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The purpose is to show that the equation E = mc^2 was already implicit in Maxwell's 1861 paper "On Physical Lines of Force" and that it doesn't mean that mass is equivalent to energy, but rather it relates to the propagation of electromagnetic radiation through a sea of rotating electron-positron dipoles which pervades all of space.
The Positronium Orbit in the Electron-Positron Sea
Frederick David Tombe,
Northern Ireland, United Kingdom,
24th January 2020
Abstract. The purpose is to show that the equation E = mc2 was already implicit in
Maxwell’s 1861 paper “On Physical Lines of Force” and that it doesn’t mean that mass
is equivalent to energy, but rather it relates to the propagation of electromagnetic
radiation through a sea of rotating electron-positron dipoles which pervades all of
Electron-Positron Pair Annihilation
I. Unlike in the case of a Kepler planetary orbit, the positronium orbit involving
an electron and a positron, is a spiral orbit. When the two particles appear to
touch each other, they seem to metamorphose into two gamma photons. This is
much like in the case in one of Helen Bannerman’s stories for children, where a
group of tigers chase each other around a tree until they all turn into ghee,
which is then used to make pancakes. In the positronium case, the energy in the
gamma photons is said to have been supplied entirely from the mass of the
electron and the positron, and meanwhile, just like the tigers, these two particles
have ceased to exist entirely.
Alternative and more realistic explanations have been offered, akin to the
manner in which a stage magician makes a rabbit vanish from a hat, [1], [2], [3].
The rabbit never actually disappears. It still exists in a latent state close by, as
perhaps in a bag hanging under the table. It will here be proposed that the
electron and the positron do not metamorphose at all, but rather that the full
positronium orbit remains intact in a concentrated and latent state at the locality
where the two particles were believed to have mutually annihilated, and that the
orbit is now bonded into an already existing background medium comprised of
identical tiny rotating electron-positron dipoles in a totally stable state. So, in
fact, the apparently disappeared electron and positron very much continue to
exist, and in a state totally indistinguishable from their neighbouring electron-
positron dipoles in the wider electron-positron sea.
Such an approach is usually rejected quite swiftly on the back of the totally
tautological argument that such an electron-positron medium wouldn’t be stable
because positronium is unstable, and so the electrons and positrons would
annihilate each other. In other words, because the textbooks teach that electrons
and positrons annihilate each other, then there can be no possible physical
explanation for what might really be happening when a positronium orbit
appears to decay. Let’s now take a closer look at the positronium orbit.
The Positronium Orbit
II. At first there would appear to be no theoretical reason why a positronium
orbit involving an electron and a positron should be any different than a
Keplerian orbit. The electrostatic force of attraction between the two particles
obeys an inverse square law just like in the case of gravity, and so the dynamics
should be identical. The full trajectory should trace out an eccentric ellipse, and
when the electron and the positron reach closest approach, there should be a
recoil due to centrifugal force, as like in the case of a comet at perihelion.
There is however a slight difference in the manner in which the centrifugal
force arises in the positronium orbit. In a Keplerian orbit, the centrifugal force is
sourced at the interface between the two gravitational fields and is due to the
shear interaction between the two fields, [4]. This cannot be so however in the
case of the positronium orbit. Where gravitational attraction is monopolar, such
that the field lines between the two gravitating bodies spread outwards from
each other and meet laterally, enabling the centrifugal force to engage at the
interface, the attractive force in electrostatics, on the other hand, is dipolar, and
so the field lines connect directly between the two charged particles. It will now
be shown in the case of a positronium orbit, that the centrifugal force is
intertwined with the creation of a magnetic field, and that it only kicks in, in
earnest, during an abrupt fusion event, and this can only be explained if space is
already densely packed with tiny electron-positron orbitals, [2], [3]. This
background dielectric sea serves as the physical medium for the propagation of
light. The wider stability of this dielectric sea, in three dimensions, is explained
in “The Double Helix Theory of the Magnetic Field”, [2].
The electrostatic field pulls the electron and the positron together. In this
situation, we have an electric current which consists fundamentally in the pure
aethereal fluid that flows in a single direction, out from the positron and into the
electron, while the two particles move together in opposite directions to each
other. This aethereal current is represented by its momentum, A, known
variously as the electrotonic state, the electromagnetic momentum, or the
magnetic vector potential. See sections IV and V in “The Double Helix and the
Electron-Positron Aether”, [5]. This momentum is also the basis of Maxwell’s
displacement current, especially in the dynamic state when the aether flows
from an angularly accelerating (or precessing) electron-positron dipole to its
immediate neighbour, [6].
While the positronium orbit is collapsing, and hence decaying, the electron
and the positron are moving in opposite directions to each other, both radially
and transversely, while the aethereal current is flowing between them in a single
direction. This principle carries through to electric current in general, [7]. A
more fundamental aethereal undercurrent flows in one direction only through an
electrolyte, while the ions flow in both directions.
Returning again to the positronium decay, at the moment of transition into
the bound state, the mutual transverse speed between the electron and the
positron will be so high that the aethereal current flow connecting the two
particles will break. The two streams of flow will then meet laterally while
flowing in opposite directions to each other, and so they will be pushing each
other apart with centrifugal force in the equatorial plane. The excess centrifugal
pressure will then be ejected in the form of two gamma photons, leaving the
remaining centrifugal pressure within the dipole in a state of equilibrium with
the centrifugal pressure pushing in on it from the neighbouring dipoles. The
dipole will now be hemmed in, and the two branches of aethereal current within
the trapped dipole will each be spiralling, both upwards and downwards, to the
neighbouring dipoles in the axial direction. The dipole will now be bonded
within the double helix alignment of the wider background magnetic field. As
the trapped dipole rotates, the aethereal current spirals into the electron and out
of the positron with a vorticity, H, expressed in the form, ×A = μH, where, H,
is the magnetic field strength.
The Speed of Light and E = mc2
III. In Part III of Maxwell’s 1861 paper “On Physical Lines of Force” [8], he
introduces elastic displacement (and later displacement current) within the
context of a dielectric solid that pervades all of space. Maxwell applies
elasticity theory in order to link the dielectric constant with the transverse
elasticity of this solid medium. He is able to utilize the result of an experiment
performed in 1855 by German physicists Wilhelm Eduard Weber and Rudolf
Kohlrausch, [9], in order to equate the speed of light with the ratio of the
dielectric constant to the magnetic permeability, and hence also with the ratio of
the transverse elasticity to density in this luminiferous medium. Since the latter
ratio forms one side of Newton’s equation for the speed of a wave in an elastic
solid, Maxwell is able to conclude that light is a transverse wave in an elastic
solid that is also the cause of electric and magnetic phenomena. Hooke’s law
appears at equation (105) in Maxwell’s 1861 paper in the form,
R = −4πk2h (1)
where R is electromotive force, k is a coefficient depending on the nature of
the dielectric, and h is displacement. Maxwell doesn’t actually use the letter k in
his paper, but it has been chosen here in order to avoid confusion with the
normal symbol for energy which will appear later in the analysis.
The purpose now will be to show how equation (1) can be related to
Newton’s equation,
V2 = σ/ρ (2)
where V is the speed of a wave in an elastic solid, σ is the coefficient
transverse elasticity, and ρ is the density. Maxwell didn’t actually use the
symbol σ for transverse elasticity in this equation (equation (132) in his paper),
but it will be used here to avoid confusion with the usual symbol for mass
which appears later in the analysis. Maxwell equated the transverse elasticity σ
to k through equation (108) in his paper as per,
k2 = πσ (3)
and he equated density ρ to magnetic permeability µ (which he called the
coefficient of magnetic induction) through equation (133) in his paper as per,
µ = πρ (4)
Hence combining equations (2), (3), and (4), we obtain,
V2 = k2(5)
which is equation (135) in Maxwell’s paper and equivalent to E = mc2, as
will be demonstrated in the next section. Maxwell didn’t know the actual
density of his elastic solid but he was only concerned with the ratio k2, and by
comparison with the results of the 1855 experiment of Weber and Kohlrausch in
which the ratio of electrostatic units of charge to electrodynamic units of charge
had been established by the discharging of a Leyden jar (a capacitor) [7], he was
then able to establish that the dielectric coefficient k equated with the speed of
light (equation 131 in Maxwell’s paper) as measured optically by Fizeau.
The objective now will be to show how equation (5) can be derived from
the sea of tiny aethereal vortices described in Part I of Maxwell’s 1861 paper. In
this part, in order to explain the magnetic field and magnetic repulsion, Maxwell
utilizes the concept of tiny aethereal molecular vortices that press against each
other with centrifugal force while striving to dilate, [10].
The Fine-Grained Vortex Nature of the Elastic Solid
IV. It is now further proposed that Maxwell’s molecular vortices will be
dipolar, having both a sink (electron) and a source (positron) in mutual orbit
around the edge of the vortex, [2], [5], and since Maxwell has all immediately
neighbouring vortices spinning in the same direction, the effective speed for the
purposes of centrifugal potential energy will be the mutual transverse speed,
which will be twice the circumferential speed. Centrifugal potential energy is
the same thing as transverse or rotational kinetic energy, and summed over the
two particles of each dipolar vortex this will be equal to m(2V)2, or 4mV2,
where 2m is the combined mass of the two particles, and where V is their
circumferential speed. Mass is considered to be a measure of the amount of
aether. The centrifugal potential energy will be equal to the maximum linear
kinetic energy as resolved along a diameter in relation to the projected simple
harmonic motion. This in turn will be equal to the maximum potential energy
that we obtain from Hooke’s law. Since we are dealing with shared elasticity
over the two particles within each dipole, this maximum potential energy will
be 2πk2h2. Therefore,
4mV2 = k2h2 (6)
and hence,
2mV2 = πk2h2 (7)
The centrifugal potential energy, 4mV2, is the resultant of an outward
centrifugal force and an equal and opposite inward centrifugal force generated
by the neighbouring dipoles. As such, if we double the outward centrifugal
potential energy, we will split the dipole. The input energy needed to split an
electron-positron dipole is therefore 2mV2. We also know from the 1932 Carl
D. Anderson experiment that this energy is the 1.02 MeV associated with
gamma radiation, and that it corresponds exactly to 2mc2, where c is the speed
of light [1]. Hence it follows that the circumferential speed of the electrons and
positrons in the dipoles that make up of this elastic solid is equal to the speed of
light, [6], [12], and that,
c2 = k2 (8)
where μ is the areal density, 2m/πh2, of an electron-positron dipole.
Equation (8) is equivalent to equation (135) in Maxwell’s 1861 paper, and it is
more familiar nowadays in the form,
c2 = 1/με (9)
where ε is the electric permittivity and where µ is the magnetic
permeability. By multiplying the top and bottom lines of equation (9) by area,
we end up with,
E = mc2 (10)
where E is the centrifugal potential energy. It is the compressed orbit
syndrome that gets rid of the factor of one half that appears in the standard
formula for kinetic energy.
Maxwell never knew the size of his molecular vortices, but it would be
reasonable to assume that they are small enough to flow through the interstitial
spaces between the atoms and molecules of ponderable matter, as like water
flows through a basket. We could assume that the circumference of these
dipolar vortices is equal to half of the Compton wavelength for an electron,
since gamma radiation of this wavelength, or lower, can resonate with the
dipoles and split them apart, as has just been explained above. This would make
their diameter 0.3863 picometres, hence setting them at about one thousandth
the size of the average atom. The density of the vortex sea will however be
difficult to calculate because the balance between the electrostatic force in the
axial direction and the centrifugal force in the equatorial plane would point to
inter-particle spacings between neighbouring vortices on the femtometre scale.
Since this is very much less than their actual diameters, the magnetic lines of
force will in effect become tubes of force. Then on the issue of the density, as
an absolute minimum, if we were to simply consider only the diameter of the
vortices, the density of the vortex sea will already be into the region of fourteen
hundred times denser than lead, but it will surely be many orders of magnitude
yet higher than that still.
V. Contrary to popular belief, a positronium atom doesn’t decay. The deeply
ingrained belief that it decays, and that the constituent electron and positron
annihilate each other, is based purely on the fact that the actual details of what
does happen at the crucial moment are unknown. When the gamma radiation is
released, the electron and the positron continue to exist in a stable and bound
state, propped up by centrifugal potential energy (centrifugal pressure)
quantified by the equation E = mc2. Space is already densely packed with
rotating electron-positron dipoles pressing against each other with centrifugal
force while striving to dilate. The circumferential speeds equal the speed of
light, and this dielectric sea serves as the medium for the propagation of light. A
positronium atom is merely a liberated component which falls back naturally
into its bound state within this all-pervading medium.
This event happens in like manner to when an escaped vapour particle
fuses back into the main body of the liquid, releasing a latent heat of fusion.
[1] Simhony, M., “The Electron-Positron Lattice Space, Cause of Relativity and Quantum
Effects”, Physics Section 5, The Hebrew University, Jerusalem (1990)
[2] Tombe, F.D., “The Double Helix Theory of the Magnetic Field”, Section IV (2006)
Galilean Electrodynamics, Volume 24, Number 2, p.34, (March/April 2013)
[3] Tombe, F.D., “The Speed of Light”, Section 2 (2014)
[4] Tombe, F.D., Aether Friction in the Planetary Orbits, Section IV (2021)
[5] Tombe, F.D., “The Double Helix and the Electron-Positron Aether” (2017)
[6] Lodge, Sir Oliver, “Ether (in physics)”, Encyclopaedia Britannica,
Fourteenth Edition, Volume 8, Pages 751-755, (1937)
In relation to the speed of light, 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 propagationand would
transmit them at a rate of the same order of magnitude as the vortex or circulation speed”
[7] Tombe, F.D., The Absolute Direction of Alternating Current(2022)
[8] Clerk-Maxwell, J., “On Physical Lines of Force”, Philosophical Magazine, Volume
XXI, Fourth Series, London, (1861)
[9] Tombe, F.D., “The 1855 Weber-Kohlrausch Experiment” (2019)
[10] Whittaker, E.T., “A History of the Theories of Aether and Electricity”, Chapter 4,
pages 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 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.”
[11] Tombe, F.D., “Induction of Electrostatic Repulsion by Strong Gravity” (2017)
[12] O’Neill, John J., “PRODIGAL GENIUS, Biography of Nikola Tesla”, Long Island,
New York, 15th July 1944, Fourth Part, paragraph 23, quoting Tesla from his 1907 paper
“Man’s Greatest Achievement” which was published in 1930 in the Milwaukee Sentinel,
“Long ago he (mankind) recognized that all perceptible matter comes from a primary
substance, of a tenuity beyond conception and filling all space - the Akasha or luminiferous
ether - which is acted upon by the life-giving Prana or creative force, calling into existence,
in never ending cycles, all things and phenomena. The primary substance, thrown into
infinitesimal whirls of prodigious velocity, becomes gross matter; the force subsiding, the
motion ceases and matter disappears, reverting to the primary substance”.
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The Electron-Positron Lattice Space, Cause of Relativity and Quantum Effects
  • M Simhony
Simhony, M., "The Electron-Positron Lattice Space, Cause of Relativity and Quantum Effects", Physics Section 5, The Hebrew University, Jerusalem (1990)
Pythagoras's Theorem and Special Relativity
  • F D Tombe
Tombe, F.D., "Pythagoras's Theorem and Special Relativity" (2018)