@[[User:Leaderboard|Leaderboard]] ...
in your "Mathematical Consequences" section, you try to find .
Are A and B matrices,...?
No.
vectors, ...?
No.
...or what? You then perform cross-product on them, but isn't matrix multiplication an inner product operation? — This is not applicable since these are not matrix computations.
"A" is the real coefficient of a complex number.
"B" is the coefficient associated with the imaginary term of a complex number.
Both of these, namely: this format, could be considered equivalent to a linear polynomial of two terms: a real term and an imaginary term.
So, their ''double'' cross product is just two of the possible combinations resulting from finding: . The other two products are the squaring of the "A" term and the squaring of the "iB" term (which, in the case of electrical engineering, "i" would be replaced with the symbol of: "j").
All of this squaring business is for a purpose...
The inversion of the phase of current relative to the phase of voltage has to come from somewhere. From where does it come?
It comes from the squaring of the imaginary term of a complex number if the inlet, the input port, of a circuit's real voltage is kept extremely low. Or else, it comes from a spark gap flashing ON.
The squaring of a complex number happens during each cycle of calculations for determining the outcome of a circuit per time-frame when that circuit also contains reactive components.
Since I have discovered from six years of simulated trial and error that a reactive circuit fed a starvation diet of input voltage through a single portal of inlet – with no other chance for escape since any other outlet is not made available to this type of circuit (unless I gain the skillfulness of getting away with having additional grounded escape outlets while retaining this second requirement of restrictive throughput to disallow the formation of a normal direction for current to flow), then this type of circuit has a high likelihood of succeeding in producing a runaway condition of output surging at a rate which is faster than the thermodynamic rate of decline imposed by conventional experience.
Maybe I did not make this clear in the text? Since you asked, then I have to assume that I am not clearly stating the situation to prevent your confusion.
Also, where are you getting your theories from?
When students of electrical engineering are taught how to perform the same calculations that a simulator performs upon a "live" circuit (such as the format of equations taught at Khan Academy; I'm sure there are other locations), and when a simulator can do this for me without me having to do them, myself, then simple logic is staring me in the face that answers the timeless question, "From where does free energy come from if not from the loony bin of fantasy?"
Can you cite relevant sources that describe what you are trying to say in your book?
I remember reading (somewhere) that a voltage source is equivalent to voltage regulation; that the amplitude of a voltage input is directly related to its ability to regulate the voltages of a "live" circuit and prevent reactance from becoming a positive feedback. This positive feedback is what I design my simulated circuits to possess in which the inductive and capacitive reactances of each cycle, or half-cycle, of the circuit's oscillations become the inductances and the capacitances for each subsequent cycle, or half-cycle. This is where reactive impedance becomes our friend: under conditions of starvation (stimulating a circuit without feeding it any significant amount of power) and a restricted throughput (to discourage the formation of current) produces a backlash similar to the short-lived responses of a diode whenever voltage polarity switches and just before the diode cuts off the flow of current. This backlash is the inversion of current whose sustained consequence is the increase of voltage differences rather than their thermodynamic equalization.
This, then, is what constitutes electrical free energy if power factor conversion (of the inverted current) is taken care of (such as through a simple resistive load or a full-bridge rectification involving a square formation of diodes).
So, unless I overlooked something, I am missing two citations...
# Khan Academy
# Equating the term, of: "Voltage regulation" with the term and function of a: "voltage source".
# And a hole of knowledge never fed to budding students of electrical engineering, but can only be gained by their experience.
This third point I bank on since I am one of a kind. I have no one's quota of expectations to fulfill, but my own, which is: to make discovery and share.
[[File:Capacitors are always placed in parallel across inductive loads to save energy and stabilize its usage.png|thumb|Capacitors are always placed in parallel across inductive loads to save energy and stabilize its usage]]
Electrical engineering goes to a lot of trouble avoiding surges. They are never studied except how to subdue them as quickly as possible. They are certainly not studied for their value of renewability unless its according to prescribed plans already in use, such as: synchronous generators/motors, or a simple capacitor placed in parallel with a motor (see, screenshot, to the right).
Anyone who has studied math knows that there are infinitely various approaches to a solution of a problem. And electrical engineering is heavily engrossed in the math which models their subject.
The study of physics kills this incentive to find a solution by telling us that we can't discover anything new, or old and forgotten. But this limitation is intended for little children. It is not relevant to adults – if by adult, is to suggest someone who can think for themselves.
Conservation of energy does not pertain to reactive power since reactive power is not power; it is merely reactance. It cannot be conserved under the circumstances outlined, above, since it is not being "stored" and then "released" to, and from, inductors and capacitors. It is being "reflected" without storage and without discharge. Storage and discharge would entail a delay due to an assumption of "energy" being transmitted from one component in a circuit to every other component. This delay prevents overunity of output.
This "reflection" is what diodes do on a momentary basis. But if inductors and capacitors can be induced to do this as well, and in a sustained manner, then inductors and capacitors become analogous to the reversal of current inside of a spark gap with the added advantage of manipulating amplitude and frequency to a much better degree than the limitations of a spark gap could accomplish all alone and by itself without any assistance from inductances and capacitances outside of itself.
So, ... Is this Original Research?
You can bet that it is! Where else are you going to find this except from personal experience: yours and mine. You're not going to find this in a book or from taking a class due to it being against social protocol of a well-regulated society. Just as operating from the assumption that you have to calculate the requirements of a load and feed it that much, plus a little extra (to cover thermodynamic inefficiencies), will suppress reactive feedback, likewise do we seek an authoritative answer outside of ourselves with similar results of missing opportunities of self-discovery.
Did I miss something?
Thanks for asking. -- ~~~~