Like any NLHV theory, the Cordus theory proposes that particles are not zero dimensional points but instead have internal structures that provide the observed functionality (charge, mass, spin, etc.). It makes specific predictions about the identity of these structures at the sub-particle level [1]. The key difference compared to other theories is that the particle is proposed to comprise two reactive ends some short distance apart, connected by a fibril, see Figure 2. The fibril does not interact with other particles, instead the interaction occurs at the reactive ends. The reactive ends are energised at the de Broglie frequency, at which time they emit discrete forces into space in each of three spatial directions (r, a, and t, see Figure 2) [10] [11]. For massy particles the discrete forces are encapsulated into extended fibril structures that propagate into space—these are called flux tubes. The aggregation of these in space makes up a fabric of discrete forces [12].

A general mechanism for force has been proposed within this theory [13]. The reactive end moves as it goes through its energisation cycle, and traces out a cyclic locus in space. This locus is then distorted by the incoming discrete forces of the external field. As a consequence the mean position of the reactive end changes. This provides a mechanism whereby the reactive end is able to sample the spatial distribution of field around it, i.e. the gradient of the field, and move accordingly. The direction of motion adjustment is along the gradient in the direction of greater compatibility of discrete force emissions. Generally this means

the type of emissions, e.g. the phase energisation sequence (matter-antimatter), and direction of emission (charge). Hence force arises as “coerced displacement of the reactive end” [13].

The flux tube has three geometric properties of linear strength (radial emissions), curvature (bending), and twist (torsion). It is proposed that these geometric properties provide the mechanisms for the electrostatic, magnetic, and gravitational (EMG) force interactions respectively. This concept arises from [7] and [8], and is further elaborated below. A fourth attribute of the discrete forces (not so much of the flux tube) is the synchronisation of emission between two particles [10], and this is proposed as the mechanism for the strong interaction (see below). The weak (decay) interaction is proposed to have an altogether different cause (see below).

The above are the general principles for how force operates within the Cordus theory. Next these principles are applied to offer explanations for the different interactions.

The theory proposes that the electrostatic interaction arises from the direct linear action of the incoming discrete force on a remote particle. It applies in a direction along the line of the flux tube, and the effect is to move the remote particle B closer or further from the emitting particle A depending on the relative charge.

The underling mechanism is proposed to be that the recipient reactive end attempts to emit its own discrete forces, but is affected by the incoming discrete force. It may be enhanced or inhibited depending on the compatibility between the native and external discrete forces. This changes the position of the reactive end, with the displacement being along the axis of the fibril. A similar mechanism for the spatial readjustment of the reactive end has been proposed for photon absorption and emission [15]. The direction of the discrete force is the basis for the sign of the electric charge. This is presumed to be the direction of action of the discrete forces within an outward travelling flux tube. Negative charge is assumed outwards—this is merely a sign convention.

Consider the interaction between two electrons, being a typical like-charge case. Electron A is the basal one and is nominally assumed to be fixed, while B is the remote test charge that reacts to A. Each electron has two reactive ends (1 and 2)

per this theory. The reactive end A₁ of electron A emits discrete forces packages in a flux tube, which propagate out into space at the local speed of light and impinge on reactive end B₁ of remote test electron B.

Consider now the energisation of dormant reactive end B₁. As B₁ begins to energise it encounters incoming discrete forces from A₁ that are incompatible with its own emissions. Per lemma 1, this ranged interaction is transphasic, since the particles have like charge, and the synchronous interaction therefore operates to put the emissions π/2 out of phase. However B₁ cannot delay its energisation indefinitely. This is because energisation state and frequency are determinants of particle identity and energy respectively [16] [17]. Consequently B₁ has to adjust its location to move with those imposed forces, in the repulsive direction.

If the remote charged body has physical depth, i.e. comprises many particles, then the incoming discrete forces apply displacements to the foremost parts of the body, then pass through and apply displacements to the deeper layers. Hence a charged macroscopic object feels the electrostatic effect and moves holistically.

At the macroscopic scale of a negatively charged sphere, each of many electrons generates its own discrete forces and flux tubes. Macroscopic bodies tend not to exhibit quantum behaviours. The Cordus theory interprets such bodies as discoherent assemblies of matter, wherein the particle spans are not aligned [2]. Hence a discoherent sea of electrons can be expected to generate flux tubes pointing in random directions. This is consistent with the observation of an electrostatic field that is smooth, continuous, and uniform in all directions. The theory predicts that the field will however be granular at the frequency of the charge emitters.

The electrical force F e B between two particles of charge q_A and q_B is:

F e B = − K q A q B r 2 r ^ (1)

where r is the radial separation, r ^ is the radial direction and K is a constant. A qualitative explanation for the form of this relationship follows. The reason for the product of charge (q_Aq_B) is that charge determines the number of discrete forces involved: the amount of displacement coercion (hence force) experienced by particle B is determined by the strength q_A of the incoming discrete forces, and the strength of its own response q_B, hence a multiplicative relationship. The inverse square relationship 1 / r 2 arises from the expansion of the discrete forces on a spherical front. This expansion occurs because the discrete forces are emitted in three orthogonal directions in surface shells at each energisation cycle.

Irrespective of the relative orientation (spin) of A and B, there is always a component of B’s emissions that is radial to A, i.e. in the direction r ^ . The electrostatic interaction may be simplified to only this component.

Dissimilar charges attract even across the matter-antimatter species. This implies that the energisation sequence—which differentiates the species—is immaterial for the electrostatic interaction.

An electric field is known to be shieldable by a Faraday cage, whereas gravitation is not. The present theory predicts that discrete forces penetrate all matter, but in a Faraday cage the electric field only appears to be shielded, because electrons in the conductive cage material have sufficient mobility to move in response to the external field and set up a countering field.

In contrast the photon can be shielded: it can be absorbed, by mechanisms identified in [15]. Applying this to interaction of electromagnetic radiation photons from an antenna or reflector, the present theory explains that the frequency and span of the photons is inversely related [1], which is consistent with the observation that the conducting elements of the antenna need to be closer spaced for higher frequency radiation. As the photon frequency rises still further, the required conductive loops are of the order of atomic spacing, i.e. the shield must be of a continuous material. For even greater frequencies the electrons cannot encounter all the discrete forces in which case the photons pass straight through.

A flux tube is a directional propagation of discrete forces. It is proposed that this may be bent by movement of the basal emitting reactive end. Per Lemma 8, motion of a reactive end occurs in discrete displacements during its de-energised state. This results in emissions expanding from each progressive location of energisation. Consequently the flux tube, which is continuous, has kinks. The new curvature moves outward with the discrete forces at the local speed of light. If the speed of light was infinite, i.e. disturbances propagated instantly, then there would be no magnetic effect.

Under these premises the magnetic interaction arises interpreted as the action of the incoming discrete forces in a recurved flux tube, causing a yaw adjustment in the velocity of a remote moving charged particle [7]. A remote test particle B moving with velocity V_B receives at reactive end B₁ the discrete forces and the re-curved flux tube emitted by A. This causes a coerced displacement of B₁, which provides a yaw moment that changes the direction of motion of B to be more parallel or antiparallel (depending on the charge) to the velocity of A. See Figure 4.

How does a curved flux tube create the magnetic force on the moving remote test charge? If the remote test charge is stationary, then any curvature of the incoming discrete forces in their flux tube only re-orients the direction of the electrostatic force, i.e. momentarily changes spin. Since the flux tube is recurved, this imposes a transient change in orientation that integrates to zero. However, if the test charge is also moving, and encounters a curved flux tube, then the magnetic interaction attempts to realign the locus of the moving test charge to the same handed direction of motion as the basal charge.

When the discrete force in its flux tube reaches the remote moving test charge B, it upsets the geometric location for the reactive end B₁ of the moving test charge. Whether it delays or advances that reactive end depends on the sign of the magnetic field, i.e. the relative direction of the velocity of B, and the relative charges. The discrete force pulse prevents B₁ from advancing forward as far as it usually might during a frequency cycle, or it pushes it forward.

The incoming discrete forces are not consumed but pass on outward to the other reactive end of the remote particle. The effect on B as a whole is additive rather than being negated, since the direction of the flux tube is reversed when it reaches its other reactive end. This sets up a yaw moment across the fibril of the remote particle, thereby adjusting the direction in which the remote charge is moving.

Magnetic fields represent the motion of the charge (basal generator) that is emitting the discrete forces. A remote moving charge changes direction to be more closely parallel (or antiparallel depending on charge sign) to the locus of the basal charge [18]. The magnetic force F m B in the radial direction r ^ , experienced by particle B of charge q_B and velocity v B in a magnetic field created by particle A with q_A and v A is:

F m B = μ 0 4 π q A q B r 2 v A × v B (3)

where r is the radial separation, and μ₀ is a constant. A qualitative explanation for the form of this relationship follows. The reasons for the product of charge (q_Aq_B) and the inverse square relationship 1 / r 2 are as before. Having more charges q moving in the same direction does not increase the curvature but simply means that there are more discrete forces reaching the remote test charge, i.e. the effect simply scales for increase in either of the charges. The direction of the magnetic field is perpendicular to the plane in which the curvature of flux tube occurs. The velocity dependency arises because the faster the basal charge moves v A the greater the curvature of the flux tube. The greater the velocity v B the greater the rate at which the kinks are encountered, hence a multiplicative relationship. The magnetism effect depends not simply on the speed of the charges, but also their relative directions. The effect depends on the component of curvature that is apparent to B in its direction of motion, hence the cross product. Thus magnetism only works in remote particles that already have some degree of alignment of their locus with the velocity of the basal charge.

It is proposed that the reason for the effect being right-handed is due to the way that reactive ends emit discrete forces in an energisation sequence (see Figure 2), and the dominance of the matter species. Each package of discrete forces has three orthogonal sub-forces and these are energised in a sequence. This sequence has been proposed as the distinguishing structural feature of the matter-antimatter species [19], the anti-electron structure [20], and the basis for annihilation [21].

A common illustration of magnetism depicts a moving charge being forced into a circular trajectory in the presence of a uniform magnetic field. Our explanation is that when the magnetic field is large and uniform, then the transecting moving test charge is forced into a circular path which is the same motion as the large basal current required to make that magnetic field. In this case the magnetic field dominates the interaction, and the moving test charge tends to move into a circular or helical trajectory (its own back-reaction is miniscule). However the case of the uniform field obscures the important fact that creation of that uniform field requires charges to be moving in a circular path too. Uniform magnetic fields are therefore a special case. It is the interaction of two moving charged particles where the more interesting mechanics occurs. The geometrically simplest form of magnetism, two particles affecting each other, is surprisingly complex. The moving test charge is not simply a passive participant, but also radiates its own discrete forces in their flux tube. If the basal charge is of similar size, it will be affected in turn by the magnetism of the test charge. For this and relativistic considerations see [22] and earlier work by [18]. We propose it can be qualitatively interpreted as one moving charge attempting to force another to conform to the same direction of motion: it is a type of alignment effect.

If the test charge is not moving, then the effect of incoming magnetism is to align the remote test charge, which means interfering with its orientation (spin). This is consistent with behaviour of permanent magnets and magnetic resonance imaging. In both cases the spins of all the electrons in the macroscopic body tend towards alignment. Again this shows that magnetism is primarily an alignment effect.

A permanent ferromagnet has a magnetic field, but no apparent electric field. The usual explanation is that that the electron and nucleon spins are aligned across a domain (region of atoms). The present theory explains this based on the orientation of the particle. It is proposed that the alignment of the span of electrons and nucleons, i.e. spin, results in the discrete forces in their flux tubes pointing in the same direction along the axis of the magnetic poles, but randomly orientated in the transverse directions. Hence the effect is summated along the axis, and neutralised laterally. The magnet does not appear to be charged or to emit an electric field because of the equal contribution of positive and negative charges. Nonetheless it emits discrete forces in their flux tube. The magnetic domains are proposed to be formed in the first instance because electron discrete forces extend to neighbouring atoms and encourage alignment of other electrons. We suggest that within the magnetic material the electrons themselves move, either through their unfilled orbitals, or as current flow within the sub-lattices of the material, and this generates curvature of the discrete forces in their flux tubes and thus magnetic fields.

Up to here the discrete forces have been implied to be discrete, and represented diagrammatically as arrows. However this is a simplification of a deeper mechanics. They are instead believed to take the form sin 2 ( θ / 2 ) and to comprise emissions in three orthogonal directions (r, a, t) [13], see Equation (4). Thus the potential energy U B 1 in the flux tube has three components offset at thirds of the phase angle θ B :

U B 1 ( r ) = sin 2 θ B 2 (4a)

U B 1 ( a ) = sin 2 ( θ B 2 − 120 ∘ ) (4b)

U B 1 ( t ) = sin 2 ( θ B 2 − 240 ∘ ) (4c)

See Figure 5 for a representation of these three phases for a matter species (electron). This energisation sequence results in a torsional effect on remote particle B, which moves closer or further along the field gradient depending on the mutual compatibility.

There are several implications. The first is that the reactive end is never fully de-energised. While any one discrete force does momentarily go to zero in strength, the reactive end as a whole maintains its energisation. This satisfies another part of the theory which showed that the Lorentz and relativistic Doppler could be derived on the premise of a stretchable flux tube [23].

A second implication is that the potential energy function for reactive end B₁ has a circular function, and the reactive end moves in reaction to trace a small cyclic locus in space [13]. The locus is circular with normal [1, 1, 1] in the [r, a, t] directions. However when an external field is imposed, then the reactive end expands its excursion asymmetrically, and this moves its mean location.

A third implication concerns the question of why the gravitational interaction between matter and matter is attractive when the electrostatic interaction repels like charges. The answer is that for the electrostatic the opportunity for greater coordination between particles arises if their directions of emissions (charge) are opposite, irrespective of the energisation sequence (species). In contrast for gravitation the opportunity arises if the emissions have the same hand: receiving particle B is attracted to the transphasic interaction [13] whereby it energises within the null points in the incoming (r, a, t) emission. This it can only do if the energisation sequence is the same, which always arises for when both particles are matter species.

In this theory the energisation sequence (r, a, t) vs. (a, r, t) determines the matter-antimatter species [19] [24]. Thus we predict that antimatter-antimatter gravitation is attractive, and matter-antimatter repulsive. The reasoning follows. For the case of an anti-electron the energisation sequence is (a, r, t) and the charge is inverted. The corresponding energy locus for the reactive end is shown in Figure 6 for the electron and antielectron. This shows that the rotation is opposite in direction for antimatter. It logically follows that the gravitational interaction between two antimatter particles would be attractive, and repulsive between matter and antimatter.

The gravitational force F g B in the radial direction r ^ , experienced by particle B of mass m B in a gravitational field created by particle A with m A is conventionally:

F g B = G m A m b r 2 (5)

The reason for the product of charge ( m A m b ) is that that the effect is enhanced by more incoming discrete forces ( m A ) per lemma 1, and a greater frequency of response ( m b ) per lemma 8. The inverse square relationship 1 / r 2 is because of the dilution of discrete forces across an expanding spherical shell, as before.