Unless Heaviside and Lorentz did rigorous calculations in a work we have not yet uncovered, we could not find any development of the functions and equations required for computing the numerical ratio of the unaccounted Heaviside "dark energy flow" {nondiverged energy flow component that misses the circuit), to the tiny Poynting energy component thai strikes the surface charges of the conductors {211} and is diverged into the wires to power the circuit when the surface charges precess laterally into the wire.
Consequently, we performed a very crude "special case" estimation {212} — a back-of-the-envelope type, with highly simplifying assumptions — for a very simple circuit in which one resistor is powered by a DC source. Our crude estimate showed that about 1013 times as much EM energy flow misses the circuit, is not diverged, and is wasted — as strikes the circuit, gets collected, and then is dissipated in the circuit to power the load and losses. Until electrical physicists re-examine the energy flow theory and involvement of the transverse current. Quoting: "...the transverse current... extends over all space, even if J is localized. " One notes that present electrical power systems concentrate exclusively on the J current, making no attempt to collect and utilize the recognized but rather ignored transverse current.
84 Note, however, that this Heaviside energy flow component differs from ExH. The
Heaviside component is totally nondiverged (being actually in curl or swirl form), and since E and H are both diverged energy components assumed around an
Interacting unit point static charge, there is neither E nor H in the electrical engineering sense prior to interaction with charge. So the energy flow in both the Poynting and Heaviside components is in a force-field-free form until intercepted by and interacted with charge. Poynting's component, e.g., assumes only that energy component that does interact with charge and get withdrawn into the circuit. Heaviside's component assumes only that energy component that does not interact with charge and does not get withdrawn into the circuit.
again recover the Heaviside unaccounted component in it, that brute force estimate will have to suffice as at least an illustrative example.85
What does that 1013 ratio mean? For a little 1 watt generator of that DC type with that specific size conductors and that specific resistor, the Heaviside unaccounted energy flow component was about 10 trillion watts, occupying all space surrounding the wire,86 if all of it could be intercepted, collected, and used to power loads {213}. But the little circuit was only intercepting and collecting — and using to power loads — about 10-13 of the available energy flow surrounding the circuit, ifall of it could have been intercepted, collected, and used to power loads.87
We have never had, and we do not now have, an EM energy shortage or problem. We never will have one, due to nature's bounty in providing us with the giant negentropy of the common dipole and of the charge considered as a composite dipole. Instead, we have the two problems that
(i) only a tiny, tiny component of the available 3-energy flow extracted from the vacuum (decompressed from time-energy) by
85 We would very much welcome a much more accurate functional expose by a capable higher group symmetry electrodynamicist!
86 We also point out that none of this nondiverged energy flow component is accounted in conventional electrodynamics and electrical engineering (the closest it comes is Jackson's mention of the transverse current over all space), and neither has it been accounted or even investigated by biophysicists seeking to determine the effects of EM radiation and fields upon biological systems. We strongly suspect (and have done a little work on the problem) that these "force-free fields" and neglected excess "strange energy" flows do have interactions throughout the highly nonlinear cells of the body, and can indeed have profound long term effects on longexposed biological systems. We particularly stress the potential for time-charging and subsequent combined scalar and longitudinal photon pair decay of time-charge excitation in the body. Several major areas of electrodynamics — such as the transverse current effects, Heaviside component effects, and internal Whittaker structuring (engines) effects of EM radiation — have not been investigated by the scientific community.
87 We accent that time-energy may be regarded as spatial EM energy compressed by the factor c2. Hence one second = 9xl016 joules of EM spatial energy, if decompressed by time-energy interaction with charge. The crude estimate for one circuit of 1013 times as much energy being wasted in the Heaviside energy flow component as is caught and used in the Poynting component, is thus quite reasonable when one recognizes that all the EM energy flow appearing in the circuit or outside it actually comes from the time domain, hence constitutes decompressed time-energy.
the source dipole and poured out of the terminals of the power source, is caught and used by the circuit, and
(ii) in the closed current loop circuit, half of that small spatial EM energy component that is intercepted and caught, is used by the circuit only to destroy the source dipole and cut off the free flow of EM energy from the vacuum faster than it powers the load.
We have previously discussed this further in several papers {214}.
One must occasionally keep one's sense of humor. The real problem that the Department of Energy should be working on, with massive resources, is simply the alteration of the closed current loop circuit so that it does not destroy the source dipole faster than it powers the loads. Secondly, they should then be working on how to close-loop the COP>1.0 EM systems that readily emerge from that research. Yet it appears that this fundamental energy problem — and the only energy problem — has no conventional work being openly done on it anywhere in the open Western world.88
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Do we really want the one thing that gives us its resources unconditionally to suffer even more than it is suffering now? Nature, is a part of our being from the earliest human days. We respect Nature and it gives us its bounty, but in the recent past greedy money hungry corporations have made us all so destructive, so wasteful.