THE BOHREN EXPERIMENT II
(John D. Kraus, Electromagnetics, Fourth Edn., McGraw-Hill, New York, 1992)
"A drawing of the huge Poynting energy flow filling all space around the conductors, with almost all of it not intercepted.
From the beginning, Poynting only considered that component of the energy flow that actually enters the circuit. He considered only the "boundary layer" right on the conductor surfaces, so to speak. Heaviside considered that component that enters the circuit, and also uncovered and recognized the gigantic component in the surrounding space that does not enter the circuit but misses it entirely.
Heaviside had absolutely no explanation for the enormous and startling magnitude of this energy flow that "misses the surface charges of the conductors and is wasted". One can see an elementary illustration of the "point intensity" of this Poynting diverged energy flow component.
Most of that available energy flow is not intercepted and thus not diverged into the circuit to power it. The remaining huge component discovered by Heaviside is not shown on Kraus's diagram.
Each of Kraus' contours of energy flow in space, around those power line conductors, shows only that part of the energy flow in space that is being drawn into the circuit. It does not show the remaining huge energy flow that (i) is not intercepted, (ii) does not enter the circuit, and (iii) is wasted. Presently no texts illustrate this Heaviside nondiverged energy flow component.
In the 1880s, Poynting and Heaviside independently (and rather simultaneously) discovered EM energy flow through space.
J. H. Poynting, "On the transfer of energy in the electromagnetic field."
Phil. Trans. Roy. Soc. Lond. A, Vol. 175, 1884, p. 343-361
O. Heaviside, "Electromagnetic Induction and Its Propagation," The Electrician, 1885, 1886, 1887, and later. A series of 47 sections, published section by section in numerous issues of The Electrician during 1885, 1886, and 1887
With respect to circuits, from the beginning Poynting assumed only that small amount of
EM energy flow that enters the circuit. Here are Poynting's {28} own words:
“This paper describes a hypothesis as to the connexion between current in
conductors and the transfer of electric and magnetic inductions in the
surrounding field. The hypothesis is suggested by the mode of transfer of
energy in the electromagnetic field, resulting from Maxwell’s equations
investigated in a former paper (“Phil. Trans.,” vol. 175, pp. 343-361,
1884). It was there shown that according to Maxwell’s electromagnetic
theory the energy which is dissipated in the circuit is transferred through
the medium, always moving perpendicularly to the plane containing the
lines of electric and magnetic intensity, and that it comes into the
conductor from the surrounding insulator, not flowing along the wire.”J. H. Poynting, “On the connexion between electric current and the electric and magnetic inductions in the surrounding field,” Proc. Roy. Soc. Lond., Vol. 38, 1984-85, p. 168
As can be seen, Poynting considered only the energy flow actually entering the wire, and
subsequently being dissipated in the circuit. Poynting also got the direction of the flow
wrong, later to be corrected. Hence Poynting never considered the huge EM energy flow component around the circuit that is not diverged, misses the circuit entirely, does not contribute to the energy dissipated by the circuit.
Heaviside's theory was an extension of what Poynting had considered, and he also
corrected Poynting as to the direction of flow. Heaviside was fully aware of the enormity
of the "dark energy" flow missed by Poynting, but had absolutely no explanation as to
where such a startlingly large EM energy flow—pouring from the terminals of every
dipole, generator, or battery—could possibly be coming from. Consequently he was very
cautious in referring to it, usually doing so only obliquely in terms of the angles and
components. In Heaviside's own words:
“It [the energy transfer flow] takes place, in the vicinity of the wire, very
nearly parallel to it, with a slight slope towards the wire… . Prof.
Poynting, on the other hand, holds a different view, representing the
transfer as nearly perpendicular to a wire, i.e., with a slight departure
from the vertical. This difference of a quadrant can, I think, only arise
from what seems to be a misconception on his part as to the nature of the
electric field in the vicinity of a wire supporting electric current. The lines
of electric force are nearly perpendicular to the wire. The departure from
perpendicularity is usually so small that I have sometimes spoken of them
as being perpendicular to it, as they practically are, before I recognized
the great physical importance of the slight departure. It causes the
convergence of energy into the wire.”O. Heaviside, Electrical Papers, Vol. 2, 1887, p. 94
As can be seen, Heaviside was fully aware that the energy flow diverged into the wire
was only a minuscule fraction of the total. And he was fully aware that the remaining
component was so huge that the energy flow vector remaining—after the divergence of
the Poynting component into the circuit—was still almost parallel to the conductors.
However, he had no explanation at all of where such an enormous and baffling energy
flow could possibly originate.
Had Heaviside strongly stated the enormity of the nondiverged component of the energy
flow, he would have been viciously attacked and scientifically discredited as a perpetual
motion advocate. So his words were measured and cautious, but there is no doubt that he
recognized the enormity of the nondiverged EM energy flow component.
Lorentz Disposed of the Problem Rather than Solving It
Lorentz entered the EM energy flow scene to face the terrible problem so quietly raised
by Heaviside. Lorentz understood the presence of the Poynting component, and also of the Heaviside component, but could find no explanation for the startling, enormous magnitude of the EM energy pouring out of the terminals of the power source (pouring from the source dipole) if the Heaviside component was accounted. Had he developed and retained this enormous dark energy flow component, even the Lorentz would have been castigated as a perpetual motion advocate.
Unable to solve the dark energy flow problem by any rational means, Lorentz found a
clever way to avoid it. He reasoned that the nondiverged Heaviside component was
"physically insignificant" (his term) because it did not even enter the circuit. Since it did
nothing, he reasoned that it could just be discarded.
So Lorentz simply integrated the entire energy flow vector (the vector representing
the sum of both the Heaviside nondiverged component and the Poynting diverged
component) around an assumed closed surface enclosing any volume of interest. A priori
this mathematical procedure discards the dark Heaviside energy flow component because
of its nondivergence. It retains only the intercepted Poynting diverged component that
enters the circuit.
A century later, electrodynamicists are still happily avoiding the dark energy flow
problem by continuing to use the Lorentz integration procedure to dispose of all but
the Poynting component that enters the circuit and is then dissipated by the circuit. As a
result, the "Poynting energy flow" has come to be loosely regarded as "the" entire EM
energy flow, though electrodynamicists find it necessary to give stringent warnings about
it. E.g., Panofsky and Phillips state it this way:
"…only the entire surface integral of N [their notation for the Poynting
vector] contributes to the energy balance. Paradoxical results may be
obtained if one tries to identify the Poynting vector with the energy flow
per unit area at any point."
W. K. H. Panofsky and M. Phillips, Classical Electricity and Magnetism, Addison-Wesley, Reading, MA, 1962, 2nd edition, p. 181
Most electrodynamicists note the freedom to add a vector—few call it an energy flow
vector, though that is the type of vector being discussed, and one must add apples to
apples—which has zero divergence. Jones states:
"It is possible to introduce the Poynting vector
S, defined by
S = E×H,
and regard it as the intensity of energy flow at a point. This procedure is
open to criticism since we could add to
S any vector whose divergence is
zero without affecting [the basic integration procedure's result]."
D. S. Jones, The Theory of Electromagnetism, Pergamon Press, Oxford, 1964, p. 52
Jackson says it even more plainly, and also uses Lorentz's "no physical significance" argument for disposing of any energy flow vector with a zero divergence.
Quoting:
"...the Poynting vector is arbitrary to the extent that the curl of any vector
field can be added to it. Such an added term can, however, have no
physical consequences."
J. D. Jackson, Classical Electrodynamics, 2nd Edn., John Wiley & Sons, New York, 1975, p. 237
Needless to say, any energy flow vector which is the curl of a vector field will have zero
divergence, by elementary vector algebra. In short, to be pertinent at all, it must be an
energy flow vector (since energy flow is what
S = E×H is all about. Since the curl of any vector has no divergence a priori, then any energy flow vector that is a curl of a vector field will be part of the Heaviside dark energy flow component, rather than part of the Poynting energy flow component. It will also be discarded by Lorentz's closed surface
integration.
Jackson errs in assuming such a divergence free vector (energy flow) can have no
physical consequences. That is true so long as one does not intercept and diverge—and
utilize—some of the otherwise nondiverged energy flow. If one inserts intercepting
charges into that nondiverged energy flow component, the charges will immediately
diverge some of the formerly nondiverged energy flow around them and hence "collect
additional energy". "
[The Lorentz concept of integrating the Poynting vector around a closed cylindrical surface surrounding a volumetric element. This is the procedure which arbitrarily selects only a small diverged component of the energy flow associated with a circuit—specifically, the small Poynting component being diverged into the circuit to power it—and then treats that tiny component as the "entire" energy flow. Thereby Lorentz arbitrarily discarded all the extra huge Heaviside curled energy transport component which is usually not diverged into the circuit conductors at all, does not interact with anything locally, and is not used.]
"The total energy flow in space surrounding the conductors has two components as follows:
1) A tiny Poynting component of the energy flow directly along the surface of the
conductors strikes the surface charges and is diverged (deviated) into the conductors to power the circuit.
2) The huge nondiverted Heaviside component filling all space around the circuit, misses the circuit entirely.
The Heaviside nondiverged energy flow component was arbitrarily discarded by H.A. Lorentz, who integrated the energy flow vector itself around a closed surface enclosing any volumetric element of interest. This discards any nondiverted (nondiverged) energy flow components, regardless of how large, and retains only the diverted (diverged) component, regardless of how small.
Effectively Lorentz arbitrarily changed the energy flow vector into its diverted flow component vector—a fundamental non sequitur. In one stroke he discarded the bothersome Heaviside component, reasoning that it was "physically insignificant" because—in single pass circuits—it does not enter the circuit and power it.
This is rather like arguing that all the wind on the ocean that does not strike the sails of a
single sailboat, is "physically insignificant." A moment's reflection shows that the "insignificant" remaining wind can power a large number of additional sailing vessels. A very large amount of energy can be extracted and used to do work, if that "physically insignificant" wind is intercepted by additional sails.
Suppose Lorentz had not arbitrarily discarded the huge Heaviside energy flow component
surrounding the circuit and not contributing to its power. In that case, electrodynamicists in the 1880s would have been confronted with the dilemma of explaining where such an enormous flow of energy—pouring forth out of the terminals of every generator and battery—could possibly have come from.
To avoid strong attack and suppression from the scientific community on grounds of
advocating perpetual motion and violation of energy conservation, in the 1880s there was no other choice but to discard the Heaviside component on some pretext. So Lorentz simply discarded the vexing component. He could not solve the problem so he got rid of it.
Lorentz further reduced the already seriously reduced symmetrized Heaviside equations, in order to specifically eliminate the newly discovered giant Heaviside curled EM energy flow that – unknown to our present electrical engineers – accompanies every Poynting energy flow component (which is diverged into the circuit to power it), but is itself (the curled component) not diverged and thus is just wasted because it normally does not interact.
Lorentz altered the actually-used energy flow vector by throwing away that giant Heaviside component quite arbitrarily. Thus the Heaviside giant curled EM energy flow component is no longer accounted or even recognized in electrical engineering, but it still physically accompanies every accounted Poynting energy flow component in every EM system or circuit.
Heaviside and Poynting independently discovered EM energy flow theory. Poynting conceived only that small component of the energy flow which enters the conductors. On the other hand, Heaviside recognized that all space around the circuit's conductors was filled with EM energy flow. A small "boundary layer sheath" component of this energy flowing outside the circuit moves right along the surface of the wires, where it strikes the surface charges and is diverged into the circuit. This small Poynting energy flow component enters the circuit and provides the energy subsequently dissipated in the circuit's loads and losses.
However, the "sheath layer" Poynting component is only a tiny fraction of the truly enormous energy flow pouring out of the generator or battery terminals and flowing through surrounding space, with most of it missing the circuit entirely.
Lorentz considered this huge nondiverged Heaviside flow component "physically insignificant" (his term) and logically felt free to neglect it because it did not enter the circuit and did not contribute to powering the loads and losses. However, in aether theory any change in spatial energy density represents a curvature of the aether (potentials/Whittaker longitudinal waves), hence produces gravitational effects.
Bohren's experiment collects 18 times more energy from the usually nondiverged Heaviside component, just by resonating the charge and thereby sweeping out a greater geometrical reaction cross section than the static charge that is used to calculate the Poynting flow component. It follows that "the" field and "the" potential input to the intercepting charge have far more energy "in the vicinity of" an interacting point static charge and of a unit dipole than what is accounted for in the conventional EM model where the magnitudes of the fields and potentials are erroneously taken as being the magnitudes of the energy diverted from them by a unit point static charge. This enormous extra energy, however, does not participate in the interaction and is the "dark energy" component recognized by Heaviside and then erroneously discarded by Lorentz."
" Heaviside himself recognized the gravitational implications of his extra component of energy flow, which is in closed circular loops. Beneath the floorboards of his little garret apartment, years after his death, handwritten papers were found where Heaviside used this component for a unified EM approach to gravitation.
See E. R. Laithwaite, “Oliver Heaviside – establishment shaker,” Electrical Review,
211(16), Nov. 12, 1982, p. 44-45.
Laithwaite felt that Heaviside’s postulation that a flux of gravitational energy combines with the (
ExH) electromagnetic energy flux, could shake the foundations of physics.
Quoting from Laithwaite: “Heaviside had originally written the energy flow as
S = (
ExH) +
G, where
G is a circuital flux. Poynting had only written
S = (
ExH). Taking p to be the density of matter and
e the intensity of a gravitational force, Heaviside found that the circuital flux G can be expressed as p
u + c
e, where
u represents the velocity of p and c is a constant.”
To prove the existence of the Heaviside flow, Bohren performed the experiment where the intercepting charges in the circuit are in resonance, and thus "sweep out" a larger geometrical cross section of interception of the impinging energy flow. These charges do sweep beyond the static unit charge cross section conventionally assumed in the definitions of field intensity (e.g., of the fields E and H in the Poynting vector S in S = (E x H). If the defining unit point charges are in resonance and sweep out a greater cross section, then the assumed Poynting vector S, for the static case, changes in magnitude by some ratio k for the resonant case to the vector S
R, so now S
R = k
1E x k
2H = k
3(E x H). Since k
3 is just the ratio of the actual geometrical cross section swept out by the charge to the standard geometrical cross section swept out by the static charge, then for a static charge k
3 = 1.0, and for a resonant charge k
3 >1.0. Hence the Bohren experiment, with k
3 = 18 or so, produces 18 times as much collected (Poynting) energy "out" as we erroneously think we input by normal calculations ignoring the input Heaviside nondiverged component."