Description of the neutron

Description of the neutron.

The proposal is the following:

The neutron is a "bound-unstable" system made by a proton and an electron.

The electron makes an orbit around the proton, at a distance so close and at a speed so high, that allows it to set in a special orbit in which the central force is stronger than the standard Coulomb force for those charges and that distance. (See below).

The thesis is therefore that, in a neutron, the electron follows a special orbit in which the centripetal force is significantly stronger (more than twice) than the corresponding standard Coulomb orbit for the same radius.

More specifically:

The classic centripetal Coulomb force exerted by a proton on an electron is, as is well known:

(N-1)

with

k    a constant (Coulomb's constant).
r    distance between the electron and the proton.
e    electric charge of the proton (the charge of the electron being –e).

(See foot Note N-a below).

What is now being proposed is that, at the special orbit followed by the electron in a neutron, the attraction force of the proton is:

(N-3) with g > 2

where g is a numerical (adimensional) constant bigger than 2. (See below why the condition g > 2 is necessary).

The reason for such special centripetal force suffered by the electron would be that in such orbit the electron keeps the same orbital angular speed of rotation than the intrinsic angular speed of rotation of the proton. Because:

As has been explained in other places of the "Eve model of the aether", the particles of matter with internal structure, like for instance the proton, modify (redistribute) the velocities of the aetherinos that collide with them with the consequence that from those material particles emerges a distribution of aetherinos capable to produce forces on other particles. But the distribution of aetherinos re-emerging from the proton is not isotropous but depends on the direction, or more precisely, on the angle that such direction makes with some characteristic axis of the proton. (This is what can be expected from a particle that has intrinsic angular momentum and magnetic momentum).

There will exist some directions of the proton by which emerge a distribution of aetherinos capable to produce stronger forces on a test particle than those due to the distributions emerging by other directions. It can then be interpreted that the classic Coulomb force (N-1), exerted by a proton on an electron, is somehow the average of the forces suffered by an electron when in presence of a statistical sample of protons with axis randomly aligned (although the subject becomes a bit more subtle if it is admitted that a proton is always performing an intrinsic rotation).

The physical fact called in mainstream Physics "spin" of the proton, suggests here that some characteristic internal axis of the proton rotates in space (spins) at some specific angular speed w. (This is what can be expected from a particle with inner structure whose components (subparticles, quarks?) it is reasonable to suppose that are performing inner orbits that equilibrate their binding forces).

This scenario allows to consider plausible that an electron performs an orbit around the proton with an orbital angular speed exactly equal to the intrinsic angular speed w of the proton. If the two vectors representing those angular speeds (the orbital of the electron and the intrinsic of the proton) remain parallel, the electron will remain in its orbit always facing the same given intrinsic direction of the proton by which emerges a strong distribution of aetherinos (i.e. able to produce a stronger force). Such "strong" distribution of aetherinos would manifest itself producing a force like that of (N-3) with g > 2 and otherwise the electron would perform that orbit in a standard fashion (the centrifugal force cancelling the centripetal one) with the only particularity that the proton would behave as if its charge was g e instead of e.

The force with which the proton attracts the electron is a force subject to statistical fluctuations, like all forces implemented by aetherinos. The forces exerted at very close distances of the particle that originates the force, in this case the proton, are subject to fluctuations of relatively high intensity in comparison with the average value of such force. This is consequence of the fact that when the particle that originates the force (in this case the proton) is affected by a fluctuation in the local aether that bathes it, the redistribution being created by the particle has anomalies in the speeds of practically all the aetherinos emerging from the proton at that time. And if the electron is very close to the proton, wider is the speed range and hence more are the aetherinos (emerged from the proton during the brief fluctuation) that reach the electron in some given small time interval, due to what, their anomalies (i.e. the anomalies in the number of aetherinos of the different speeds) cooperate to produce in the force suffered by the electron a stronger anomaly (compared with the average force suffered by the electron at that distance), doesn't matter if it is only during a very short time.

In a neutron, the electron has some probability to get free from the proton due to those fluctuations of the aether. When the fluctuation is small the electron will move a small amount away from the centre of the "intense force zone" but will return rapidly to it because the force gradient dictates so. But in some cases the fluctuation will be strong enough to move the electron irreversibly out of its orbit. In the scenario of the special electronic orbit that takes place in the neutron, "moving out of the orbit" means that the electron ceases to have an orbital angular speed equal to the intrinsic angular speed of the proton and therefore ceases to be subject to the intense stabilized force that characterizes such orbit (passing quickly to suffer a force of intensity similar to the classic Coulomb force that somewhat averages the influence of the aetherinos emerging the proton in the different directions).

As is well known, for the classic Coulomb orbits, governed by a centripetal force like (N-1), the potential energy (negative) of the electron is:

E_POT = – k e² / r

while the kinetic energy (positive) has a modulus that is half that of the potential energy and is therefore:

E_CIN = + 1/2 k e² / r

as can be deduced equating the centripetal and the centrifugal forces:

(N-6) m_e v²/r = k e² / r² => m_e v²/2 = 1/2 k e² / r

Therefore the total energy of the electron is negative and the electron is "bound".

E_POT + E_CIN = - 1/2 k e² / r < 0

In the neutron, the electron is bound in the sense that it is kept in an orbit close to the proton but its energetic balance needs further discussion:

Parking away relativistic considerations, the kinetic energy of the electron in its neutronic orbit can be evaluated equating the centrifugal and the centripetal forces and extracting the classic kinetic energy:

m_e v²/r_N = g k e² / r_N² =>

E_CN = m_e v²/2 = 1/2 g k e² / r_N

But it doesn't seem now licit to suppose that the potential energy of the electron is just – g k e² / r but rather the energy (work) that should be applied to move it from its orbital radius r_N to "infinity" with a force that cancels the attracting force of the proton. But the electron, once released from the zone of influence of the strong distribution of the proton, is subject to the Coulomb, classic force of the proton (to which collaborate aetherinos emerged from all directions of the rotating proton) whose value is – 1/2 k e²/r (instead of – 1/2 g k e²/r ). Under those circumstances, the work to be done on the electron to move it to infinity opposing such force is:

- E_PN = k e² / r_N

It can therefore be considered that the total energy of the electron in its neutronic orbit is (potential energy + kinetic energy):

E_TN = E_PN +E_CN = - k e² / r_N + 1/2 g k e² / r_N

that for g > 2 implies E_TN >0. This positive net energy of the electron is consistent with the experimental fact that the neutron has a binding energy characterized by an excess of mass (instead of the mass defect that is normal in the stable-bound systems), the mass of the neutron being bigger than the sum of the masses of the products of the disintegration (proton + electron).

But it is also reasonable to expect that the aether fluctuation, that pushes the electron out of its neutronic orbit, steals a small part E_f of the electron's kinetic energy whose exact amount will depend on the features (intensity, etc,...) of such fluctuation. On the whole, the net energy of the electron just derailed from its orbit will be:

E_TN = E_PN + (E_CN – E_f) = – k e² / r_N + 1/2 g k e² / r_N – E_f

Assuming that g > 2, the net energy of the derailed electron will be positive as long as the kinetic energy E_f stolen by the fluctuation is small (smaller than some threshold value imposed by g). But if its total energy is positive, the electron ceases to be "bound" and it will move indefinitely away from the proton (it will escape) with a speed that will decrease asymptotically towards some limit speed v_L , leaving finally the electron with a zero potential energy (at its "infinite" distance of the proton) and with a remnant kinetic energy 1/2 m_e v_L²

There will be cases in which the fluctuation leaves the electron with insufficient kinetic energy (initial speed) to escape from the proton and there will be some exceptional case in which the fluctuation leaves the electron with "just" the precise kinetic energy to escape so that the electron, as it moves away from the proton, approaches asymptotically a zero speed. In this event the electron will appear after the disintegration with a practically null kinetic energy.

There is therefore no need to postulate the existence of a neutrino to explain the experimental fact that in the disintegration of a neutron, the electron emerges in general with less energy than the corresponding to the mass defect (m_N –(m_e+m_P)) c² (where m_N, m_e, m_P are respectively the rest masses of the neutron, electron and proton). What happens is simply that the energy is not conserved in these beta-decay events because the aether fluctuation steals some energy from the electron and does not return it back to it (being in this respect different from other quantum statistical phenomena in which the fluctuations steal energy in some events but return it in others so that there is a compensation along time).

Note: It is interpreted that energy is not strictly conserved in quantum microscopic events. (This is also implicitly assumed in quantum mechanics when it deals for example with quantum tunnelling, vacuum fluctuations, etc,...). Energy should be considered a "statistically conserved magnitude" meaning that it is approximately conserved in macroscopic phenomena that include many microscopic events. The fact that in the disintegration of the neutron there is always a random amount of missing energy (never an excess of energy) does not invalidate the assumption that energy is statistically conserved in nature because plausibly the missing energy of these events is basically returned to nature in the inverse processes, creation of neutrons (e.g. in the fusion of Hydrogen atoms in stars).

Another explanation that seems less plausible to the author, is that the missing energy at the disintegration of the neutron is not actually lost but (similarly to what happens in the emission of radiation) the energy is temporarily resident in the aether in the form of some moving disturbance (shock wave?) that can be returned when it encounters matter. It is the arrival of this aether disturbance what would be observing the presumed detectors of neutrinos (Kamiokande, Gran Sasso, etc) although it seems more cautious to think that what those detectors observe are, again, statistical fluctuations of the aether whose origin need not be the beta-decays. In fact the mainstream theory of neutrinos does not seem very convincing since it manifests incapable of deciding about their masses (and hence their speed, according to Relativity) and since it needs to make some grotesque hypothesis (of mysterious mechanisms) like those that assert that during their journey the neutrinos change their type (electronic, muonic, tauonic).

The author neither understands why mainstream Physics invokes as an argument, in favour of the neutrinos, the conservation of spin since, the spin being a vector, there seems to be no problem that the neutron, the proton and the electron have each a spin of modulus equal to 1/2hbar since it is possible to have two vectors whose modulus is 1/2hbar adding to give a resultant vector whose modulus is also 1/2hbar. Suppose for instance that the two component vectors (in this case the spins of the proton and of the electron, when inside the neutron) make an angle of 120º.

Relation between the binding energy and the mass defect.

The mass of a composite material body whose components are bound by internal forces (e.g. a nucleus, an atom, a neutron, ...) differs from the sum of the masses of its components by an amount called "mass defect".

For example:

A nucleus of Helium-4 is a bound system made by 2 protons and 2 neutrons. Calling m_He the mass of the Helium nucleus, m_P the mass of the proton and m_N the mass of the neutron it is observed experimentally that:

2 m_P + 2 m_N - m_He > 0

and the difference

(N-15) Dm_He = 2 m_P + 2 m_N - m_He

is called "mass defect" of the Helium-4 nucleus.

According to the mainstream interpretation induced by the theory of Relativity, "the energy has mass" (E = mc²) and the mass defect Dm of a bound material system is related with the binding energy E_B of its components by that same relation. i.e.

(N-16) Dm = E_B/c²

where the Binding energy E_B is equal to minus the sum of "the potential energy (negative in general) ascribed to the cohesion forces that keep the system bound" and "the kinetic energies of the component particles of the system".

For example, in an atomic nucleus in which the cohesion forces of the nucleons are the so called "strong force", the potential energy of the system (energy that should be spent to bring apart the nucleons overcoming those strong forces) is negative in sign but of big absolute value. The absolute value of such potential energy is much greater than the sum of the (positive) kinetic energies of the nucleons and therefore, on the whole, the binding energy E_B of an atomic nucleus is positive which would account for the fact that the mass defect of the atomic nuclei is also positive.

As another example, in the Hydrogen atom the cohesion force between the proton and the electron is the electromagnetic force. The potential energy of the atom, ascribed to the electromagnetic cohesion of its two components, is the electric potential energy of the electron whose absolute value k e²/r is, like it was said above in (N-6), twice the value of the kinetic energy of the electron. (The kinetic energy of the electron amounts to practically all the kinetic energy of the components of the atom because, in the reference frame associated to the centre of mass of the atom, the kinetic energy of the proton is negligible since its mass is much greater than that of the electron). It can therefore be assumed that the binding energy of the Hydrogen atom is:

(N-17) E_B = - (E_POT + E_CIN) = k e² / r - 1/2 m_e v² =

= k e² / r - k/2 e² / r = k/2 e² / r > 0

that being positive implies that the mass defect E_B/c² of the Hydrogen atom is also positive.

From a phenomenological point of view it is hard to understand that all energy, whatever its type, carries a mass associated with it (E=m c²). The EVE Model of the Aether suggests that, in respect to the internal energy of a system of particles, the following must be interpreted:

From a strict point of view, it is not the internal energy (or the binding energy) what increases the mass of the system when the energy is positive or decreases it when it is negative but it is the speed v of the component particles that is capable to implement a mass increase and it is the distance r of proximity of the particles that is capable to implement a mass decrease of the system.

In what respects the influence of the speed:

It is well known that according to the theory of Relativity the material particles exhibit a mass that increases with speed. More precisely, the apparent mass m(v) (called relativistic mass) of a material particle of nominal (rest) mass m₀ is:

(N-18)

For example, when a particle initially at rest acquires a speed v it suffers according to (N-18) a mass increase:

(N-19)

but according to the theory of Relativity the kinetic energy of a particle of mass m₀ and speed v is:

(N-20)

and therefore Relativity predicts indeed that when a body of mass m₀ is given a kinetic energy K(v) it suffers a mass increase Dm = K(v)/c²

For small speeds (v << c) the expression (N-19) can be approximated by:

(N-19b)

where E_CIN(v) = 1/2 m₀ v² is the Newtonian kinetic energy (valid for small speeds) of a particle of mass m₀.

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NOTE-1: The theory of Relativity, in spite of its correct prediction of this issue, does not explain what is mass and neither penetrates into the nature of inertia, leaving the feeling that the mass increase with speed is still a mystery.

The EVE Model of the Aether, though of course not claiming to say the last word, suggests the following explanation of the mass increase with speed:

The forces between material particles, and in particular the force between electrically charged particles, depends on the velocities of the particles as follows:

(It is not the magnetic force that is being analysed but a more general feature of forces due to which, for example, the force between 2 charged particles moving face to face along the same straight line does also depend on their velocities).

Let A be the particle "origin" of the force and let B be the particle target of the force that is being described. The particle A "originates" the force due to the redistribution of aetherino speeds that it produces. It happens according to the model that the aetherinical force suffered by B depends both on its absolute speed (across the local aether) and on the direction of the velocity of B relative to A. The most recent developments of the EVE Model of the Aether and in particular those of its Annex-A suggest that the force suffered by B decreases with its absolute speed u according to a law of the type:

(N-21)

where k_D is an adimensional constant that depends on the direction of the velocity of B relative to A. In particular, when B moves face to face towards or away from A (along the straight line AB) it is k_D = 1. The constant k_D takes smaller values for other relative directions reaching a minimum value (plausibly of the order of k_D = 0.3) for the case in which B moves in a direction perpendicular to the direction AB.

(Other analysis suggest that the factor (1- k_D u²/c²) is only an approximation of a more precise Gaussian function factor that decreases asymptotically towards 0 when u tends to infinity).

The assertion that the speed u is absolute (relative to the aether) has the consequence that the forces between material particles do not fulfil Newton's 3rd law (which is a common feature with the forces of the theory of Relativity). I.e. in general it will happen that F_AB =/= F_BA because A and B will have in general a different absolute speed. This is the reason that, in the high energy accelerators, the relativistic particles (of absolute speed close to c) when interacting with slow target particles cause to the later a great global speed increase while the fast incident particles loose in comparison only a small amount of their speed. Some paradoxes of Relativity can be removed acknowledging the influence of the absolute speeds. (Section 12 of the EVE Model, although pending a revision, treats this issue in greater detail).

Acknowledging also, as does the model, that an aetherinical force of strength F_AB produces on a particle B of mass m₀ an acceleration F_AB/m₀ , independently of the absolute speed of this particle, it is easier to understand why mainstream Physics, that does not recognize in its Theory that the force decreases according to (N-21), must describe the experiments asserting that the apparent (relativistic) mass of the moving particle increases with its speed. But according to the predictions of the aether model, the relativistic mass increase invoked by Relativity should be quantitatively corrected and be given by:

(N-22)

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In what respects the influence of the distance:

Strictly speaking, it is not the negative potential energy the ultimate cause of the mass decrease of a bound system of particles but the screening (to the aetherinos that come from outside) that the particles exert on each other due to their proximity. The distances between the particles are therefore the fundamental variables that condition the mass defect of the system commonly ascribed to the potential energy. What happens is that the potential energy is directly related to those distances. This relation is now analysed in the light of some assumptions:

In an aether model of aetherinos it is reasonable to suppose that the mass of an elementary particle is proportional to its cross section to aetherino collisions. Therefore the following hypothesis will be made:

(N-31) m_P = k₁ s_P

where m_P is the mass of the particle, s_P is the cross section (geometrical in the model) that the particle exhibits to collisions with aetherinos and k₁ a constant.

For example, in respect to inertial mass, the model finds fruitful to postulate that when an aetherino collides at a relative velocity v_R with a material particle of cross section s_P it gives to the particle an increment of velocity Dv = q v_R/s_P where q is a constant. From this postulate Newton's second law can be deduced. (In Section 2 of the EVE Model of the Aether an equivalent hypothesis is made, although its formulation and area of applicability are slightly different).

In respect to the gravitational mass, it is reasonable to expect that the bigger the cross section s_P (to aetherino collisions) of a material body, the greater will be the redistribution of aetherino speeds of the local aether that it originates, which implies a stronger gravitation field.

Example. Mass defect of the Hydrogen atom.

Let a be the "radius" of the proton. The cross section (geometric, in this context) exhibited by the proton to collisions with aetherinos will then be p a². (Since a different "radius" can be assigned to the proton in other contexts, perhaps here a more adequate name could be "aether-radius" of the proton).

NOTE-2. In the EVE model of the aether it is postulated that all material bodies are ultimately composed by a special type of particles called Simple Particles (SP) that are opaque to the aetherinos and whose geometric cross section is s. If it is supposed that the proton is made of n_P Simple Particles and, to simplify the description, it is supposed that those particles are sufficiently apart so that they do not screen themselves significantly, then on the whole the proton exhibits a cross section to aetherinical collisions equal to n_P s. But for the present purposes, and to simplify the description, the proton can instead be supposed to be an opaque sphere of radius a such that its cross section p a²= n_P s.

Similarly, let b be the "radius" (aether-radius) of the electron, having therefore a cross section p b².

It will also be supposed that the electron is much smaller than the proton, meaning b << a.

Let r be the radius of the electron orbit (around the proton) in the pertinent state of the Hydrogen atom. To simplify it will be considered a circular orbit.

If it is supposed, for description purposes, that both the proton and the electron are spheres of matter opaque to the aetherinos then the average cross section of the Hydrogen atom to aetherino collisions can be estimated for example as follows:

Consider the aetherinos that travel towards the atom along a given direction of space. To characterize the direction imagine a point O at an infinite distance of the atom. The pertinent aetherinos, whose screening by the atom wants to be calculated, will then be those travelling along the semi-direction OP that joins the point O with the proton. It could be the case that the atomic electron remains in an orbit whose plane is perpendicular to OP in which case the geometric section of the electron is always entirely contributing to the cross section of the atom. (From a strict point of view, this implies that the mass as has been defined in (N-31) depends on direction). But the particular cases are not of interest here. What is of interest is the average section presented by a statistical sample of atoms in which all possible orientations have the same probability. This average case can be considered represented by an imaginary atom in which the electron travels, instead of along a circular orbit, along a spherical surface of radius r, having the same probability to be found in any point of the sphere. The distant observer O will then observe that when the electron is in front or behind the proton, so that the straight line OE (O-Electron) intercepts the proton, then the electron does not screen any additional aetherino that the proton wouldn't have intercepted by itself. Since to single out the direction O is placed at an infinite distance, any straight line OE can be considered parallel to OP and therefore, in the sphere of radius r being travelled by the electron there are only two zones of areas approximately equal to p a²(the area projected by the proton in a sphere of radius r >> a) in which the electron does not contribute to the cross section of the atom.

For the purpose of evaluating the mass defect of the atom in a state in which the electron is supposed to travel a circular orbit of radius r, it can therefore be considered that the proton (bigger than the electron) does not contribute to the mass defect, since a cross section p a² is always entirely contributing, while the electron exhibits its section p b² only during the fraction of time at which it is neither in front nor behind the proton.

Since the spherical surface "travelled" by the electron in such "average atom" has an area 4p r², that means that the electron does not contribute to the cross section of the atom during a time fraction equal to 2p a² / (4p r²) and therefore the time fraction during which it does contribute is:

(N-32) (approximation for r >> a )

Hence, since the so called "mass of the electron" (the one it would have at rest, averaged for all directions of space, and at an infinite distance form all material bodies so that any distortion due to screening would have diluted into the statistical construction of the aether) is according to the hypothesis (N-31) equal to k₁ p b² , then the "mass defect" of the electron caused by its proximity to the proton would be:

(N-33)

because the "mass defect" of one particle can somehow be defined as:

nominal mass (isolated and at rest) - effective mass (in a specific scenario)

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But such Dm_e[r] would correspond only to the mass defect due to screening but otherwise it assumes that the electron is at rest and therefore does not include the correction due to speed mentioned above.

In respect to the increase of the apparent mass of the electron due to its speed, it must be realized that the electron ceases to exhibit itself to the aetherinos that reach it from the distant point O when its is screened by the proton, i.e. when it is behind the proton but not when it is in front. Hence the time fraction during which the electron actually receives aetherinos from the semi-direction OE and the speed of the electron must be taken into account is:

(N-34) (approximation for r >> a )

Before continuing the evaluation, an ad hoc correction must be made of the time fractions (N-32 and N-34) just discussed. It has been found in the tests that, using those time fractions f_D and f_V the model makes incorrect predictions of the atom's mass defect. "Correct" predictions are obtained when those expressions are replaced by the two following:

(N-32-b) (approximation for r >> a )

(N-34-b) (approximation for r >> a )

where j_D is the fraction of time during which the electron contributes to the mass of the atom in respect to screening corrections and j_V is the fraction of time during which is of application to the electron the mass correction due to speed.

(If possible will be added here a qualitative justification of these new time fractions j_D and j_V based on the hypothesis that the proton has a very flat (disk type) structure and on the hypothesis that the orbital plane of the electron is coincident with the "plane" of the proton). An alternative hypothesis would be that the mass defect prediction of the model based on the natural time fractions f_D [N-32] and f_V [N-34] is indeed correct and what must be revised is the mainstream assumption that the equation DE = Dm c² applies also to the potential energy (and not only to the kinetic energy).

The expression (N-33) giving the "proximity mass defect" of the electron must hence be replaced by:

(N-33-b)

In what refers to the contribution of the speed to the electron's mass defect" (actually here a negative mass defect or mass increase with speed), it is guessed that the expression (N-22) with a constant k_D = 1/2 represents adequately the mass of an electron of speed v averaged for all the possible directions of its velocity (in a statistical sample of atoms with orbits randomly aligned). Therefore, assuming that the average mass of the electron when in a state of speed v is:

(N-22-b)

the mass defect of the electron, due to its speed, that contributes during only a fraction f_V of the total time is:

(N-35)

(Note: Using the expression (N-18) of Relativity instead of (N-22-b) a quantitatively very similar result would be obtained).

and the total mass defect of the electron (and in this case also of the Hydrogen atom) due to both its distance to the proton and its speed is (after doing some algebra):

(N-36)

that, as said, is an average mass defect but also the one measured in normal experiments.

Considering now that, according to the classical mechanics description of an Hydrogen atom the orbital speed and the radius of the electron are related (equating the Newtonian centrifugal force to the Coulomb centripetal force) by:

(N-6) m_e v²/ r = k e² / r² => v² = k e² / (m_e r)

and interpreting that the mass m_e that appears in the expression of the centrifugal force is simply the "mass of the electron" (isolated and at rest) that in this context is k₁ p b², then:

(N-37)

that replaced in (N-36) leads to the following prediction of the model for the net mass defect of the Hydrogen atom:

(N-38)

where:

a   "radius" of the proton
b   "radius" of the electron
r    radius of the orbit of the electron
e   the elementary electric charge (that of the proton)
c   speed of light
k   Coulomb's constant
k₁ constant that relates in the model the mass of a particle with its cross section to the aetherinos

On the other hand, as recalled above in (N-17), classical Physics establishes that the "bounding energy" of an Hydrogen atom is equal to "minus the net energy of its electron", i.e.:

(N-17b) E_B = -(E_POT + E_CIN) = - ( - k e² / r + 1/2 m_e v²) = k e² /(2 r)

that implies a mass defect:

(N-40) dm = E_B/c² = k e² /(2 c² r)

The prediction (N-38) of the model here proposed has been compared with the calssical prediction (N-40) assigning to the constants somewhat arbitrary, though qualitatively reasonable, values. The agreement is "good" for many sets of constants.

Example 1. Taking arbitrarily:

c=1 a=1 b=0.1 e=1 k=1

a good fit is obtained as long as the constant k₁ is assigned the value k₁=43 as is shown in the two, very similar, following graphics:

Fig-1.In arbitrary units, mass defect of the Hydrogen
atom versus the radius of the electronic orbit.
(classic in blue; of the model in red).

(with the values assigned in this example to the constants, the speed of the electron in an orbit of radius r=1000, i.e. a thousand times the "aether-radius" of the proton, would be (see N-37) v = 0.086 c)

Example 2. Taking arbitrarily:

c=1 a=1 e=1 k=1 k₁=1

a good fit is obtained as long as the aether-radius b of the electron is assigned the value b=0.67

It is therefore recognized that several ambiguities remain to be solved by the model (like for instance physical relations between the constants c, e, k, k₁, b) before being able to predict, for example, how many times bigger is the radius a of the proton than the radius b of the electron. Part of the problem is that mainstream Physics doesn't help in this respect since it dosn't throw any light on the possible (and plausible) relations between its physical constants e, c, k,...

Binding energy of the neutron.

Let r_N be the orbital radius of the electron in the special neutronic orbit (for which the orbital angular speed of the electron is equal to the intrinsic angular speed of the proton).

If instead of the "neutronic" orbit, the orbit of radius r_N were a "normal" (hydrogen-type) orbit (in which the electron suffers a centripetal force corresponding to an averaged aetherinical field of the proton instead of being anchored in front of the intense zone) then the classic kinetic energy (1/2 m_e v²) of such "normally-behaved" electron would be according to (N-6):

(N-44) 1/2 m_e v² = k e² / (2 r_N)

But if the orbit of radius r_N is the neutronic orbit, the kinetic energy of the electron is g times the former because, as was said above in (N-3), in the neutronic orbit the electron suffers a centripetal force:

(N-3-b) (with g > 2)

that equating, the centrifugal and the centripetal forces, now predicts

(N-45) 1/2 m_e v_N² = g k e² / (2 r_N)

Hence, in a neutronic orbit of radius r_N the electron has g times more kinetic energy than it would have if the orbit of radius r_N was not neutronic but governed by the standard (averaged) centripetal force of the proton. It is also true that the potential energy that mainstream Physics would assign to such neutronic orbit would also be g times bigger than the energy it would assign to it if such orbit of radius r_N was not neutronic, but as has been explained, in what respects the mass defect the basic conditionant is not the nominal potential energy of the electron but its proximity to the proton (that in this comparison has been supposed the same to that of an hypothetic non-neutronic orbit). Therefore, supposing g > 2, it can be understood that the electron can have, due to its greater speed at the same hypothetical distance to the proton, a negative mass defect.

The mass defect of the neutron predicted by the model can be obtained following the same steps that were done above to calculate that of the Hydrogen atom, but substituting now (N-37) by:

(N-37-b)

that leads to:

(N-46)

that corresponds simply to (N-38) where the constant k has been replaced by g k.

It can be seen that assigning the constants {e, c, k₁, k, a, b} the same values of the above example and taking g > 2, the prediction is that (independently of the orbital radius r as long that r > a) the mass defect of the neutron is always negative which is consistent with the experimental fact that the mass of the neutron is bigger that the sum of the masses of a proton and an electron.

(It can also be seen that with the above set of constants, i.e. {c=1, e=1, k=1, k₁=43, b=0.1} together with g=2.1 and supposing that the electronic orbit that fulfils the angular speed equality condition is for example that of a radius r = 50, the orbital speed of the electron (predicted by N-37-b) would be v = 0.18 c)

Foot Notes:

N-a: Strictly speaking, the force, corrected by speed, that the proton exerts on an electron of speed v is according to the analysis of other sections of the "EVE Model of the Aether":

(N-2)

(although plausibly the factor (1- k_D v²/c²) is just an approximation of a more precise Gaussian type function that decreases asymptotically towards 0 as v tends to infinity).

Since the correction (N-2) does not affect significantly the introductory description it will not be considered here but only below when dealing with the "mass defect".

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