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The Double Helix Theory of the Magnetic Field

Frederick David Tombe

Belfast, Northern Ireland, United Kingdom

sirius184@hotmail.com

15th February 2006, Republic of the Philippines

Abstract. The historical linkage between optics and electromagnetism can be traced

back to the year 1855, when Wilhelm Eduard Weber and Rudolf Kohlrausch, by

discharging a Leyden Jar (a capacitor), demonstrated that the ratio of the electrostatic

and electrodynamic units of charge is equal to c√2, where c is the directly measured

speed of light. Although not initially aware of the connection to the speed of light, Weber

interpreted c√2 as a kind of mutual escape velocity for two elements of electricity in

relative motion, such as would enable the induced magnetic force to overcome the

mutual electrostatic force. A few years later, James Clerk Maxwell converted this ratio

from electrodynamic units to electromagnetic units, hence exposing the speed of light

directly. On connecting Weber’s ratio to the dielectric constant in an all-pervading

elastic solid, Maxwell concluded that light consists in the transverse undulations of the

same medium that is the cause of electric and magnetic phenomena. The differing

perspectives of Weber and Maxwell can be reconciled by linking the speed of light to the

circumferential speed of the electric particles surrounding the tiny molecular vortices

that Maxwell believed to be the constituent units of the luminiferous medium. If we

consider these molecular vortices to be tiny electric current circulations, mutually

aligned along their rotation axes to form magnetic lines of force, magnetic repulsion can

then be explained in terms of centrifugal pressure acting sideways from these field lines.

And if these molecular vortices should take the more precise dipolar form of an electron

and a positron in mutual orbit, we can then further explain magnetic attraction, this

time in terms of the more fundamental electrostatic force being channeled along the

double helix of electrons and positrons that forms a magnetic line of force.

Introduction

I. A wave requires a medium of propagation, and since light exhibits wave

behavior, it is reasonable to assume that a physically real luminiferous medium

pervades all of space, and we have further reason to believe that this medium is

a dielectric. The dielectric nature of space is inferred from the electric capacitor

circuit in the dynamic state. It is unlikely that the surrounding magnetic field

will discontinue in the capacitor region while the current is flowing. When a

dielectric slab is present in the space between the capacitor plates, we

acknowledge the existence of a polarization current, and there is no reason to

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assume that the situation would be any different when the dielectric slab is not

present. Perhaps more contentiously, the idea that space is dielectric might also

be inferred from Kepler’s second law of planetary motion. This law, which is

essentially the law of conservation of angular momentum, can be used to show

that centrifugal force is an outward radial pressure that obeys the inverse cube

law in distance. Whereby the inverse square law of gravity indicates a

monopole field, the inverse cube law suggests that space contains an electric

dipole field as well.

The Aether (The Electric Fluid)

II. E.T. Whittaker wrote,

“ - - - All space, according to the young [John] 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 - - -”, [1].

John Bernoulli was working on the refraction of light. In 1861, James Clerk

Maxwell attempted to explain the magnetic field in terms of a sea of such

excessively small whirlpools. In his paper “On Physical Lines of Force”, [2], he

used such a concept to explain magnetism on the basis that these vortices are

aligned solenoidally with their rotation axes tracing out magnetic lines of force.

He explained magnetic attraction between unlike poles in terms of a tension

existing along the lines of force that connect directly between the two poles. In

the case of magnetic repulsion, magnetic field lines spread laterally outwards in

the space between two like poles. Maxwell explained the repulsion as being due

to centrifugal pressure existing in the equatorial plane of the vortices, hence

causing a lateral pressure between immediately neighbouring lines of force.

Maxwell’s model can be better understood if we replace his molecular vortices

with rotating electron-positron dipoles, each of which consists of an electron in

a mutual circular orbit with a positron, [3], [4]. Such a vortex will then double for

an electric dipole and a magnetic dipole.

Aether, alternatively known as electric fluid or free electricity, is the stuff

of all matter. Electrons will be considered to be sinks in the aether. Aether is

pulled into these electron sinks, hence causing a tension which will cause a ‘pull

force’ to act on other particles. A positron is an aether source from which a

pressurized fountain of aether emerges. The aether is dynamical, compressible,

stretchable, and it gives fluids their characteristics. There will be a vector A

equal to ρv, where ρ is the density of the aether, and v is the velocity of an

element of the aether, and the question of what this velocity is measured relative

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to will be discussed further down. Modern textbooks refer to A as the ‘magnetic

vector potential’, but it more accurately constitutes a momentum density. The

vector A can represent both gravity and electric current. Conduction current is

however, commonly denoted by the symbol J, whereas A tends to be reserved

for the circulating current in a tiny molecular vortex. Maxwell identified the

quantity A with Faraday’s electrotonic state. If we keep the aether density

constant in time, we can expand the force expression F = dA/dt to obtain,

F = ∂A/∂t − v×B + (A∙v) (1)

where B = ×A. See Appendix A. Equation (1) is recognizable as the

‘Lorentz force’, but the terms in the Lorentz force appeared in Eqs. (5) and (77)

of Maxwell’s 1861 paper, which was written when Lorentz was only eight years

old. It would be more accurately called the ‘Maxwell Force’. Taking the curl of

Equation (1) we obtain,

×F = ∂B/∂t + (v∙)B = dB/dt (2)

which is a total time derivative expansion of Eq. (54) in Maxwell’s 1861

paper. See Appendix B. Oliver Heaviside always referred to Maxwell’s Eq.

(54) as Faraday’s law, even though it is not strictly speaking Faraday’s law as

such. Maxwell’s Eq. (54) is similar to Faraday’s law, but it doesn’t account for

convectively induced electromotive force.

The first term on the right-hand side of equation (1) represents the force due

to tension or pressure in the aether. Around a sink or a source, this tension or

pressure can be split into a radial (irrotational) component and a transverse

(angular) component. The irrotational radial component can be represented in

the form Ψ, where Ψ is a scalar potential function. The second and third terms

on the right-hand side of equation (1) are convective terms representing the

fundamental hydrodynamical basis that underlies the inertial forces, but it’s not

until we have established the physical context that is the cause of the uniform

straight-line inertial path, that we can better understand the individual

manifestations of the inertial forces, such as the Coriolis force, the centrifugal

force, and the magnetic force, F = qv×B.

Maxwell’s sea of molecular vortices provides this necessary context as well

as providing the reference frame relative to which velocity, v, is measured. In a

sea of molecular vortices, these convective forces can manifest themselves in

several fashions. The transverse Coriolis force arises in cyclones and in non-

circular planetary orbits in conjunction with the conservation of angular

momentum. We also witness a Coriolis force in a rotating rigid body when it is

forced to precess. This induced Coriolis force can prevent a pivoted gyroscope

from toppling under gravity. Meanwhile centrifugal pressure in the electron-

positron sea at the interface between two gravitational fields keeps the planets

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from falling into the Sun. In the case of a rattleback (Celtic stone) being rotated

on an asymmetrical axis, centrifugal force acting on the individual elements

causes the rotation axis to realign. This can completely reverse the direction of

rotation, [5]. The convective forces are also responsible for the magnetic force

that is induced on a current carrying wire in a magnetic field, and also for the

induced electromotive force inside a wire that is moving at right angles through

a magnetic field.

The Double Helix Alignment

III. It is proposed that the default alignment in a sea of rotating electron-

positron dipoles is the most fundamental manifestation of both the Coriolis

force and Ampère’s Circuital Law. In the steady state, the electron-positron

dipoles will all be rotating in the same direction as their immediate neighbours

and they will be aligned in a double helix fashion, with their rotation axes

tracing out magnetic lines of force. An electrostatic tension will exist along

these lines of force because the electrons and the positrons will be alternately

stacked. See Fig. 1 below,

Fig. 1. A single magnetic tube of force. The electrons are shown in red, and the positrons are shown in

black. The double helix is rotating about its axis with a circumferential speed equal to the speed of light,

and the rotation axis represents the magnetic field vector H.

The electrostatic tension in the lines of force is the cause of magnetic attraction

between unlike magnetic poles. The double helix lines of force will behave like

helical springs and pull the two unlike poles together. There is an element of

flexibility as regards the magnitude of the tension in the lines of force, in that

the helix angle can vary. In the equilibrium state, the tension along the lines of

force will be counterbalanced by a centrifugal aether pressure in the equatorial

plane between adjacent dipoles. This centrifugal pressure acts laterally from the

lines of force, and it is the cause of magnetic repulsion between like magnetic

poles.

The electron-positron sea will be referred to as ‘The Electric Sea’, in order

to distinguish it from the pure aether itself.

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The Speed of Light

IV. Referring to Part III in Maxwell’s 1861 paper, which is the elasticity and

electrostatics part, we will initially stick with Maxwell’s system of units and

symbols for ease of reference. Hooke’s law appears at Eq. (105) in the form,

R = − 4πE²h (Electric Displacement Equation) (3)

where R is electromotive force, E is the dielectric constant, and h is

displacement. This equation will now be extrapolated to the context of a

rotating electron-positron dipole of radius h, that is bonded into the greater sea

of such dipoles. These dipoles will be pressing against each other with

centrifugal force in their equatorial planes, while striving to dilate. This

centrifugal pressure between neighbouring dipoles will be the source of the

equatorial elasticity, and since the dipoles are all 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 kinetic energy, and

summed over the two particles of the dipole 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. This 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 the dipole, this maximum potential energy will be

2πE²h². Therefore,

4mv² = 2πE²h² (4)

and hence,

2mv² = πE²h² (5)

The centrifugal potential energy, 4mv², is the consequence 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

force, 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 a gamma

ray photon, and that this corresponds exactly to 2mc², where c is the speed of

light, [6]. Hence it follows that the circumferential speed of the electrons and

positrons in the dipoles of the electric sea is equal to the speed of light, [4], [6],

and that,

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c² = E²/μ (6)

where μ is the areal density, 2m/πh², of an electron-positron dipole.

Equation (6) is equivalent to the Eq. (135) in Maxwell’s 1861 paper, which he

derived from Newton’s equation for the speed of sound as it appears at Eq.

(132), and which is more familiar nowadays in the form,

c² = 1/με (7)

where ε is the electric permittivity and where µ is the magnetic

permeability. By multiplying the top and bottom lines of equation (7) by area,

we end up with,

E = mc² (8)

where E is the centrifugal potential energy, not to be confused with the

dielectric constant, E, above, or with the electric field, E, further below.

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.

Electromagnetic Radiation and Displacement Current

V. Maxwell first introduced displacement current in the preamble to Part III of

his 1861/2 paper “On Physical Lines of Force”, [2]. Converting to SI units and

using modern vector notation, the electric displacement vector, D, was

introduced through the electric elasticity equation, D = εE, where ε is the

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electric permittivity, inversely related to the dielectric constant, while E is the

electromotive force. It was introduced in connection with the displacement of

electric particles in the luminiferous medium, with the associated displacement

current, ∂D/∂t, therefore being equal to ε∂E/∂t.

Returning for a moment to Part I of the same paper, Maxwell identified the

circumferential velocity of his tiny molecular vortices, with the magnetic

intensity which we would normally write as H. Maxwell’s concept of magnetic

intensity is therefore such that it is a measure of vorticity. See Appendix C. In

Part III, Maxwell continues this theme by initially considering the displacement

mechanism to be a rotatory effect. But as the analysis progresses, it all starts to

get more like simple linear polarization, and in the years that followed Maxwell,

displacement current became closely associated with capacitors. This was

unfortunate since wireless electromagnetic waves are not an electrostatic effect.

EM radiation is tied up with time-varying electromagnetic induction. While

Ampère’s Circuital Law, in connection with Maxwell’s displacement current,

takes the form,

×B = µε∂E/∂t (9)

it is essential for the purpose of deriving the electromagnetic wave

equations, that the electromotive force, E, satisfies the Maxwell-Faraday law of

electromagnetic induction,

×E = −∂B/∂t (10)

as opposed to Coulomb’s law of electrostatics, so that E = −∂A/∂t, where

∇×A = B. The perfect physical context for these equations lies in the domain of

a rotating electron-positron dipole, because such a dipole constitutes a closed

electric current circulation. We need space to be densely filled with these

dipoles, in order to serve as relay circuits in the time-varying electromagnetic

induction process. The vector field, A, represents the circumferential

momentum, B represents the vorticity, while E represents a circumferential

force that causes a torque. As per Faraday’s Law, the circulation momentum, A,

will accelerate when it is exposed to a changing magnetic field emanating from

a neighbouring dipole, in other words when exposed to the changing vorticity of

a neighbouring vortex that is angularly accelerating (or precessing). When this

happens, excess aether swirls across from the angularly accelerating vortex to

its neighbour.

The displacement, D, as Maxwell initially suspected, is an angular

displacement, while displacement current itself corresponds to the

electromagnetic momentum, A, particularly in the dynamic state.

Electromagnetic waves are a propagation of fine-grained angular acceleration

(or precession) through the electric sea of tiny aethereal vortices, [7], [8], and the

undulations are accompanied by a net flow of pressurized electric fluid (aether).

8

The propagating pressurized aether emerges from the positron of a vortex,

overflows into its neighbour and sinks into its neighbour’s electron. This causes

a torque which causes the cycle to repeat with respect to the next vortex in the

line. This net flow of pressurized aether gives rise to radiation pressure.

Radiation Pressure

VI. Light exerts a force on a physical target. Maxwell calculated the force

associated with radiation pressure to be,

F = dp/dt = (1/c)dE/dt (11)

where E is energy, c is the speed of light, and p is momentum. By

substituting

p = mc (12)

into equation (11), where m equals aethereal mass, we obtain the

relationship,

c²dm = dE (13)

which implies that electromagnetic radiation is a net flow of aethereal mass

which is related to energy by the equation,

E = mc² (14)

But just because equation (14) relates numerical values, it certainly doesn’t

mean that mass and energy are equivalent, as is nowadays wrongly claimed to

be the meaning of this famous equation. The speed of light is the ‘Mach

number’ for the electric sea by analogy to the speed of sound in air, and it is

only in connection with electromagnetic radiation in the electric sea that this

equation possesses any physical significance. Gilbert Lewis published this

approach to the equation E = mc² in 1908, [9].

The Inertial Forces

VII. Contrary to what it says in modern textbooks, the inertial forces are not

caused by making observations from a rotating frame of reference. They are a

consequence of Newton’s first law of motion, and they are described in an

inertial frame of reference in polar coordinates relative to any arbitrarily chosen

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polar origin, this origin usually being the centre of rotation of the system under

investigation, [5]. The inertial forces, just like the convective electromagnetic

force, F = qv×B, are caused by the physical interaction of a moving object

through the electric sea. The inertial forces differ from this magnetic force only

in the manner of the physical interaction, but the general underlying principles

are the same. The electron-positron dipoles that fill all of space press laterally

with centrifugal force against all moving objects. In the case of a charged

particle moving at right angles to the lines of force in a solenoidal magnetic

field, the centrifugal force acting at right angles to the direction of motion will

act differentially on either side of the motion owing to the fact that all the

dipoles are spinning in the same direction. The result is that the moving particle

experiences a force, F = qv×B, which deflects it at right angles to its direction

of motion. B is magnetic flux density, and since B = µH, and since H = 2ω,

where ω is the angular speed of the tiny dipoles, we can write the magnetic

force in the form, E = 2µv×ω, where the magnetic permeability µ represents a

density, hence exposing the magnetic force to be a close cousin of the Coriolis

force. However, when acting directly between two neighbouring vortices, the

magnetic force manifests itself as a plain centrifugal force, in the same sense as

the water pressing against the inside walls of Newton’s rotating bucket.

Gravity, electrostatic attraction, and magnetic attraction, on the other hand,

are not inertial forces. These are caused by pure aether flow, and they obey the

inverse square law. The 1887 Michelson-Morley experiment strongly suggested

that the gravitational field of the Earth entrains an extended region of the

electric sea while it is undergoing translational motion in its orbital path around

the Sun. The entrained region of electric sea which surrounds a moving

planetary object will constitute the gravitosphere, and it will extend to the shear

region which exists at the interface with neighbouring gravitospheres. A

planetary object and its surrounding gravitosphere move as one, in like manner

to an egg yolk and its surrounding egg white. The gravitosphere is caused by a

large-scale flow of pure aether through the electric sea and into the planet. This

will exert a torque on the tiny dipoles of the electric sea, causing them to

precess such that their precession axes are aligned with the gravity flow.

Gravitational field lines from adjacent planets meet laterally and spread

outwards, and because of the precession of the tiny electron-positron dipoles at

the interface, the gravitospheres of neighbouring planets will press against each

other with centrifugal force. This centrifugal force is the cause of electrostatic

repulsion on the large scale. It will increase both with the rate of the gravity

flow and as the mutual transverse speed of the two planets increases, and

because it is sourced in the tiny dipoles at the shear region, it will increase with

an inverse cube law in distance. A reversal threshold exists where the repulsive

force dominates over the attractive force. Lorentz need have had no worry about

vortices forming at the interface since they are essential for both the centrifugal

force mechanism and as part of the medium for the propagation of light. Neither

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need Lorentz have worried about how this interface would impact upon stellar

aberration. The aberration simply takes place at the interface.

The fact that gravitational attraction obeys the inverse square law while

centrifugal force obeys the inverse cube law means that planetary orbits are

stable. It also means that weakly charged sink-based objects will attract and not

repel. Gravity is weak negative electric charge, which is below the reversal

threshold, and so planets only repel each other when their mutual transverse

speeds are high enough. Although large planetary objects entrain the

luminiferous medium while undergoing translational motion, we know from the

1925 Michelson-Gale experiment that this does not appear to be so either in the

case of rotational motion (also confirmed by the Foucault pendulum

experiment), or in the case of small objects with negligible gravitational fields

that are undergoing translational motion. It is often argued that if a luminiferous

medium existed, it would cause friction in space, and that the planets would fall

into the Sun. But rather than causing friction, the electric sea actually causes

Kepler’s laws to be the way that they are. The electric sea is the source of the

inertial forces.

In the case of an electron and a positron which are spiralling inwards in a

positronium orbit, the accumulating aether pressure between them does not

cause them to recoil at the moment of closest approach, as would occur with a

comet at perihelion. Instead, they take their place inside the double helix

magnetic field structure, and the accumulated aether pressure itself recoils in

two opposite directions in the form of gamma photons. The angular momentum

of the positronium orbit is transferred into the fine-grained angular momentum

of electromagnetic radiation. No actual electron-positron annihilation takes

place as is commonly believed, [4], [6]. The electron and the positron are still

physically present, bonded inside the background electric sea. The aether

hydrodynamical approach therefore exposes the source of centrifugal force as

lying in the fluid-like aether between two electron-positron dipoles, hence

explaining why the electric sea can behave like a fluid for the purposes of

planetary motion and yet still behave like a solid for the purposes of

electromagnetic radiation. In a planetary orbit, the shear region at the interface

between two gravitational fields, is cushioned by a centrifugal hovercraft effect,

while in electromagnetic radiation the tiny vortices maintain their positions

within the double helix solid.

Electric Current

VIII. Just as a gravitational force field involves an aether velocity field, so also

does the electric force field that drives an electric current in a circuit. This flow

of pure electric fluid is the fundamental essence of electric current, and it enters

a circuit under pressure from an external power source. When the electric fluid

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flows, the fluid will impart its acceleration to charged particles in its path, but it

does not impart its velocity to them. It pushes positively charged particles along

in the direction of the flow, while negative particles, being aether sinks, eat their

way in the opposite direction towards the current source. The terminal speed of

the electric current will be determined by the electromotive force and the

impedance of the circuit. Due to resistance, R, in a conducting circuit, the

charged particles reach terminal drift velocities that are many orders of

magnitude less than the speed of the primary aethereal component of the current.

As regards the speed of the aethereal component, if the resistance, R, is zero,

and the reactive impedance is low enough, the current can reach the speed of

light. This occurs in the case of Maxwell’s displacement current in space in

conjunction with electromagnetic radiation. This maximum speed is the average

speed that aether flows between positrons and neighbouring electrons in the

luminiferous medium, and it is widely accepted that in cable telegraphy the

aethereal current speeds are also in this same order of magnitude.

More generally, since changes in the electromotive force (aether pressure)

in an electric circuit will be transmitted by the flow, these changes will travel at

whatever the flow speed is in the particular circuit. In the case of alternating

current, when a wire loop is rotating in a magnetic field, it is actually screwing

aether out of the positrons of the electric sea. This is the basis of the AC

generator. Pressurized aether will be pumped by the generator from the electric

sea into the circuit during both halves of the AC cycle. The thing that changes

during each half of the cycle is the direction of the circulation of the aethereal

current, but net pressurized aether enters the circuit during each of the two half-

cycles.

The Tidal Force

IX. The tidal force is often wrongly attributed to the moon’s gravitational pull

on the Earth. The moon’s gravitational field does not however come into

contact with the Earth. Objects on the Earth’s surface are pulled downwards

exclusively by the Earth’s gravity acting from underneath. The tidal bulges in

the sea therefore require an alternative explanation.

We know that the tidal force obeys the inverse cube law in distance. It has

been suggested that this is because we are considering the change in the

gravitational force as between the part of the Earth farthest from the moon and

the part of the Earth nearest to the moon. This argument does not however hold

up, because the moon’s gravity does not actually pull any part of the Earth

closer to it. The fact that we are dealing with an inverse cube law should be the

clue that we are dealing with yet another effect of the electron-positron dipoles

in the all-pervading electric sea. This effect will be something different than the

inertial forces and the electromagnetic forces, yet closely related. The tidal force

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will likely be a pressure that is exerted laterally from the precessing electron-

positron dipoles within the gravitational field lines, as opposed to arising from

any pull which acts along those lines. The gravitational field line pattern for the

entire Earth-moon system exhibits cylindrical symmetry along an axis of

symmetry joining the Earth and moon, and as such, the sideways pressure from

the precessing vortices within the gravitational lines of force will constrict the

system around this axis of symmetry. This will have a tendency to elongate the

two planetary bodies along the line that joins them, and this tendency will be

particularly effective on fluids, which is why the tidal force causes the seas to

rise up relative to the land.

Conclusion

X. Maxwell introduced the speed of light into his electromagnetic theory from

the 1855 Weber-Kohlrausch experiment, [10], by connecting it to the elasticity

factor in his displacement current. Maxwell’s displacement current requires the

agency of an elastic solid in order that it can be substituted for the electric

current term in Ampère’s circuital law, a substitution which is necessary for the

derivation of the electromagnetic wave equations. Time-varying

electromagnetic induction is also involved in this derivation and so it is

proposed that the elastic solid constitutes a dense sea of rotating electron-

positron dipoles. The fine-grained rotation supplies the inertial characteristics

that are involved in magnetic induction. It is further proposed that an electron

constitutes a sink in the fundamental electric fluid, known as the aether, while a

positron constitutes an aether source. As such, each rotating electron-positron

dipole constitutes a dipolar vortex, suggesting a correspondence with the

molecular vortices mentioned in Maxwell’s 1861 paper “On Physical Lines of

Force”, [2]. In a steady state magnetic field, these rotating electron-positron

dipoles will align in a double helix fashion such that their rotation axes trace out

the magnetic lines of force. A positronium orbit does not self-annihilate as is

commonly believed, but rather, the electron and the positron merely bond into

the already existing background dielectric solid. This medium, rather than

causing friction to inertial motion, is actually the medium which is the root

cause of the inertial forces to begin with.

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Appendix A

The gradient of the scalar product of two vectors can be expanded by the

standard vector identity,

(A∙v) = A× (× v) + v× (× A) + (A∙)v + (v∙)A (1A)

Let us consider only the vector A to be a vector field. If v represents

arbitrary particle motion, the first and the third terms on the right-hand side of

equation (1A) will vanish, and from the relationship ×A = B, we will obtain,

(A∙v) = v×B + (v∙)A (2A)

Hence,

(v∙)A = −v×B + (A∙v) (3A)

Since,

dA/dt = ∂A/∂t + (v∙)A (4A)

it then follows that,

dA/dt = ∂A/∂t − v×B + (A∙v) (5A)

Appendix B

The curl of the vector product of two vectors can be expanded by the standard

vector identity,

×(v×B) = v(∙B) − B(∙v) + (B∙)v – (v∙)B (1B)

Let us consider only the vector B to be a vector field. If v represents

arbitrary particle motion, the second and the third terms on the right-hand side

of equation (1B) will vanish. If we consider the vector B to be solenoidal, the

first term on the right-hand side will also vanish due to the fact that the

divergence of B will be zero.

Hence,

14

×(v×B) = – (v∙)B (2B)

Appendix C

Let us consider the two force terms which appear as parts 3 and 4 on the right-

hand side of Eq. (5) in Part I of Maxwell’s 1861 paper, [2]. The quantities

,

,

and

which appear in Eq. (5) are terms that depend on the magnitude of the

circumferential velocity of the vortices. They are referred to as ‘Magnetic Field

Intensity’. In modern notation, we would use the vector H when referring to this

quantity, and by comparison with Maxwell’s analysis we would be considering

H to be the vorticity of v. From Eq. (5), we can see that,

F/volume =

v×(∇×v) (1C)

where,

∇×v = vorticity (2C)

In the case of a rotating electron-positron dipole, the vorticity will be equal

to 2ω, where ω is the angular velocity. With

being taken to mean inertial

mass density, we can immediately see the connection with,

F = 2mv×ω (Coriolis Force) (3C)

If we define the magnetic flux density vector B as,

B =

v (4C)

it would then appear as if B represents a magnetic analogy to the electric

current equation,

J =

v (5C)

Let us now substitute equation (4C) into equation (1C). This leads to,

F/volume = B×(∇×B/

) (6C)

Comparing with Ampère’s Circuital Law, and substituting equation (5C),

we obtain,

F/volume = B×

v (7C)

This is exactly the same as,

E = −v×B (8C)

15

Maxwell’s Eq. (5) concerns the force on a current carrying wire in a

magnetic field. In the form shown at equation (8C) it appears in Eq. (77) in part

II of the same paper, but this time it refers to the electromotive force that drives

a current in a wire that is moving in a magnetic field. In both cases, it is the

same force, acting in a different context. Although nowadays credited to

Lorentz, it in fact first appeared in Maxwell’s papers many years earlier.

References

[1] Whittaker, E.T., “A History of the Theories of Aether and Electricity”, Chapter 4, pages 100-102, (1910)

[2] Clerk-Maxwell, J., “On Physical Lines of Force”, Philosophical Magazine, Volume XXI, Fourth Series,

London, (1861)

http://vacuum-physics.com/Maxwell/maxwell_oplf.pdf

[3] 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

[4] 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

[5] Tombe, F.D., “Magnetic Repulsion and the Gyroscopic Force” (2014)

http://gsjournal.net/Science-Journals/Research%20Papers-Mathematical%20Physics/Download/6220

[6] 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

[7] Lodge, Sir Oliver J., “Ether (in Physics)”, Encyclopaedia Britannica, Fourteenth Edition, Volume XIII,

Pages 751-755, (1937)

In relation to the speed of light, it says in the section entitled, “POSSIBLE STRUCTURE.__ The question arises

as to what that velocity can be due to. 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 order of magnitude as the vortex or circulation speed--”

http://gsjournal.net/Science-Journals/Historical%20Papers-

%20Mechanics%20/%20Electrodynamics/Download/4105

[8] 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”.

http://www.rastko.rs/istorija/tesla/oniell-tesla.html

http://www.ascension-research.org/tesla.html

[9] Lewis, G.N., “A Revision of the Fundamental Laws of Matter and Energy”, Phil. Mag. 16, 705-17, (1908)

[10] Tombe, F.D., “The 1855 Weber-Kohlrausch Experiment” (2019) http://gsjournal.net/Science-

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5th July 2022 amendment