Summary

Feynman's contention: Young's double split experiment can not be explained in any classical way, is accepted, however, it is also noted that the experiment can not be explained with the current ideas of the electron, -neither as a monolithic particle nor as a wave-, in any reasonable way, consequently the electron must have some undetected properties, and/or consist of more fundamental particles. The N's of the N-field *, are -in a first attempt- used for a possible solution. This results in the following:

Introduction

Stated this way, it challenges one to find such a mechanism. It is absolutely clear that an electron as a primary, a fundamental particle, can not perform such tricks in any 'normal' way. If one does not accept the super natural, there is only one conclusion; an electron is not a fundamental particle, it is formed of a (considerable) number, of still smaller particles.

Light in the presence of gravity, shows that light can not consist of simple projectiles. This conclusion is confirmed by the calculation of the gravity red shift. Atoms, molecules and gravity determine the energy and frequency of light (light to stand for all electro-magnetic radiation).

The dependence of the velocity of light on the strength of gravity suggests that the transmission of light can be compared to the type of energy transfer that can be demonstrated with a well-known desk toy. Five, or more, hard steel spheres, suspended in line, are at rest just touching. When one sphere is made to hit the others they remain at rest until the energy reaches the last sphere, and that sphere, and that one only, will move.

This is a rather useful model for light. It indicates that light can indeed consist of particles. When energy is fed in at one end the energy is -without noticeable loss- transferred. At the other end the transmitted energy causes one or more particles to move and causes e.g. an electron to 'jump'.

It makes a definite choice between: is light a wave with particle-like properties, or is it a particle with wave-like properties. The output, with this model, is a particle with a wave-like summation for the particles. The summation depends on the phase of the 'swing', which makes it possible for 'phase' differences to occur when the 'hits' do not arrive simultaneously, and an longitudinal wave pattern forms, that accounts for the observed phenomena.

It seems logical to use the N's as the particles that form electrons and positrons. That means the N's must be capable of reacting strongly to an imbalance and behave then like an electrical field etc. The truly enormous difference between the forces is easily accommodated. The difference between, sufficient large, opposing forces can have any magnitude, including the truly enormous difference between the force of gravity and the Coulomb-force.

Assume, for now, that such a scheme of things is possible, if it is not it will not produce acceptable results*. Name the particles, for obvious reasons, electrino and positrino. The ratio electric charge to mass to be the same as for the electron and positron.

Using the N's for the Hydrogen atom, does result in an easy to understand model that obeys the common laws and properties of macro-physics. This makes it possible to explain the following 'extraordinary' properties of atoms and/or quantum mechanics in terms of 'macro-physics':

A shell of electrinos

A spherical shell of electrinos surrounds the positive nucleus. The total negative charge of the electrinos balances the positive charge of the nucleus. The number of electrinos required is n².

For equilibrium the resultant repulsive force between the electrinos must balance the attractive force between each electrino and the nucleus and so 'support' it. The repulsive force, on a particle in a shell, is equal to the force produced by a concentrated shell in the centre of that shell. This repulsive force is also equal to the force that keeps a particle, at that distance, in a circular orbit.

With this it is possible to find an expression for the radius. This radius is a minimum for the Hydrogen atom when the virtual orbital velocity equals u = c / n. This minimum radius, with that velocity u, determines the minimum energy h_bar.

It is then possible to find an expression for n in known constants. This gives the well-known number 137.04 for n. If all electrons are indeed identical, some 18780 (an integer) electrinos are required to form one shell. The radius b, with this value for n, works out at .529 Å. The Bohr-radius.

The algebra

The force between an electrinoand the nucleus e is:
[09-01]

The resultant of the opposing forces, between the's, is equal to this force F and is also equal to the force that keeps a particle in a circular orbit. Therefore: [09-02]

Re-arranging, and with e = n² . gives: [09-04]

This shows that R is a minimum for c = n . u, substituting this, and with m_e = n². m
gives: [09-05]

[09-06]And:

The factor u² . R is constant, and the velocity u is therefore fixed and a maximum for R_min.
Consequently the right hand side, in the preceding expression [09-05], is a minimum, and equal to h_bar, a minimum because m_e.u = m.c !

[09-07]This gives for n:

[09-08]And the expression for h_bar:

[09-09]Gives for R_min:

The quantum jumps

The quantum jumps are regarded as THE typical quantum mechanical property and are supposed to be without an explanation in macro physics. This model makes it possible to explain, and show, that the jumps are dependent on ordinary physical laws. The algebraïc derivation follows.

[09-10]From:

[09-11]Follows:

[09-12]And from:

A minimum quantity can only occur in integer multiples, this means that when k equals:

No mystery, and no waves required for real insight and understanding on 'what is going on.'

Summary.

Applying the method of (09) to the Helium atom, does not work. Equilibrium, with double the number of electrinos is, on a spherical shell, not possible. Sommerfeld's ideas with elliptical orbits give, with this model, an ellipsoid as a solution: He-I.

A spherical solution is possible for electrinos in pairs. An arrangement with two electrinos in very close proximity, not in conflict with the large opposing forces is, however, very difficult to imagine.

Nevertheless, accepting this arrangement -or one that has that effect- does give the spherical solution: He-II, (with halve the Bohr radius).

This special -co-operating- property of the electrinos, gives more spherical solutions. It results in the spherical shells of the inert gases, with radii equal to the Helium radius.

The other spherical solutions

From the standard expressions we obtain:
[10-01]

Accepting that further spherical solutions are limited to shells with an even number of electrinos, P is an even integer and equal to the number of protons not balanced by inner shells. ( A equals 2 for all spherical shells. )
From the above, with u_p= u . p and R_p a minimum:
[10-02]

[10-03]And:

From this follows that p^² is an even integer, and that p.q is also an integer.

This limits p , q and C ( = A . q . p ) to certain definite combinations.

The number of protons in the nucleus, the atom-number, Z is equal to the sum P, the number of 'electrons' in the shells:

The arrangements are, at first glance, not as expected, but considering that equilibrium and minimum energy are both required, still easy to understand. The last column shows that the difference in the number of electrinos, for spherical shells, agrees with the calculations. It is easy to understand the construction, with the internal forces in equilibrium, and with minimum overall energy.

It is interesting to note that the Bohr-radius is 137 ² times the minimum radius between electrons.
That means that the area of the Helium shell is 137 ² times the area of a circle that has that minimum distance as radius.
That radius, is in turn 137 ² times the minimum distance between electrinos.

This allows the shell(s) to 'shrink' to accommodate the increased forces.

01-A Mechanism for Gravity.

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