Abstract: The theoretical foundation and fundamental equations for the unification of all forces were identified in previous papers. They are herein applied, demonstrating that the strong and weak nuclear forces devolve to those of classical mechanics and electrodynamics or their generalization. A synthesis of electromagnetic and gravitational forces has also been achieved, but is specifically excluded from this paper. Parties interested in technological development of the theory may contact the author.

Introduction: A significant portion of this paper was discovered over 10 years ago. However, the major problem in completing the work was the lack of a general theory. This was achieved and presented in a paper in July of 2002¹. A corroborative extension was completed in the early part of 2003². These two papers contain the theoretical basis for the unified theory. Apart from being logically consistent with classical physics and the experimental data of the last century, its strength lies in the exclusive use and reinterpretation of accepted classical and relativistic formulae. Further, it is proven that classical mechanics and special relativity are precisely equal with respect orbital mechanics and at oblique angles, demonstrate inertial effects.

To summarize, the theory identifies a fundamental duality in mechanical and electromagnetic attributes. Application of the relativistic equations to orbital and sub-orbital motion showed that the electron and proton are aspects of the same fundamental particle and that an inversion of all phenomena takes place at the classical electron radius.

The analyses contained in the previous papers identify the underlying universal substructure as entirely deterministic. Additional support for this statement can be found in the proliferation of physical constants. Equally, experimental accuracy often exceeds 8 significant figures so that probability approaches unity. Although physical laws may be expressed in any language³, a deterministic and therefore simple representation is vastly preferable. This is covered in more detail at http://wbabin.net/babin/dvp.htm

Conservation of mass is a fundamental law of classical mechanics. An equivalent status is hereby claimed with respect to fields. This is most evident in the results of the Michelson-Morley experiment and the logical derivations⁴ thereof. As currently acknowledged, electric charge is invariant. Since the Bohr equivalence equates the squared charge with mass and field, they must also be considered invariant! This is a precise logical derivation, which is validated by experiment and can only be negated by same. Electromotive and mechanical forces are therefore induced and are distinct from invariant primary fields.

It is posited that electrons and protons form pairs in mechanical and electromagnetic equilibrium so that no excess charge and field is available to accommodate more than one charged particle at a given distance. This explains why in multi-electron atoms the atomic radius is not significantly larger than in hydrogen since excess charge must be compensated at a specific distance⁵. It also explains the shell model application to both the orbiting electrons and the nucleus. As a consequence, a single unpaired proton determines the charge of the nucleus. The mutual exclusivity of nucleons (interaction only with immediate neighbours) is further evidence that electron-proton pair is the dominating force. From this, we must conclude that there is no distinct nuclear force.

The dimension of the classical electron radius is,

where e = electron charge (statcoulombs), m_e = electron mass, r_e = classical electron radius, r_b and v_b = the radius and velocity of the first Bohr orbit.

According to V.F. Weisskopf⁷, the radius [r_e] approximates the radius limit [r_n = 2.8 x 10^-13 cm] of the Yukawa nuclear strong force. The ratio is approximately [1.0064]. The reason for this and for the comparable length is not understood.

The angular momentum of the electron and proton must be equal with respect to the centre of mass. The radii are therefore inversely proportional to their masses. Surprisingly, the ratio of the proton orbital radius [r_bm_e/m_p] to [r_n] is the ratio of the nuclear "strong force", [g²], to the squared charge!

This is confirmed by Weisskopf’s formula⁸,

The reason for this ratio is also not understood.

Although the speed of light and the proton mass are involved in the ratio of (3), they are not explicit. Einstein’s relativistic formulas for squared momentum identify the ratios [(m²–m_o²)c² = m²v²] which have been shown to apply to orbits. It should be noted again that the momentum of both the proton and the electron are equal. Experimenting with various combinations provides an astounding result,

When the electron orbits at c, the equivalent momentum for the proton is [m_p((g²/e²) x10³)^1/2]. Here, [c] is in imperial miles, and the ratio of the strong and electromagnetic forces is a squared velocity!

While numerically correct, it exceeds the ratio of (3) by a factor of 1000. This appears nonsensical, but when all physical quantities are converted to imperial measure, the ratio between the classical electron radius and the radius limit of the nuclear force is easily identified.

also,

where I = the proportional constant (gravitational analogue)

Electron collision experiments indicate that their radii must be less than 10^-16metres⁹. This new determination of [r_n] derived from [r_e] approaches this measure in the transformation of electron to proton. It should be noted that the charge and mass radius of nucleons are nearly equal¹⁰ which adds credence to the above calculations.

The strong force (disregarding 10³ for the moment) is simply [e²(m_e²c²/m_p²)] which is the ratio of squared momentum relative to the centre of mass/charge! Then the ratio of [r_n] to [r_b] is [m_e/m_pv_p²]

Note the relationship with Einstein’s equation relating squared momentum and kinetic energy, indicating again that they and the Compton derivations apply to orbits. Note also, the astounding simplicity and elegance of the classical derivations where masses, fields, velocity and distances are proportional. There are no other systems of measurement remotely capable of providing the above results. The possibility that it is a chance occurrence is infinitesimal. All subsequent calculations will be based on imperial measure.

The beta decay "strength constant" is identified¹¹ as,

The initial term equals [3.4356 x 10^-5] in imperial measure (statcoulombs). The basic numerical value is easily identified as the ratio of the magnetic moment of the electron to the squared charge. However, the dimensions are not correct. In the Weinberg-Salam electroweak model¹², various parameters are given. One such, the dimensionless weak strength G is given as,

Apart from redundancy, it is difficult to determine the physical significance of either the bracketed term or the parameters. If we take the inverse ratio of [g₁] and the numerics,

This is simply the ratio of the strong force[/10³] and electric charge squared divided by a proportionality factor, [J]. The value of the proportionality factor is the ratio,

so that it reduces to an energy term and has nothing to do with the weak force. However, all is not lost. In the precise evaluation of a residual amount in these calculations we find the ratio,

It is not difficult to understand the magnitudes of the [m_w] and [m_z] "particles" (80.8 and 92.9 GeV) in view of the massive increase in fields both before and after inversion¹³. Their ratio within experimental error is

All unknown quantities associated with the nucleus are reconciled with the use of imperial measure. For example, the anomalous factors in the magnetic moment of the proton, [a_p], and the neutron, [a_n], is found to be,

where u_p is the proton’s magnetic moment and I = proportional constant (gravitational analogue)

There is no satisfactory explanation in contemporary physics for the accumulation of multiple nuclei in an atom. For example, the repulsive force at nuclear distances precludes the absorption of a proton whereas a dual electron-proton pair does not combine. A plausible method is herein described.

An electron to spirals towards the centre of mass-charge¹⁴, the proton’s momentum increases in proportion and its energy is in inverse ratio to mass, [m_ec²/m_p.] This is the ratio of [r_b to r_n].

The proximity of the proton after inversion does not allow the transition from electron-neutron to proton and is the reason neutrons occupy the outer fringes of the nucleus. We must expect to find quantities relating to the neutron and the binding energy either slightly before or after the point of inversion. If we replace the proton mass with that of the neutron, [m_n,] and the mass defect, [m_d], at [2c²] (the angular speed) we find,

e²/2m_dc²m_n = (m_e/m_p) x 10¹¹ (16)

If we identify [e²] as [m_ev_b²r_b], we see that the radius at this point is [r_bm_p/m_e2c² = r_n/2] and presume emission of [m_d ]and the formation of the unstable neutron.

It should be noted that external and internal configurations are incident, then the 10¹¹ and 10^-8 of equations (13) and (16) provide a de facto explanation for the factor of 10³ identified in equations (4) and (5). While it is not entirely clear in what context it is used, the [q _w ] factor in (10) is most probably [m_e/m_d].

Approaching 90^o deflection (initial photon/electron), the relativistic masses approach the Newtonian This applies to all orbitals and proves that regarding this application, no difference exists between classical mechanics and relativity. Perturbations and collisions entail accelerations and decelerations and the appearance of inertial effects which are now identified with dual states. Obviously the ratio is not related to mass, but to velocity, induced fields, and their growth to the point of inversion. This is evident in equation (a), ~ 2m₁c cos(f)/(m₁ + m₂) which is simply the Newtonian velocity [v_n]. Since the angle [f] represents the path of the particle moving at [v_m] we must ascribe a negative motion to [v_n] - [f+180^o]. Note specifically that this another demonstration of the obvious fact that the hydrogen atom represents a precise equilibrium. No force is required to maintain it.