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The Gyroscopic Theory of Electromagnetic Radiation
Frederick David Tombe,
Northern Ireland, United Kingdom,
sirius184@hotmail.com
21st July 2024
Abstract. In 1873, Scottish physicist James Clerk Maxwell proposed the plane wave
theory of electromagnetic radiation, whereby mutually perpendicular oscillating electric
and magnetic fields propagate at the speed of light, in phase with each other and
perpendicular to the propagation direction. Meanwhile, since Maxwell’s curl equations
imply that the electric and magnetic fields in an electromagnetic wave are actually out
of phase by ninety degrees, this discrepancy will now be investigated.
Transverse Elasticity and Displacement Current
Fig. 66/67 from Maxwell’s 1873 Treatise. For magnified version, see page 7.
I. Regarding the well-known illustration of an electromagnetic wave as two
mutually perpendicular sine waves in the electric, E, and magnetic, B, fields,
and both mutually perpendicular to the propagation direction, it is generally
assumed that James Clerk Maxwell derived this idea from his electromagnetic
theory of light. Well, the picture does indeed follow from the sinusoidal
solutions to the electromagnetic wave equations that were derived by Maxwell,
but that doesn’t mean that the sinusoidal solutions themselves represent the full
picture. If we simply assume the diagram, Fig. 66/67 above, as being the full
picture, then the sinusoidal solutions do follow, and vice-versa, but to do so
leads to a discrepancy with respect to the curl equations with which Maxwell
derived the electromagnetic wave equations in the first place. These curl
equations, when analysed directly, tell us that E and B are actually out of phase
in time and space by ninety degrees, when in an oscillating context.
In Parts I and II of his 1861 paper, “On Physical Lines of Force”, [1],
Maxwell physically constructed the magnetic field from a sea of tiny aethereal
vortices, and from this context he then explained both magnetic force and
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electromagnetic induction. Meanwhile, in Part III of this same paper, Maxwell’s
sea of vortices morphed into a dielectric sea and he linked the dielectric
constant to the transverse elasticity. After applying this linkage to Newton’s
equation for the speed of a wave in an elastic solid, he numerically linked this
speed to the ratio between electromagnetic units and electrostatic units.
Meanwhile this speed had been identified with the speed of light in 1857 by
Gustav Kirchhoff, [2], while Kirchhoff in turn was basing this observation on the
results of the famous experiment carried out in 1855 by Weber and Kohlrausch,
in which they discharged a Leyden jar to Earth through a conducting wire, [3].
It was this sequence of reasoning that led Maxwell to believe that light
waves are transverse waves in the same medium that is the cause of electric and
magnetic phenomena, and he conceived the concept of displacement current in
connection with dielectric polarization in space. Ironically therefore, Maxwell
ignored his vortex sea theory when it came to guessing the physical nature of
electromagnetic waves. Years later though, somebody else who remains
unknown invoked the involvement of vortices to explain the physical nature of
electromagnetic waves. A summary of their explanation is recorded in the 1937
Encyclopaedia Britannica article, “Ether (in physics)”. In connection with the
speed of light, the article says, [4],
Possible Structure. −, “The most probable surmise or guess at present is
that the ether is a perfectly incompressible continuous fluid, in a state of fine-
grained vortex motion, circulating with that same enormous speed. For it has
been partly, though as yet incompletely, shown that such a vortex fluid would
transmit waves of the same general nature as light waves— i.e., periodic
disturbances across the line of propagation—and would transmit them at a
rate of the same order of magnitude as the vortex or circulation speed”
While it is unlikely that this medium is actually incompressible, the wave
displacement mechanism will however be fine-grained angular in nature and
will not therefore hinge on whether the medium is compressible or not.
Time-Varying Electromagnetic Induction
II. It was in Maxwell’s 1865 paper, “A Dynamical Theory of the
Electromagnetic Field”, [5], where he actually first derived the electromagnetic
wave equation in B, by which time, but without actually highlighting the fact,
he had altered the concept of displacement current by replacing the electrostatic
E field of linear polarization with the E field that is associated with time-
varying EM induction. Meanwhile, immediately after the derivation of this
electromagnetic wave equation, Maxwell stated that the direction of
magnetization of the magnetic disturbance lies in the plane of the wave, but this
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conclusion only followed because the derivation began on that condition from
the outset.
The Plane Wave Solutions
III. In Maxwell’s 1873 Treatise, [6], in Chapter XX entitled, “Electromagnetic
Theory of Light”, Maxwell continues with his long-standing assumption that
electromagnetic waves are plane waves, with the A, B, and E, fields lying in the
plane of the wave. This is the chapter where Fig.66/67 above appears. A
particularly interesting feature in this derivation of the electromagnetic wave
equations is the way that Maxwell imposes the plane wave restriction into the
equation ∇×A = B, leading to the modified equation (13), which is the starting
equation in the analysis. But in doing so, he loses the vortex relationship that is
implied by the full equation. In the full equation, A and B are in phase, but by
applying it to the dynamic state in connection with a wave, and then restricting
the spatial differentiation to the propagation axis while ignoring all components
of A and B that are not perpendicular to the propagation axis, the remaining
perpendicular components of A and B will now be out of phase with each other
by ninety degrees in the context of a sinusoidal wave. Meanwhile the electric
force, E, in the wave, arises from time-varying EM induction, and since E =
−∂A/∂t, then in general, E and A, (and hence E and B), will be out of phase by
ninety degrees. But based on the plane wave restriction, their perpendicular
components will now be in phase with each other.
We cannot however assume that the plane wave solutions represent the full
physical picture. They ignore the involvement of vortices in the electromagnetic
wave-carrying medium.
Conclusion - The Vortex Solution
IV. It is here proposed that an electromagnetic wave is a propagated fine-
grained precession through a sea of tiny aethereal vortices, with the precession
axis being perpendicular to both B and the propagation direction. The wave
propagation mechanism is therefore independent of the already existing
orientation of the vortices within the prevailing background steady state
magnetic field alignment. Then, in order to account for the dielectric property of
this wave-carrying medium, it is proposed that the vortices are dipolar, each
containing a sink (electron) and a source (positron) in mutual orbit with each
other, and with their circumferential speeds equal to the speed of light, [7], [8].
The momentum within an electromagnetic wave is then explained by aether
(electric fluid) swirling at the speed of light from the positron of one vortex to
the electron of its immediate neighbour along the line of propagation as the
wave passes through. Electron-positron pair annihilation never actually happens
as such. When it appears to have happened, what has really occurred is that a
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liberated electron and positron have bonded back into the vortex sea while
releasing two gamma ray pulses. This released energy is analogous with the
latent heat of fusion that we observe in the case of ponderable matter, [9], [10].
Fig. 66/67 is therefore only a two-dimensional shadow, in the xy-plane, of
what is actually taking place, and indeed neither E nor B should be crossing into
the negative quadrant. The E field is in fact the propagating causal force, always
positive, and acting tangentially or axially on the vortices, hence causing a
torque. This torque propagates through the sea of vortices, causing them to
precess, and so the graph should really look like a case of full-wave
rectification, with neither a negative E nor a negative B being involved. In order
to illustrate this mechanism with reference to Fig. 66/67, consider the particular
case in which an electromagnetic ray is perpendicular to the prevailing
background magnetic field, such that B will be perpendicular to the propagation
axis when in the undisturbed state. As the wave passes through, E will force B
to tumble/precess about an axis perpendicular to the propagation direction and
to itself. As it tumbles, B will increase in magnitude, but as in the way that
rotational motion can be converted to linear simple harmonic motion in a
shadow, B will appear to reduce down to its minimum in Fig. 66/67, since the
perpendicular component of B will be vanishing. The same argument holds for
any initial orientation of B, except that the time phase of B will be different in
each case, with respect to Fig. 66/67. And note, that while E reduces to zero
during every cycle, B only reduces to a minimum steady state value.
Meanwhile, the full equation, ∇×A = B, tells us that A is a circulating
momentum and that B is a vorticity, and hence B represents fine-grained kinetic
energy. Equation ∇×A = B also tells us that A and B are in phase with each
other, and so if we fix the coordinates within the body of the vortices rather than
only considering a two-dimensional projection of the precessions, this will bring
the phase relationship, as between E and B, into line with the standard position
that a force and a kinetic energy in an oscillating system are always out of phase
with each other by ninety degrees. E and B will therefore be out of phase with
each other by ninety degrees when the full vortex picture is considered.
References
[1] Clerk-Maxwell, J., “On Physical Lines of Force”, Philosophical Magazine, vol. XXI, Fourth
Series, London, (1861)
http://vacuum-physics.com/Maxwell/maxwell_oplf.pdf
[2] Kirchhoff, G.R., “On the Motion of Electricity in Wires”, Philosophical Magazine, vol. XIII,
Fourth Series, pp. 393-412, (1857)
English translation by Professor A.K.T. Assis, vol. 3, chapter 8. See page 214 regarding the
connection between Weber’s constant and the speed of light.
https://www.ifi.unicamp.br/~assis/Weber-in-English-Vol-3.pdf
A summary by Professor A.K.T. Assis can be found on pp. 280-282 in this link,
https://www.ifi.unicamp.br/~assis/Weber-Kohlrausch(2003).pdf
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[3] Weber, W. E. and Kohlrausch, R.H.A., “Elektrodynamische Maassbestimmungen insbesondere
Zurueckfuehrung der Stroemintensitaetsmessungen auf mechanisches Maass”, Treatises of the
Royal Saxon Scientific Society, vol. V, Leipzig, S. Hirzel, (1856)
For an English translation by Professor A.K.T. Assis, see chapters 6 and 7 in this link, and especially
page 179 regarding mentions about the speed of light.
https://www.ifi.unicamp.br/~assis/Weber-in-English-Vol-3.pdf
Prof. A.K.T Assis has also written an excellent summary of this work in an article entitled “On the
First Electromagnetic Measurement of the Velocity of Light by Wilhelm Weber and Rudolf
Kohlrausch”,
https://www.ifi.unicamp.br/~assis/Weber-Kohlrausch(2003).pdf
Weber and Kohlrausch further wrote a short precis of their paper, and this can be found in
Poggendorf’s Annalen, vol. XCIX, pp. 10-25. An English translation of this precis is presented in the
appendix at the end of Prof. Assis’s paper.
See also, Tombe, F.D., “The Commonality between Light and Electric Current”, (2022)
https://www.researchgate.net/publication/364337354_The_Commonality_between_Light_and_Electri
c_Current
[4] Lodge, Sir Oliver, “Ether (in physics)”, Encyclopaedia Britannica, Fourteenth Edition, vol. 8, pp.
751-755, (1937)
See pp. 6-7 in the pdf file in the link below,
http://gsjournal.net/Science-
Journals/Historical%20PapersMechanics%20/%20Electrodynamics/Download/4105
[5] Maxwell, J.C., “A Dynamical Theory of the Electromagnetic Field”, Philos. Trans. Roy. Soc.
London 155, pp 459-512 (1865). Abstract: Proceedings of the Royal Society of London 13, pp. 531--
536 (1864). The derivation of the electromagnetic wave equation in H begins on page 497 in the first
link. Then see the note at the top of page 499 in the second link.
http://www.zpenergy.com/downloads/Maxwell_1864_4.pdf
http://www.zpenergy.com/downloads/Maxwell_1864_5.pdf
[6] Maxwell, J.C., “A Treatise on Electricity and Magnetism” Volume II, Chapter XX, ‘Plane
Waves’, Section 790, pp. 389-390 (1873)
https://en.wikisource.org/wiki/A_Treatise_on_Electricity_and_Magnetism/Part_IV/Chapter_XX
[7] Tombe, F.D., “The Double Helix Theory of the Magnetic Field”, (2006)
Galilean Electrodynamics, vol. 24, Number 2, p.34, (March/April 2013)
https://www.researchgate.net/publication/295010637_The_Double_Helix_Theory_of_the_Magnetic_
Field
[8] Tombe, F.D., “The Double Helix and the Electron-Positron Aether”, (2017 )
https://www.researchgate.net/publication/319914395_The_Double_Helix_and_the_Electron-
Positron_Aether
[9] Simhony, M., “The Electron-Positron Lattice Space, Cause of Relativity and Quantum Effects”,
Physics Section 5, The Hebrew University, Jerusalem (1990)
http://web.archive.org/web/20040606235138/www.word1.co.il/physics/mass.htm
[10] Tombe, F.D., “The Positronium Orbit in the Electron-Positron Sea”, (2020)
https://www.researchgate.net/publication/338816847_The_Positronium_Orbit_in_the_Electron-
Positron_Sea
[11] Whittaker, E.T., “A History of the Theories of Aether and Electricity”, chapter 4, pp. 100-102,
(1910)
“All space, according to the younger Bernoulli, is permeated by a fluid aether, containing an
immense number of excessively small whirlpools. The elasticity which the aether appears to
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possess, and in virtue of which it is able to transmit vibrations, is really due to the presence of these
whirlpools; for, owing to centrifugal force, each whirlpool is continually striving to dilate, and so
presses against the neighbouring whirlpools.”
Summary
In an electromagnetic wave, the electric field, E = −∂A/∂t, is the propagating
force. It acts tangentially/axially on the tiny rotating electron-positron dipoles
that fill all of space and which make up the electromagnetic wave-carrying
medium. This results in a torque which causes the vortices to precess about an
axis that is perpendicular to both the direction of propagation and to the
magnetic field, B, and as in the case of a gyroscope, the precession axis will
also be perpendicular to the torque axis.
Meanwhile, the equation ∇×A = B fits within the vortices such that A is the
circumferential momentum, while the magnetic field B is simply the vorticity. If
z is the propagation axis, we can always orientate the picture such that B will be
rotating in the yz-plane about an axis in the zx-plane. As such, it doesn’t matter
at what angle a ray of electromagnetic radiation crosses the prevailing
background magnetic field. If we take a starting point in time, then B will be
pointing in the y direction in the case of a ray that is perpendicular to the
prevailing magnetic field, and it will begin to rotate in the yz-plane at the
moment when the E force strikes. In the case of a ray that is parallel to the
background magnetic field, B will begin parallel to the z axis. This principle
then extends to all propagation angles in between the perpendicular case and the
parallel case.
As the vortices precess, electric fluid (aether) emerges from the positron
source of one vortex and swirls across and into the electron sink of its
immediate neighbour. This is the basis of the wave’s momentum which is
observed as radiation pressure. Meanwhile, the speed of this wave-like electric
fluid flow is determined by the circumferential speed of the vortices, which is
the speed of light.
In the case of the steady state background magnetic field, where the
vortices are undisturbed, no net electric fluid passes between neighbouring
vortices. The vortices must be precessing in order to facilitate a net fluid
exchange. In the steady state, the vortices are aligned in a double helix
arrangement such that an electrostatic tension prevails along the magnetic lines
of force. This is due to the electrostatic attraction between the electrons and
positrons, the rotating dipoles being mutually aligned along their rotation axes.
This is the basis of magnetic attraction between unlike magnetic poles.
Meanwhile a centrifugal pressure emanates in the equatorial plane of the
vortices as they strive to dilate but are all hemmed in by each other, [11]. This is
the basis of magnetic repulsion between like-magnetic poles, since in this case,
the two sets of magnetic field lines push sideways against each other.
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Fig. 66/67 from Maxwell’s 1873 Treatise
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The Steady State
The figure above portrays a single magnetic field line comprised of a double
helix of rotating electron-positron dipoles. The vertical lines marked in the
diagram represent the equatorial planes of these dipolar vortices, and due to
centrifugal force and the fact that the aether (electric fluid) can’t pass through
itself, then, when in the steady state, no electric fluid crosses between the
electrons and positrons at right angles to the field lines. In the axial direction,
however, there is a mutually cancelling bi-directional flow. A ray of light can,
however, cross such magnetic lines of force at any angle. The precession of the
vortices, when in the dynamic state, allows for the electric fluid to pass between
neighbouring vortices at any angle, irrespective of their default alignment when
in the steady state, and it is this net flow of electric fluid that constitutes
electromagnetic radiation. Electromagnetic radiation is therefore a relay of tiny
electric currents in space, and these electric currents are what gives rise to
radiation pressure.