chaotic circuit?
It is generally realized that Maxwell’s equations are purely hydrodynamic
equations and fluid mechanics rigorously applies [5]. Anything a fluid system
can do, a Maxwellian system is permitted to do, a priori. So ‘‘electrical energy
winds’’ and ‘‘electrical windmills’’ are indeed permitted in the Maxwell–
Heaviside model, prior to Lorentz’ regauging of the equations to select only
that subset of systems that can have no net ‘‘electrical energy wind’’ from the
vacuum. Specifically, this arbitrary Lorentz symmetric regauging—while indeed
simplifying the resulting equations and making them much easier to solve—also
arbitrarily discards all Maxwellian systems not in equilibrium with their active
environment (the active vacuum). In short, it chooses only those Maxwellian
systems that never use any net ‘‘electrical energy wind from the vacuum.’’
Putting it simply, it discards that entire set of Maxwellian systems that interact
with energy winds in their surrounding active vacuum environment.
Since the present ‘‘standard’’ U(1) electrodynamics model forbids electrical
power systems with COP 1.0, my colleagues and I also studied the derivation
of that model, which is recognized to contain flaws due to its >136-year-old
basis. We particularly examined how it developed, how it was changed, and how
we came to have the Lorentz-regauged Maxwell–Heaviside equations model
ubiquitously used today, particularly with respect to the design, manufacture,
and use of electrical power systems.
The Maxwell theory is well known to be a material fluid flow theory [6],4
since the equations are hydrodynamic equations. In principle, anything that can
be done with fluid theory can be done with electrodynamics, since the fundamental
equations are the same mathematics and must describe consistent
analogous functional behavior and phenomena [5]. This means that EM systems
with ‘‘electromagnetic energy winds’’ from their active external ‘‘atmosphere’’
(the active vacuum) are in theory quite possible, analogous to a windmill in a
wind. In such a case, symmetry is broken in the exchange of energy between the
environment (the atmosphere) and the windmill. However, the present EM
models used to design and build an electrical power system do not even include
the vacuum interaction with the system, much less a broken symmetry in that
interaction.
So the major problem was that the present classical EM model excluded such
EM systems. We gradually worked out the exact reason for their arbitrary
exclusion that resulted in the present restricted EM model, where and when it
was done, and how it was done. It turned out that Ludvig Valentin Lorenz [7]
symmetrically regauged Maxwell’s equations in 1867, only two years after
Maxwell’s [8] seminal publication in 1865. So Lorenz first made arbitrary
changes that limited the model to only those Maxwellian systems in equilibrium
in their energy exchange with their external environment (specifically, in their
exchange with the active vacuum). This arbitrary curtailment is not a law of
nature and it is not the case for the Maxwell–Heaviside theory prior to Lorenz’
(and later H. A. Lorentz’) alteration of it. Thus, for electrical power systems
capable of COP 1.0, removing this symmetric regauging condition [9–14] is
required—particularly during the discharge of the system’s excess potential
energy (i.e., during discharge of the excitation) in the load.
Later H. A. Lorentz [15],5 apparently unaware of Lorenz’ 1867 work,
independently regauged the Maxwell–Heaviside equations so that they represented
a system that was in equilibrium with its active environment. This indeed
simplified the mathematics, thus minimizing numerical methods. However, it
also discarded all ‘‘electrical windmills in a free wind’’—so to speak—and left
only those electrical windmills ‘‘in a large sealed room’’ where there was never
any net free wind.
B. Implications of the Arbitrarily Curtailed Electrodynamics Model
Initially an electrical power system is asymmetrically regauged by simply
applying potential (voltage), so that the system’s potential energy is nearly
instantly changed. The well-known gauge freedom principle in gauge field
theory assures us that any system’s potential—and hence potential energy—can
be freely changed in such fashion. In principle, this excess potential energy can
then be freely discharged in loads to power them, without any further input from
the operator. In short, there is absolutely no theoretical law or law of nature that
prohibits COP1.0 electrical power systems—or else we have to abandon the
highly successful modern gauge field theory and deny the gauge freedom principle.
Although the present electrical power systems do not exhibit COP 1.0, all
of them do accomplish the initial asymmetric regauging by applying potential.
So all of them do freely regauge their potential energy, and the only thing that
the additional energy input to the shaft of a generator (or the chemical energy
available to a battery) accomplishes is the physical creation of the potentializing
entity: the source dipole [16]. [Note: The key is to apply Whittaker’s 1903
decomposition of the scalar potential existing between the poles of a dipole.
Whittaker showed that any EM scalar potential dipolarity continually receives
longitudinal EM wave energy from the time domain (complex plane) and
outputs real EM energy in 3-space. Thus the potential’s dipolarity (voltage)
placed on a circuit by a generator or battery actually represents free regauging
energy coming from the time domain of the 4-vacuum, and therefore having
nothing to do with the 3-space energy input to the shaft of the generator or with
the 3-space chemical energy available in a battery.]
It follows that something the present systems or circuits perform in their
discharge of their nearly free6 regauging energy must prevent the subsequent
simple discharge of the energy to power the loads unless further work is done on
the input section. In short, some ubiquitous feature in present systems must selfenforce
the Lorentz symmetry condition (or a version of it) whenever the system
discharges its free or nearly free excitation energy.
Lorentz’ [15] (see also footnote 5, above) curtailment of the Maxwell–
Heaviside equations greatly simplified the mathematics and eased the solution
of the resulting equations, of course. But applied to the design of circuits,
particularly during their excitation discharge, it also discarded the most
interesting and useful class of Maxwellian systems, those exhibiting COP 1.0.
Consequently, Lorentz [15] (see also footnote 5, above) unwittingly discarded
all Maxwellian systems with ‘‘net usable EM energy winds’’ during their discharge
into their loads to power them. Thus present electrical power systems—
which have all been designed in accord with the Lorentz condition—cannot
freely use the EM energy winds that arise in them by simple regauging, as a
result of some universal feature in the design of every power system that
prevents such action.
We eventually identified the ubiquitous closed current loop circuit [17]7 as
the culprit that enforces a special kind of Lorentz symmetry during discharge of the system’s excitation energy. With this circuit, the excitation-discharging
system must destroy the source of its EM energy winds as fast as it powers its
loads and losses, and thus faster than it actually powers its loads.
Also, as we stated earlier, and contrary to conventional notions, batteries and
generators do not dissipate their available internal energy (shaft energy furnished
to the generator, or chemical energy in the battery) to power their external
circuits and loads, but only to restore the separation of their internal charges,
thereby forming the source dipole connected to their terminals. Once formed,
the source dipole’s giant negentropy [16] then powers the circuit via its broken
symmetry [18,19] [see the following subsection (Section II.B.1) also].