Dear John,

Most any way that is suitable for you to get into higher symmetry electrodynamics is okay.   The higher symmetry EM will continue to interface with and turn into quaternions, which is a higher topology algebra than vectors and tensors.  Several kinds of mathematics get involved, such as spinors, twistors, Pauli algebra, etc. which have been extensively applied in particle physics.  Clifford algebra and Grassmann algebra also.

A simulation of Maxwell's original 20 equations in 20 unknowns (specifically shown in his 1865 paper) would be most interesting as I have never seen one (though such may exist).

And as you are aware, the struggle to acquire a working ability with these various math systems is a large effort in which the scientist has to make a substantial investment of his time and life.  But it then equips him (or her) to think "out of the box" of the usual U(1) electrodynamics.

In my own view, the major problem with U(1), particularly as used in electrical engineering, is that it erroneously  assumes a flat spacetime and also assumes no net interaction with the active vacuum.  Let me explain the significance of that.

First, we consider the supersystem, which consists of (1) the EM system and its dynamics (the ordinary stuff), (2) the active local vacuum and its dynamics, and (3) the active local curved spacetime and its dynamics.  All three components of the supersystem interact with each other, and that interaction is significant, a priori, in any COP>1.0 electrical power system.

We may now consider the other two components --- the active local vacuum and the active local curvatures of spacetime --- as the active environment of the system.  By assuming these two components to be either zero or with no net interaction, U(1) electrodynamics has assumed away any net effects from the active environment.  In other words, it has assumed net equilibrium, and that puts the resulting model firmly in agreement with classical equilibrium with its infamous second law.  Such a system that behaves according to that model, can never exhibit COP>1.0.  Only systems in disequilibrium with their active environment, can receive excess energy from it and thus exhibit COP>1.0.  For such systems, classical thermodynamics does not apply.  Instead, the thermodynamics of systems far from equilibrium with their active environment applies.

In short, U(1) electrodynamics inherently and arbitrarily discards all permissible COP>1.0 Maxwellian systems by discarding the other two components of the supersystem.

It follows that, to deal with the supersystem and with COP>1.0 EM devices, one must utilize a higher symmetry electrodynamics, a priori, since only such an electrodynamics will include the disequilibrium systems discarded by U(1).

The minimum necessary is to remove the Lorentz symmetrical regauging from U(1) electrodynamics, therefore converting it to a sort of U(1+), to do violence to group symmetry concepts.  That reverts back to the Maxwell-Heaviside equations, prior to symmetrizing by Lorentz.  These do not have the variable separated, so most often will require numerical methods. But at least that step can simulate and model at least the COP>1.0 disequilibrium condition.

The higher step is to change the fundamental algebra in which the physics is embedded, so that the entire model covers both "asymmetry with the environmental energy exchange" as well the usually assumed "symmetry with

the environmental energy exchange".

Even so, some of the physics ideas associated with the increased model must be changed from the old ideas.  The broken symmetry of the source dipole in its vacuum exchange, once the dipole is created, must be modeled and not assumed.  Also, if only closed current loop circuits are allowed without severe alteration of the closed loop aspect (at least momentarily for potentialization (re-gauging freely), the circuit itself guarantees self-restoring of Lorentz symmetry, continuously.  Such a self-symmetrizing circuit will continuously destroy its source dipole faster than it powers its load.

These are the fundamental requirements of overunity systems and their modeling.  They are highly nonlinear, at least in certain parts, and will most often require numerical methods and higher symmetry EM modeling.

Obviously one winds up utilizing a unified field theory, whether using it in "parts" to try to stay "electromagnetic", or whether using it deliberately, as in using the Sachs unified field theory while using O(3) electrodynamics as an important subset of the Sachs electromagnetics portion.

It is surprising that the better universities, already dealing with higher symmetry electrodynamics and general relativity in their physics and particle physics departments, do not modernize the rather hoary old Maxwell-Heaviside-Lorentz electrodynamics taught and used in their electrical engineering departments.  Particularly since, after the discovery of broken symmetry, just to view an electrical power system sitting on its pad quietly and running and delivering power, is to prove its exchange with its active environment.  It is already well-known in physics that there is no symmetry at all of a mass system and its dynamics, unless one includes the vacuum (environmental) interactions.  An observable implies asymmetry, while symmetry implies non-observable.  Hence there can only be "symmetry" in the mass system to begin with, if there is an ongoing interaction with the environment --- in this case, the other two components of the supersystem.

A simple way to say it is that no system analysis is complete until the supersystem has been analyzed.

In my view, the higher symmetry modeling is essential, and whatever point one wishes to enter that higher symmetry modeling is sufficient.  One must just be cautious about the seemingly "innocent" assumptions of symmetry without environmental exchange, which is a falsity a priori.

Very best wishes

Tom Bearden

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Sent: Wednesday, September 05, 2001 2:32 AM

To: Tom Bearden

Subject: Quaternions, Tait, Hamilton, and Maxwell

I am currently learning the calculus of Quaternions as put forth by Tait,

and an associate is studying Hamilton's lectures on the subject. We have found

the 20 Original Maxwell Equations readily available, and I plan to attempt a

numerical computer simulation based on them.

In your opinion, is this a wise start, or would my time be better spent

understanding the Maxwell 20, and moving on to the mathematics necessary to

understand Sachs' work, with the focus being on making a simulation from

those works instead? I am aware that I may be adding two more years onto the time before I can attempt a Sachs O(3) (or derivative) numerical simulator.

There may be others who are floating between the theorems and their

application, so please post your reply in the Correspondence section if you

choose.

        Thanks!

        John A.