Keywords
electron, quark, up quark, down quark,electric field,, polarization of space, inertia, inertial mass, field of motion, gravity, gravitation, gravitational mass, force of gravity, centripetal acceleration, centrifugal force, Bohr radius (1) (2)
Introduction
Real electrons, up quarks and down quarks are somewhat of a mystery, physics describes them as having mass, electric charge and magnetic moment, which are externally measurable properties. In addition quantum mechanics attributes other properties to them. We cannot directly observe them, but we can observe their electric fields. At any distance, they are primarily electric charges. The Pure Charge Model strips away all the complications and investigates how matter could be assembled from electric charges which have no property other than their charge.
The most remarkable thing about the universe is that space is able to sustain electric and magnetic fields. Without that ability, the elementary charged particles which are the building blocks of matter would simply drift past each other in the dark without interacting. The Pure Charge Model starts with these fundamental properties of empty space.
Space had the ability to be electrically polarised. It is as if space has two three dimensional layers, one of negative electric charge and the other of positive electric charge. Its properties allow these two layers to be stretched apart or displaced relative to one another.
Charges
An electric charge can be formed by polarising space towards a point in a spherically symmetric fashion. The Pure Charge Model assumes that this is how charges are made without asking how they are held together. This polarization of space is symmetric in all aspects except inside-outward-ness. The negative and positiveness of space is everywhere balanced except at the edges of the polarisation. Two layers of charge are to be found, one positive and one negative. One on the inside of the spherical region and one on the outside. The inner one forms the surface of the charge and the outer one is at infinity and therefore spread with infinite thinness.
Work has to be done in creating a charge because its electric polarisation field has an energy density. The total energy stored in the charge's field is inversely proportional to its radius. Modern physics claims the electron to be point sized which would give it an infinite energy. The Pure Charge Model avoids such mysteries by assuming that every charge has a definite radius.
Electrons, up quarks and down quarks have different masses and different charges. In the Pure Charge Model, this is achieved very simply by giving them the correct radii.
Inertial mass
In the Pure Charge Model, the movement of the charge relative to other charges generates a magnetic field surrounding the charge. This is called its field of motion. Magnetic fields have an energy density and it is found that this field of motion has a total energy content proportional to the square of the velocity of the charge. Furthermore it is found that the energy in the field of motion can be perfectly accounted for in terms of the work done in accelerating the charge. The mathematics is somewhat complicated, but anyone with the equivalent of an English A level in Further Maths or an English First Year Maths Unit of a science or engineering degree should be able to master it.
What we find is that the energy in the field of motion is equal to 2/3 of the electrical energy in the charge multiplied by its velocity, as a fraction of the speed of light, squared. This is rather reminiscent of the formula for kinetic energy 
. The pure charges have the property of inertia. When they are in motion, their velocity generates kinetic energy which is stored in their fields of motion as magnetic field energy. Individually, they obey Newtons laws of motion so long as no external magnetic fields are present. With a magnetic field present, the law of conservation of energy is obeyed, but momentum is not conserved. The law of conservation of momentum can only be applied with care.
In the Pure Charge Model, we set the radii of the charges to give them the correct inertial mass. The pure charge model of the electron is 2/3 of the radius Bohr attributed to real electrons.
These inertial properties of pure charges would be of little consequence but for the fact that when we consider one moving in a circular path, we get the correct answer for the centrifugal force which we have to counter in order to keep it on course. When we consider accelerating the charge at an angle to its velocity, we see that there are two distinct effects: the field of motion changes in size and it rotates. These two effects perfectly match Newton's 
and the 
of centrifugal force.
We can say that a pure charge has an inertial mass. This phrase uses a careful choice of words because there is no place in the Pure Charge Model for mass as we understand it. We come to physics with the concept of atoms firmly embedded in our culture. Learning that atoms are not hard round solid balls simply enables us to transfer the concept to the electrons, protons and neutrons. Learning that protons and neutrons are made of quarks only allows us to transfer the concept once again. We still want to think of hard round balls of mass which have electrical and mechanical properties attached. The Pure Charge Model does not involve that kind of mass, but I am powerless to banish the word mass from the English Language. So I will always prefix it to give the terms "inertial mass" and "gravitational mass". What is in a word? Nothing, but its the concept I want to banish. Those balls in our mental picture of matter have to loose their solidness.
The brace theory of gravity shows us that gravitational forces are generated by the presence of electric and magnetic energy density fields and not by the presence of "mass". Inertial mass and gravitational mass are both determined by the energy content of the matter and are therefore equivalent.
Real matter is composed of a milliard of moving charges in orbital and thermal motion. It can be shown how the summing of the inertial properties of individual charges accounts for similar behaviour of gross matter. The Pure Charge Model enables us to construct a model of matter in which the laws of Classical mechanics are obeyed.
This sets lower limits to their radii.
The equivalence between an accelerating reference frame and a gravitational field is broken. The force of gravity is entirely different from the inertial force resisting linear acceleration and from centrifugal force resisting centripetal acceleration. At the level of the individual particle, gravity, linear acceleration and centripetal acceleration have distinct effects on the fields of motion of the electrons and quarks from which matter is built.
The increase in inertial mass at near light speeds is predicted, though the exact mathematical analysis has not yet been done. The motion of the magnetic field of motion generates an electric field along radii to the line of motion in the opposite sense to the electric field of the charge. The exact effect of this is complex, but it is thought that this might result in a reduction in the size of the charge in accordance with theory worked out at the end of the Nineteenth Century but dismissed because it gave silly results. With the corrections to the laws of electricity and magnetism I have introduced, these could well account for the increase in mass. As the charge becomes smaller, its decrease in volume is equalled by an increase in the volume of its electric energy density field which is responsible for all or for a good part of its inertial mass.
Bohr attributed a radius of 2.818 x 10-15 to the electron. If this is correct, then the energy in its electric polarisation field is equal to ½ of the value given by
One thing is certain, a small magnetic dipole with the magnitude attributed to the electron should have in inertia 50 to 100 times the inertial mass of the electron and a point sized magnetic dipole will have an infinite inertia. The Pure Charge Model casts grave doubts over our current understanding of the electron.
Implications
The Pure Charge Model tells us that the electric fields of real electrons, up quarks and down quarks posses inertial properties.
but confirms its spirit.
. It would be nice to think that the electron consists of equal amounts of electrical and magnetic energy. The motion of a magnetic field generates an electric field of motion, but the geometry of the most intense regions of the magnetic field is unknown. We can do a calculation for a very small magnetic dipole, but the results are messy. A magnetic field generated at the surface of the electron equivalent to the field of a small dipole at its centre aligned with its direction of motion could be made to account the discrepancies in inertial mass and energy content to give the electron an energy equal to . The only problem is that the magnitude of such a magnetic dipole would be about one fiftieth of its accepted value.
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See a mathematical derivation of the Pure Charge Model.
© Copyright Bruce Harvey 1997.