| Subject:
RE: Electrodynamic equations Date: Sat, 4 May 2002 16:12:38 -0500
Dear Moshe,
Yes, the history gets
muddled a bit.
Maxwell's seminal theory is contained in
James Clerk Maxwell, "A
Dynamical Theory of the Electromagnetic Field,"
Royal Society Transactions,
Vol. CLV, 1865, p 459. Read Dec. 8, 1864. Also in
The Scientific Papers of James Clerk
Maxwell, 2 vols. bound as one, edited by W. D. Niven, Dover,
New York, 1952, Vol. 1, p. 526-597. Two errata are given on the
unnumbered page prior to page 1 of Vol. 1. In this paper Maxwell
presents his seminal theory of electromagnetism, containing 20 equations
in 20 unknowns. His general equations of the electromagnetic field are
given in Part III, General Equations of the Electromagnetic Field, p.
554-564. On p. 561, he lists his 20 variables. On p. 562, he
summarizes the different subjects of the 20 equations, being three
equations each for magnetic force, electric currents, electromotive
force, electric elasticity, electric resistance, total currents; and one
equation each for free electricity and continuity. In the paper,
Maxwell adopts the approach of first arriving at the laws of induction
and then deducing the mechanical attractions and repulsions.
The notation is different
from the modern quaternion notation, and so perhaps should be referred
to as "quaternion-like" in the modern sense.
So resistant to quaternions
were the times, that Maxwell himself began simplifying his theory
farther away from quaternions. As an example, after the first edition
of his Treatise (book) in 1873, the outcry was so great that he began
rewriting and simplifying his own theory. He died before the second
edition could be finished and published, but he had changed more than
half the chapters. The second edition therefore differs fairly
significantly from the first edition, and particularly from the 1865
paper.
Also, in 1967 Ludwig Lorenz
developed a parallel theory of electrodynamics very similar to
Maxwell's, and he also symmetrically regauged his equations (which is a
dramatic simplification, indeed one which arbitrarily discards any net
interaction between an active environment and the physical system being
modeled). Lorenz got very shabby treatment at the hands of the
scientific community, and some years later when H.A. Lorentz published
his version of Maxwell's theory with symmetrical regauging of the
equations, credit was erroneously given to Lorentz (and still is) for
that action.
Our wry comment is that this
symmetrical regauging --- whether of Maxwell's equations or Heaviside's
truncated version --- discards all permissible Maxwellian systems that
are open systems far from equilibrium in an active environmental energy
exchange. In modern terms, this discards the local curved spacetime and
also the local active vacuum, insofar as any net usable exchange with
the system is concerned.
Yet the symmetrical
regauging assumes two separate and simultaneous free changes of the
potential energy of the system. Unless one wishes to discard the
conservation of energy law, that in turn implicitly assumes (in modern
terms) that energy from the vacuum has entered the system in two ways
(changing two potentials) but very selectively and just so that the
resulting two new and free force fields that result are everywhere equal
and opposite.
Interestingly, that assumes
that a continuous exchange of energy between the active vacuum and the
system is ongoing, but all the net energy entering the system is "locked
up" as a stress potential with a net translation vector summation of
zero.
But a stress potential
change means that one has assumed INTERNAL work continuously being
performed on the system, by its peculiar exchange of energy with the
external active environment. In short, that continually produces and
maintains the assumed increased stress.
Further, the increase in
potential energy of the system is also an increase in the local energy
density of the vacuum (i.e., the local energy density of spacetime).
That represents at least a rotation of the system frame out of the
laboratory frame of the observer.
So the standard statement in
all the EM textbooks that the symmetrically regauged Maxwell-Heaviside
equations describe exactly the same system as the unregauged equations
described, is quite a non sequitur. It's like saying that a system
operating between two elephants pushing against it in opposite
directions, is identically the same system without the elephants.
Anyway, that little trick
--- the Lorenz/Lorentz symmetrical regauging -- ARBITRARILY discarded
the entire permissible class of EM systems that are far from equilibrium
in their active exchange with (1) the local vacuum, and (2) the local
curvatures of spacetime (every energy density change in the system
produces a curvature of local spacetime, negating the Lorentz regauging
assumption of a flat local spacetime.
So electrical engineers do
not perform a thorough analysis on their power systems at all. To do
that, one has to analyze the supersystem, consisting of (1) the
physical system and its dynamics (normal sense), (2) the active vacuum
and its dynamics, and (3) the local curvatures of spacetime and their
dynamics. All three components of the supersystem interact with each
other, so it's highly nonlinear.
To do such an analysis, one
has to discard the standard U(1) classical EM model used by electrical
engineers, and utilize an EM model in a higher group symmetry algebra.
O(3) EM advanced by Evans and Vigier is really good, as are
quaternions. To see what Tesla's patented circuits are doing, one has
to analyze them in such a higher group symmetry electrodynamics. The
novel actions do not even show to a tensor analysis (as shown by
Barrett).
Tesla was unique in his
approach to electrodynamics. He was a tireless and highly innovative
experimenter, and thought in terms of material fluid theory as did just
about everyone else (Maxwell's theory is indeed a material fluid
dynamics theory, and still assumes a material ether in its equations
which were never changed after the destruction of the material
luminiferous ether by the Michelson-Morley experiments.). But Tesla had
a photographic mind, and also incredible powers of visualization (as he
wrote, until he was 12 he visualized things in his mind so vividly that
he could not differentiate between physical objects observed and his own
thought images. He had to find a "trick" that allowed him to tell the
difference).
So he used simple algebra,
but also used what we can only call "super simulation" in his own head.
It's as if he had a great simulation program going on continually in his
head, in a very large supercomputer. So he would do an experiment 100
times in excruciating detail in his mind/vision/simulator, and adjust
the variables and components used in his mind-simulation until he
obtained the results he sought.
So this was the real secret
of Tesla's great discoveries. He did so many experiments, and fitted
his mind-simulation so accurately, that he was the equivalent of a group
of researchers using modern highly sophisticated computer simulation
tools.
And quite a bit of what he
"saw" is still outside electrodynamics. But he saw it the way nature
did it, because he fitted that simulation to thousands of experiments.
He was correct that there was no transverse EM wave in vacuum, but it
will take probably another two centuries before the scientific community
will give up their love of substituting the effect for cause (something
absolutely rampant in physics, from mechanics to electrodynamics to
particle physics). Our instruments measure a transverse EM wave in a
receiving antenna, sure, but they are actually measuring the electron
precession waves (accounting for the fact that electrons move
longitudinally down a wire with great difficulty, with only the Drude
drift velocity of, say, a few inches per hour). Instead, since an
electron in the Drude gas is spinning in its 3-d aspects and thus acts
partly as a gyro due to the longitudinal constraints, the electron
precesses laterally in the wire. The old guys thought that a "shaking"
material ether had entered the wire and "perturbed" or entrained the
"material electric fluid", so that the shaking of the material electric
fluid in the wire was exactly the same as the shaking of the material
ether fluid outside the wire. (the electron and atom and nucleus had
not been discovered, there was no particle physics to speak of, no
special or general relativity, no quantum mechanics, and no quantum
electrodynamics --- and in fact, no Drude gas theory as yet).
And that, together with
Faraday's notion that his field lines were physical, like taut strings
in space, meant that perturbation of the "field lines" in space gave a
set of "plucked string" or transverse wave oscillations. And that
seemed to them to be completely consistent with what they measured in
their circuits! They never even thought to differentiate electron
precession waves from longitudinal forces pressing on the gyroscopic
electrons --- because there were no electrons (as far as anyone knew at
the time).
So the foundations of
classical EM are very old (at least 137 years or more) and have not been
updated to reflect lots of physics discovered since Faraday's
researchers and Maxwell's 1865 paper (and the various truncations of
that theory).
Anyway, that's my take on
all of it.
Best wishes,
Tom Bearden
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