On Oct 6, 6:38 am, Matt Whiting wrote:
Really? Many books still can't agree on the definition of current.
Some say it is the movement of electrons and some say it is the movement
of positive charge and some say it us both. Which is the absolute
truth, Mr. Wizard?

The truth is that the electrons move, not the protons.

If you are referring to holes http://en.wikipedia.org/wiki/Electron_hole
and electrons in semiconductors http://en.wikipedia.org/wiki/Semiconductor
, where the descriptions of flow of charge through a semiconductor
lattice shows both positive and negative charge flow, in opposite
directions, in the present of an electrical field, the negative charge
being represented by electrons, the positive charge being represented
by holes.

Every book in electrical engineering is likely quite explicit in
telling students up front, (more like forming an agreement with the
students), that the holes are to be modeled as physical particles
because that it is mathematically equivalent to the true phenonmenon,
which is a void moving through the lattice, that, although there are
people who are quite capable of modeling the truth, which is based on
stochastics and energy-band http://en.wikipedia.org/wiki/Energy_band
theory, they will use the one that is simpler since the two models are
functionally equivalent. Note that any professor writing a book
claiming that holes are real particles would probably be barred from
teaching. In the world of electrical engineering, it would be like
saying that the Santa Claus really does exist, knowing that the
professors themselves created the figment of Santa Claus. I cannot
emphasize enough that there is no confusion whatsoever in the minds of
the students about what is actually going on inside the lattice.
There is no doubt in their minds that there are no such thing as
physical particles called holes moving through a lattice. There is no
doubt because professors conscientiously created this fiction, and
tells their students: "We all know that there are no hole
particles...but.." You will notice that the Wikpedia description of
holes uses the word 'conceptual' in the first sentence.

A related concept is something called phonons: http://en.wikipedia.org/wiki/Phonon
These are quantum mechanical pseudo-particles. Electrical engineers
and physicists know that they do not exist. They know because they
made them up, just like the made up the holes.

There is nothing wrong with doing this. In each case, there is no
untruth being spoken, because the scientists say up front: "We are
about to tell you something that is not really true. Just keep in
mind what the real truth is as we go along, please." This implies
that the EE students know the real truth, which they do, because those
same professors tell them that also. The aerodynamicists say: "We are
about to tell you something that is true.", and they say nothing more,
because they think that what they are about to say is not a
mathematically equivalent model of the truth, but truth itself.

Consider the case where one might do a systems problem to find the
voltage across a capacitorhttp://en.wikipedia.org/wiki/Capacitor, and
end up with something like...

V(t) = 12 * Integral(Delta(t)) + u(t)*e^-3t*e[jwt/(4*pi)]

j is the square root of negative one (-1)
w = angular frequency http://en.wikipedia.org/wiki/Angular_frequency
t = time u(t) is Heaviside step function http://en.wikipedia.org/wiki/Unit_step_function
Delta(t) is the Dirac-delta function http://en.wikipedia.org/wiki/Dirac_delta)

This voltage contains complex numbers sitting n an exponential. It
also contains a phenomenon that occurs so quick that is is
mathematically impossible to observe in time, yet its effect during
that brief moment is infinite. This is ridiculous. We know with
certainty that no such things exist in real-life. But that's ok,
because we made these things. Electrical engineers looking at this
will know immediately what the truth is, what the math represents.
What is odd is that one eventually reachs a point where no uneasiness
at all comes from moving between the real and the unreal. They are,
in an abstract sense, in separable.

Futhermore, concerning the point you made, if the above voltage V(t)
is positive, then by the formula for charge on a capacitor, Q=CV,
since C, the capacitance, is [ahemm....always positive...please, if
you are a EE reading this, please don't start up with me about general
impedance converters ], the the charge is possitive, but we just
noted in the semiconductor example above that one does not find
positive charge running around in circuits because the are constrained
to the nuclei of atoms http://en.wikipedia.org/wiki/Atomic_nucleus
with their neutron buddies. This does not bother electrical engineers
because they see the formula and immediately see the image of what is
going on, the truth of physics as it occurs. Note that, if the
formula claims that there is positive charge on one plate of the
capacitor, there really is no positive charge "on the plate" so to
speak, but a depletion of negative charge, which is mathematically
eqivalent model of truth, just as there is no such thing as square-
root of negative number in real life, but if you use Euler's Formula
http://en.wikipedia.org/wiki/Euler's_formula, a Taylor expansion of
the formula about t http://en.wikipedia.org/wiki/Taylor_expansion, you
will see that the V(t) comes out to the nice sine waves that you would
see on an oscilloscopehttp://en.wikipedia.org/wiki/Oscilloscope .

Contrast this with what the aerodynamicists are doing. They are not
issuinig disclaimers saying, "this is not really what is happening, we
all know that, but let us pretend to make the math simpler for now".
They claim what they are illustrating *is* the truth.

-Le Chaud Lapin-