get to an
unoccupied (bring in Pauli too) orbit. Just the notion that quantum
mechanics often denies the availability of a continuum of states and
can
then "trap" a particle in a state without a definable "trapping force"
should allow them to model a lot - still thinking in terms of forces.

Sorry I rambled - it's your fault!

-Bob

Bob Sciamanda
Physics, Edinboro Univ of PA (ret)
trebor@velocity.net
http://www.velocity.net/~trebor

-----Original Message-----
From: Ludwik Kowalski <kowalskiL@Mail.Montclair.edu>
To: phys-L@atlantis.uwf.edu <phys-L@atlantis.uwf.edu>
Date: Sunday, October 04, 1998 9:20 AM
Subject: Re: IONS in metals


Bob Sciamanda wrote:

Forces are human inventions which help us model our
observations. However, quantum mechanical models are
not always simply understandable in terms of this concept.

As far as I remember, the central concept of QM is potential, V.
We must specify a potential function to write down the
Schroedinger equations for specific problems, for example,
Coulomb's potential in the case of the single hydrogen atom.
What prevents me from using F=-grad(V) and to think that
there is a force behind any smooth potential function?

The concept of F remains central in QM. I tell students that
QM is an extenuation of classical physics, just like relativistic
kinematics is an extenuation of classical kinematics. Quantum
granularity does exist for ordinary macroscopic objects but
the steps are so small that for all practical purposes we can
say that all energies are allowed. What is wrong with this?

At the end of the message Bob writes:

(As a pedagogical crutch, you might introduce the "exchange
force" to help in some cases where the Pauli exclusion
principle is the controlling factor under discussion.)

Keep in mind that my hypothetical student (see below) was
in an introductory physics course. He would only be confused
if I follow your suggestion. I do not like "borrowing from the
future" why EXPLAINING things. Let me propose an
alternative. Here is the situation to which Bob is referring:

How to deal with this hypothetical situation? It is a
pedagogical issue. I have no problem in pretending that
Galilean kinematics is exact, but I will now face a problem
of pretending that electrostatics I teach is logically
consistent with mechanics. Galilean kinematics is at least
approximately correct in common situations. Something
is missing in our ways of introducing e&m. What is it?

In other words, what is the nature of the "glue" binding
excess electrons to the surface of a metallic object? Let me
improvise the answer by using an analogy. Consider
static friction. We pull an object and it does not move. We
pull stronger and it still does not move. But eventually
"the glue" can not hold it.

Some kind of binding force must exist to keep electrons on
the surface. We can give it a name, for example, metallic
surface force, but this is only the first step. A good question
for future investigations. I have no idea what the nature of
this force is; I just invented it to solve our dilemma. To the
best of my knowledge, I would say, this force has not been
studied in detail.

Free charges do escape from metallic surfaces when their
concentration becomes excessive (as discovered by Franklin).
This shows the analogy between the metallic surface force
and the static friction force. Both grow, up to some limit,
and than .... The electrostatic surface tension force (another
possible name) grows with concentration of surface charges.
Is this an acceptable presentation for first physics course ?

Ludwik Kowalski







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