It is known in physics the concept of “Copenhagen quantum vacuum”, with string-like vortex-tubes of magnetic field generated as quantum fluctuations in the quantum vacuum [1][2], this concept being connected to the Copenhagen interpretation (Bohr/Heisenberg’s view of measurement & reality) with the concept of “quantum vacuum” state, (the lowest energy state, filled with virtual particle-antiparticle pairs, generated by energy fluctuations and leading to effects like vacuum polarization).

It is also known the concept of “quantum turbulence”, related to the turbulent flow of quantum fluids at high flow rates, as in the case of a superfluid, in which a form of turbulence might be possible via the quantized vortex-lines [3], (idea first suggested by Richard Feynman).

The mathematical study of vortices began with Herman von Helmholtz’s pioneering study in 1858 and it was pursued by the Maxwell’s vortex analogy for the electromagnetic field and by William Thomson’s (Lord Kelvin) theory of the vortical atom, conceived as a vortex ring in the cosmic ether considered as super-fluid, (perfect fluid) [4]. During the Maxwell’s life, the basic laws of vortices in a perfect fluid in three-dimensional Euclidean space had been established.

Superfluidity arises as a consequence of the dispersion relation of elementary excitations, in fluids that exhibit this behaviour flow without viscosity (which in classical fluids causes dissipation of kinetic energy into heat, damping out motion of the fluid).

Landau predicted [5] that if a superfluid flows faster than a certain critical velocity v_c (or if an object moves with v < v c in a static fluid), it becomes energetically favourable to generate quasiparticles and thermal excitations (rotons) are emitted, as in helium II, for example.

Quantum vortices were observed experimentally in type-II superconductors (the Abrikosov vortex [6]), liquid helium, and atomic gases (forming Bose-Einstein condensate), as well as in photon fields (optical vortex) and exciton-polariton superfluids.

A topological defect in three-dimensional space, which is characterized by the nontrivial first homotopy group, is known as the Abrikosov-Nielsen-Olesen (ANO) vortex [7], the vortex being described classically in terms of a spin-zero (Higgs) field that condenses and of a spin-one field corresponding to the spontaneously broken gauge group.

Even if the superfluid is irrotational, if an enclosed region contains a smaller region with an absence of superfluidity, for example, with a rod, a vortex is generated, with the circulation:

where ħ = h/2π, h is the Planck constant, m is the mass of the superfluid particle, and ∇ ϕ v is the total phase difference around the vortex.

Because the wave-function must return to its same value after an integer number of turns around the vortex (similar to what is described in the Bohr model), then ∇ ϕ v = 2 π n , where n is an integer. Thus, the circulation is quantized.

So, in a superfluid, a quantum vortex “carries” quantized orbital angular momentum, but in a superconductor, the vortex also carries a quantized magnetic flux, over some enclosed area S:

where A is the vector potential of the magnetic induction B.

In a nonlinear quantum fluid, the dynamics and configurations of the vortex cores can be studied in terms of effective vortex-vortex pair interactions.

In an author’s Cold Genesis theory (CGT [8]-[10]), the sub-quantum medium—considered by the Bohm-Vigier’s theory, is composed by two main categories of etherons: gravitonic etherons, (pseudo-gravitons) with mass m_s ≈ 10⁻⁷¹ - 10⁻⁶⁸ kg, considered as quanta of the gravitational field, (in a Fatio-LeSage type model) and “sinergonic” etherons, with mass m_s ≈ 10⁻⁶¹ - 10⁻⁵⁸ kg, that contribute to the gravitational fields but which also give phenomenologically the magnetic potential A by a wind-like (field-like) component.

It was argued that the “dark energy” which is considered as the cause of the cosmic expansion in astrophysics, can be considered a wind-like uncompensated component of the etheronic, sub-quantum medium [8]-[10].

In CGT it vas also argued that the lightest photonic quanta, named “quantons”, of mass m_h = h/c² = 7.37 × 10⁻⁵¹ kg, can be attracted toward the kernel of a vector photons m_v (particularly—vectons’, of mass m_v ≈ 2.3 × 10⁻⁴⁰ kg, considered as E-field’ quanta) by a gravito-magnetic force F_gm given by the gradient of the gravito-magnetic potential V g m ( r ) , produced by vortexes “sinergons”,

(with: γ → 1 ; υ h ( r h ) —the quanton’s volume and: p φ = ρ φ w —the impulse density of the vortexed sinergons), and by a “sinergonic” force of Magnus-type given by a magneto-gravitic potential, V m g ( r ) :

with: Γ h —the sinergons’ circulation at the quanton’s surface, of radius r_h, rotated with c-speed around the vector photon’s kerneloid of mass m_f, through a brownian etheronic medium of density ρ s ( r ) having the same variation as that of the vortexed sinergons, Γ μ ( r ) : ρ s ( r ) = ρ s 0 ⋅ ( r 0 / r ) ~ ρ s v ( r ) , this Γ μ -vortex of quantons being stable by the condition:

F s l = F c f of the quanton’s maintaining on the vortex-line of r-radius, with F c f —the centrifugal force:

with: ρ s 0 —the density of “sinergons” at the surface of the vecton’s centroid, by considering the quanton as cylindrical, of lenght l h = 2 r h and density ρ h [9][10].

The value of w-speed results in CGT as the maximal speed of photon’s “falling” in a gravitational field, at blue-shift, (in a Fatio/LeSage model of gravitation) corresponding to m f ( v ) = m f 0 / ( 1 − v 2 / w ) , ( w = 2 c —apparent variation of photon’ mass [10]), giving:

As argument for the vortical nature of the magnetic moment can be also mentioned the fact that at neutron’s transforming, the beta-electron is expelled with relativist speed, v e → c , (∼0.92c). As consequence, a system of three magnetically coupled atoms must have a rotation around its median atom, in vacuum, at T → 0   K , conform to CGT.

It results logically that in non-equilibrium conditions, when F s l > F c f , the sinergonic vortices can explain the forming of the photonic and electronic centroids and kerneloids.

In this paper, we analyze the critical values of etherono-quantonic vortex densities which can generate the confining of quantons up to the forming of centroids and kerneloids of electrons and vector photons, particularly—of “vectons”, ( m v ≈ 2.3 × 10 − 40 kg [8][9]).

In CGT, the relation: 2 π a 3 ⋅ ρ a = m e _, between the electron’s mass, its classical radius specific to its e-charge contained in its spherical surface, ( a = 1 / 2 a c l = 1.4085 ≈ 1.41   fm ) and its photons’ density at its surface: ρ a ( a ) = μ 0 / k 1 2 = 5.16 × 10 13 kg/m³, ( k 1 = 4 π a 2 / e = 1.56 × 10 − 10 m²/C; e—electron’s charge), was obtained_. [8][9] from the relation:

Because in CGT the electron’ mass is given by a quantity of photons confined by the etherono-quantonic vortex Γ μ ( r ) = 2 π r c of the electron’s magnetic moment, formed around its centroid, according to another relation of CGT which states that the density of confined photons, ρ f , is proportional to the local value of the magnetic induction [8][9]:

( ρ c v c —the impulse density of the quantonic vortex Γ μ ( r ) ), it results that the density: ρ 2 = ρ ( a ) can be interpreted, by the relation: m e = 2 π a 3 ⋅ ρ a , as a mean density of a cylindrical electron of the same radius, a, and a high l a = 2 a , given by confined photons.

Relation (7) can be also obtained by the equality: E = B⋅c which is valid for r ≤ r μ = λ / 2 π , ( λ = h / m e c ), and which gives: ε 0 E 2 = B 2 / μ 0 , ⇒   ∈ E 0   =   ∈ B 0 , i.e.:

From Equation (7), it results that ρ f ( a ) = ρ c ( a ) , (meaning that the mean density of a cylindrical electron is equal to the density of quantonic vortex Γ μ ( r ) at r = a ), and by generalizing, we can conclude that between the radius r_k and the mass m_k of a centroid or kerneloid of an electron or of a vector photon and the induction B_k of the magnetic field which generate a such centroid or kerneloid exists the relation:

where—because m k < m k ( e ) , ρ k cannot be lower than the density of the electronic centroid, respective—kerneloid (the centroid of the kerneloid being considerd as stably formed when its density exceed a critical density, higher than that corresponding to an electronic centroid, respective—kerneloid, i.e.:

In CGT [8][9], the electron’s centroid resulted as a half of an electron neutrino, considered with upper limit of rest mass m ν ≈ 10 − 4 m e , (mass limit: 60 eV/c²), according to older experiments [11], so—with a mass: m₀ ≈ 5 × 10⁻³⁵ kg, and it was identified with the scattering centers considered as nucleonic current quarks, in the Standard Model, so—with a radius: r₀ = 0.43 × 10⁻¹⁸ m, according to the experimental data [12], this value being concordant with that of the centers of X-rays scattering on electrons [13], (considered as the real radius of electron, in the Standard Model, but as radius of the electron’s centroid, in CGT).

So, in CGT, the density of the electron’s centroid-considered as quasi-cylindrical, in CGT, results of value: ρ 0 ≈ m 0 2 π r 0 3 = 10 20 kg / m 3 .

By Equation (10) this corresponds to a value of B-induction of the confining magnetic field, of value: 42.18 × 10¹⁷ T—a very high value, compared also to that of the highest magnetaric field considered in astrophysics: more than 10¹¹ T [14].

The question is: if after an intermediary critical density: ρ i < ρ k = 10 20 kg / m 3 , the centroidic pre-cluster of confined photons could form the final centroid by an auto-confining process.

The answer to this question can be obtained by the CGT’s model of vector photon forming, with kerneloid containing its inertial mass and an evanescent shell of quantons (for the light photons ) or mixture of quantons and kerneloids of light photons—for the heavy vector photon. We identify two theoretical cases:

A.The forming of centroids and kerneloids of photons and of electrons from a vortex of quantons having the mean speedv_c=c:

a1) The B ⁰ -field values of the forming of photonic and electronic centroids and kerneloids

It is known that the drag force in a superfluid is complex and often results in cancellation (zero drag) in the pure superfluid regime, but can appear as viscous-like ( F ∝ v ) at low speeds or as turbulent/wave-like ( F ∝ v 2 ) at higher speeds, involving quasiparticles, quantized vortices [15].In CGT [8][9], from Equation (5) it results that the dynamic equilibrium which maintains the quantonic vortex around the electon’s centroid m₀ is realized by the resulting condition: 4 π r h 2 k v ρ s 0 ⋅ r 0 = m h = h / c , i.e.—by the condition: ρ s 0 k v r 0 = m h / 4 π r h 2 = 1 2 ρ h ⋅ r h = constant .

With the value resulting from Ref. [9] for the ratio: k h = 2 π r h 2 / m h = 27.4 , (giving r h = 1.79 × 10 − 2   m —the gauge radius of the quanton), it results [10]:

The quanton’s c-speed can be maintained by a dynamic equilibrium of etheronic pressure forces F^t on the tangent direction, considered of Stokes type (F^t ∼ v), specific to a laminary flowing of the sinergonic fluid in report to the quantons, and given by the Γ_a—vortex having an impulse density ρ s ( r ) = ρ s ( r ) w and by the density ρ s ( r ) of Brownian (pseudostationary) sinergonic medium which generates a drag force: F r t = F a t ( r ) .

At dynamic equilibrium, with k ′ ρ ≈ k ρ (proportionality coefficient), we have [10]:

with γ → 1 and k ρ ≪ 1 —coefficient which take into account the particle’s radius (and its surface of interaction with the sinergonic medium, S_i) and the super-fluidity of the etherono-quantonic medium by its low kinematic viscosity (the d’Alembert paradoxe [16]), the same type of medium and the same interaction surface implying the equality k ′ ρ ≈ k ρ .

Particularizing for the case of the electron’s magnetic moment vortex, Γ μ e , for which Refs. [8][9] gives a density: ρ c ( a ) = ρ μ ( a ) = ρ e ( a ) = μ 0 / k 1 2 = 5.16 × 10 13   kg , (a ≈ 1.41 fm), and by using the formula: B = k 1 ρ c v v for the electron’s B-field [8][9], with v_v = c for r ≤ r λ c , using Equation (7) for the magnetic induction, it results that the magnetic potential is :

By taking γ = 1 , ( w = 2 c [9][10]), it results: ρ s ( a ) = 0.29 ρ c ( a ) ≈ 1.5 × 10 13 kg / m 3 .

From Equation (11) we also have: ρ s ( a ) = 1.825 × 10 − 2 / a ⋅ k v , resulting that: k v ≈ 0.86 [10], (v_h ≈ 0.86c—plausible value, being close to c), so—for r 0 e ≈ 0.43 × 10 − 18 , (considered as electron centroid’s radius, in CGT[10]), by Equation (11) we obtain: ρ s 0 ( r 0 e ) ≈ a ⋅ ρ s ( a ) r 0 e ≈ 0.49 × 10 17 kg / m 3 , for the electron’ centroid, (of radius r₀^e).

Also, for the electron’s kerneloid, of radius: r k e ≈ 10 − 17   m , in CGT [10], (corresponding to the experimentally determined electron’s radius reported by Milloni [17]), we obtain: ρ s 0 ( r k e ) ≈ a ⋅ ρ s ( a ) r k e ≈ 0.21 × 10 16 kg / m 3 .

Also, with the obtained values, considering and the possibility of vecton’s attraction in the magnetic field of the electron’s centroid/kerneloid, if we take the same k_v—value for the sinergonic vortex formed around the vecton’s centroid and around the quantons and quantonic cluster of smaller mass which form its kerneloidic shell, considering that the electron’s centroid is formed as compact cluster of centroids of vectons of mass m v 0 having approximately the same density: ρ v 0 ≈ ρ 0 = 10 20 kg / m 3 , it is possible to estimate the radius: r_vo of the vecton’s centroid by Equation (5) in which we replace r_h with r_vo and m_h with m v 0 , i.e. by the resulting relation of vecton’s maintaining at the surface of electron’s centroid, m₀:

which gives: r v 0 ≈ 3.6 × 10 − 22   m ; ρ s 0 ( r v 0 ) ≈ 5.8 × 10 19 kg / m 3 , (the density of sinergons which maintains vortexed quantons at the vectonic centroid’s surface) and: m v 0 = 2.93 × 10 − 44   kg .

With the obtained values of ρ s 0 it results by Equations (12), (14), with γ = 1 , that:

So, for the electron’ centroid, Equation (16), gives: ρ s v 0 ( r 0 ) = 1.2 × 10 17 kg / m 3 , which by Equation (7) for B 0 corresponds to: ρ c 0 ( r 0 ) = 2 ρ s v 0 = 1.69 × 10 17 kg / m 3 , and to a magnetic induction: B 0 ( r 0 ) = 0.79 × 10 16   T at r = r 0 from the center of the vortex-tube ξ B 0 which can form the electron’s centroid, considering a vectonic kerneloid as pre-kerneloid, (with r v k ≈ 10 − 20   m ).Similarly, for the forming of electron’s kerneloid ( ρ s 0 ( r k e ) ≈ 0.21 × 10 16 kg / m 3 ) it results: ρ s v 0 ( r k ) = 0.51 × 10 16 kg / m 3 and ρ s 0 ( r k ) = 2 ρ s v 0 = 0.73 × 10 16 kg / m 3 , corresponding by Equation (7), to: B 0 ( r k ) = 0.34 × 10 15   T .For the forming of the vecton’s centroid, we obtain by Equations (15) and (16): ρ s 0 ( r v 0 ) ≈ 5.8 × 10 19 kg / m 3 ρ s v 0 ( r v 0 ) = 1.41 × 10 20 kg / m 3 , which—by Equation (13), corresponds to: ρ c 0 = 2 ρ s v 0 = 1.98 × 10 20 kg / m 3 and to a magnetic induction: B 0 ( r v 0 ) = 9.3 × 10 18   T of the vortex-tube ξ B 0 which can form the vecton’s centroid, conform to CGT.

Also, considering a vecton’s kerneloid of radius ( r v k ) ≈ 10 − 20   m , containing its inertial mass, (value corresponding to a density ρ v 0 ≈ 3.6 × 10 19 kg / m 3 of its inertial mass:

m v ≈ 2.3 × 10 − 40   kg [8][9]), similarly are obtained the values: ρ s 0 ( r v ) ≈ 2.1 × 10 18 kg / m 3 ; ρ s v 0 ( r v ) = 5.12 × 10 18 kg / m 3 ; B 0 ( r v k ) = 3.37 × 10 17   T , for the vecton’s kerneloid forming.

Because the increasing of the ratio ρ s / ρ s v lowers the quantons’ v_c-speed (at ρ ′ s > ρ s 0 ( r v ) , conform to Equation (12)) permitting the forming of a vectonic centroid inside a partially collapsed vectonic pre-kerneloid, we can consider the value B 0 ( r v k ) as critical value for the vecton’s forming from quantons having the c-speed.

So, the obtained values for ρ s 0 ( r v ) , ρ s v 0 ( r v ) and B 0 ( r v k ) = 3.37 × 10 17   T can be considered as critical values specific to the actual cosmic era, (specific to v c ≈ c ), for the forming of centroids and kerneloids of vectons and of electrons from a primordial dark energy composed by an etherono-quantonic brownian component and a wind-like etherono-quantonic component with quantons having v c ≈ c , because we observe—by Equation (12), that for a density of the etheronic medium: ρ s > ρ s 0 , the attractive etheronic force F s l exceeds the centrifugal force F c f ( v h ) and the quanton’ speed decreases to a value v h < c , so we can conclude that in this case ( ρ s > ρ s 0 ) the cluster of vortexed quantons or of quantons and light photons vortically attracted by the etherono-quantonic vortex of a pre-centroid approximated as being a vectonic centroid, could generate centroids and kerneloids of heavier vector photons and of electrons, also by auto-confining, i.e. by the vortex-tubes ξ B of the B-field formed around its pre-centroids, of mass given by the confination of slowed quantons, ( i.e. by the force F g m ( r ) ), at intensities of the B-field lower than that given by Equation (10), with: 10 20 kg / m 3 ≥ ρ k > ρ c 0 ( r v k ) ≈ 7.2 × 10 18 kg / m 3 ,i.e. lower than 46.6 × 10¹⁷ T but higher than 3.37 × 10¹⁷ T—for the cold forming of vectons and of electron centroids.The A—value which characterizes the density of the sinergonic winds which generate etheronic vortex around a vectonic kerneloid in the process of its forming results—according to the previous conclusions, of value given by Equation (13):

This A-potential associated to sinergonic winds of the quantum vacuum can also explain the inertial forces: F_i = ma_i in the form: F_i ~ m(dA/dt), (Aharonov-Bohm effect for photons).

a2) The vortical model of vector photon and of electron with v_c = c for r ≤ r_λ

From Equation (5) it also results that if the density ρ s ( r 0 ) of sinergons accumulated by the Γ μ -vortex is lower than the critical value ρ s 0 ( r k ) specific to the kerneloid’s forming by a vortex-tube ξ B , (for example—as consequence of the electron’s spin precession), the attracted vectons are thereafter expelled from the electron’s quantum volume of a-radius, as consequence of the variation with r^-1 of the centrifugal force, explaining the electron’s electric field, E(r), conform to CGT [8][9].

The force F g m ( r ) = − ∇ V g m ( r ) , of etheronic density gradient, acting over the vortexed quantons, results of neglijible value compared to the etheronic force of Magnus type, F g m ( r ) = F s l ( r ) , given by Equation (12).

For example, for the electron’s vortex of quantons, by the values obtained in CGT: r h = 1.79 × 10 − 25   m , r 0 = 0.43 × 10 − 18   m , ρ s v 0 ( r 0 ) ≈ 1.2 × 10 17 kg / m 3 , it results by Equation (3) that: F g m ( r 0 ) = 0.6 × 10 − 21   N , which can confine only quantons having the speed: v h ( r 0 ) = ( r 0 / m h ) F g m ( r 0 ) < 1.87 × 10 5 m / s , while for F g m ( r ) = F s l ( r ) , with the corresponding value: ρ s 0 ( r 0 ) ≈ 0.49 × 10 17 kg / m 3 , obtained by (11), by Equation (4) it results: F s l ( r 0 ) = 1.54 × 10 − 15   N , with five size order higher (which can confine and quantons with v c → c ).

However, the force F g m ( r ) is enough strong for maintain the confined quantons, slowed to v h ( r 0 ) , in the volume of formed centriod/kerneloid, when ρ s > ρ s 0 ( r 0 ) .

We can also conclude that after the forming of the electron’s centroid and of its kerneloid and the decreasing of the density of sinergons to the value ρ s 0 ( r v ) → 2.1 × 10 18 kg / m 3 , the etherono-quantonic vortex of the electronic kerneloid’s magnetic moment is auto-sustained by a possible spiral form of the electron’s centroid, (of twisted yarn bundle type)—in CGT, characterizing its chirality, ς e = ± 1 , and this Γ μ e -vortex explains the volume of confined ‘heavy’ photons, (‘naked’ photons, virtually reduced to their inertial mass m_f), of classic radius: a = 1.41 fm, conform to CGT [8][9].

The actual density of the etheronic medium, given by pseudo-gravitonic and sinergonic etherons: ρ e t ∗ = ρ g ∗ + ρ s ∗ can be approximated by the conclusion that the maintaining of the electron’s etherono-quantonic vortex Γ μ e ( r ) with an impulse density p s v = ρ s v w specific to the value of its magnetic moment μ e corresponds to the obtained critical values ρ s 0 ( r 0 e ) ≈ 0.49 × 10 17 kg / m 3 and ρ s v 0 ( r 0 e ) ≈ 1.195 × 10 17 kg / m 3 , because the fact that the mass of electron’s centroid is not increased indicates that the quantons having the light speed c are expelled from the surface of its centroid of r 0 e -radius.

However, for explain the stability of the formed fermions, it is necessary to consider that the density ρ s ( r ) corresponds to sinergonic etherons vortically accumulated by the sinergonic vortex Γ s v ( r ) of lighter sinergons, from an initially homogenous medium of mixed etherons: pseudo-gravitonic and sinergonic etherons, with a continuous speeds’ distribution but theoretically reduced to two components: a brownian one (giving static pressure P s = ρ s c 2 ) and a wind-like component of mean speed w , resulting from components reduced theoretically to a mean component with dynamic pressure: P d = 1 2 ρ d w 2 , (c—the light’s speed).

So, for a super-fluid etherono-quantonic medium it results that the value:

ρ s ∗ ≈ ρ s 0 ( r 0 e ) + ρ s v 0 ( r 0 e ) = 1.685 × 10 17 kg / m 3 also corresponds, approximately, to the density of the etheronic medium ρ e t ∗ of pseudo-gravitonic and sinergonic etherons, which is characterized by the applicability of the Bernoulli’s law in its simplest form: ρ e s + ρ e v = ρ e t = constant , having a etheron’s mass-depending kinematic viscosity, ν ( m g ) .

This determines a much lower resistance force to the advancing with relativist speed v → c of quantons in a medium of pseudo-gravitonic etherons than that of the advancing in a medium of sinergonic etherons, (because ν ( m g ) ≪ ν ( m s ) ).

In consequence, we can approximate that the value of the ρ g ∗ -component, of pseudogravitons, ( ρ g ∗ = ρ e t ∗ − ρ s ∗ ), will not change significantly Equation (12) of dynamic equilibrium, (generated by the sinergonic component), which explains the maintaining of the fermion’s vortex: Γ μ ( r ) = 2 π r c of its magnetic moment, i.e. with v c = c up to r = r λ = λ / 2 π .

But relating to Equation(11), the density ρ g ∗ of this medium of pseudo-gravitons, will influence the interaction of the etheronic brownian component with the quanton’s sinergonic vortex by an increased total density of the brownian component of etheronic medium, ρ r e ( r ) , which also increases the magneto-gravitic (etheronic) force F s l ( r ) , as consequence to the fact that the acting of ρ g ∗ in report to the sinergons of the quanton’s vortex Γ h is significant.

In this case, this F s l ( r ) -force has a much slower decreasing with the distance r, determining the vortically attraction toward the fermion’s center of quantons and vector photons which at the surface of the fermion’s centroid are expelled with c-speed by the centrifugal force F c f ( r ) from the fermion’s proximity, on a pseudo-radial trajectory, conform to the resulting model (Figure 1).

It is explained in tis case the fact that—in the vecton’s case, even if its magnetic moment μ v is much smaller than the electron’s magnetic moment ( μ v < μ e ), corresponding to a lower density of accumulated sinergons, ρ s ( r ) , the magneto-gravitic (etheronic) force F s l ( r ) can exceed the centrifugal force, for r > r 0 e , determining the forming of the vecton’s quantonic vortex, of radius r λ = λ / 2 π = h / 2 π m f c , even if these quantons have the c-speed up to r = r λ .

The variation: v c ≈ c ( r λ / r ) of the quantons’ speed for r > r λ = λ / 2 π , in the Γ μ -vortex can be explained in accordance with Equation (12) by a density’ variation: ρ s v ( r ) ~ r − 2 , for r > r λ :

which gives v c ( r λ ) = c for r = r λ , the variation of v_c being conform to the vortex’ law.

The increasing of the ratio: ( w − v c ) / ( w − c ) with r, corresponds to the conclusions that the quantonic vortex is formed by gradually attraction and acceleration of quantons, by the sinergonic vortex formed around the fermion’s centroid up to the reaching of the c-speed at r = r λ , being thereafter expelled at the kerneloid’s surface.

B.The forming of centroids and kerneloids of photons and of electrons from avortex of quantons having the mean speedv_c<c

We observe from Equations (4), (5), (11) and (12), that for the same ratio: k v = v h / v c , if the mean speed of the vortexed quantons is lower than the light speed, ( v c < c ), the critical value ρ s 0 resulting from Equations (5), (11), remains the same as in case ( v c = c ) but the ratio: ρ s v ( r ) / ρ s ( r ) = v c / ( w − v c ) decreases. If v c = k c c , ( k c < 1 ), with w ≈ 2 c , it results that:

This means that the pre-centroid of vector photons and of electrons could be formed also by slowed quantons, ( v c < c ), by a lower value of the confining B-field, given by Equation (13), ( B = k 1 ρ s v ( r ) w ).

The question is: if the formed centroids could be stable at v c ≪ c .

Supposing that the density ρ s ( r 0 ) is lower than the critical value ρ s 0 ( r 0 ) , in this case the Magnus-type sinergonic force F s l ( r ) cannot confine vortexed quantons.

But we can deduce the quantons’ speed v c 1 for which the gravito-magnetic force: F g m ( r ) = − ∇ V g m ( r ) still can confine vortexed quantons.

Because this F g m —force is much weaker than the magneto-gravitic force F s l , it is logical that v c 1 ≪ c . In this case we have:

( w ≈ 2 c ; v c = k c ⋅ c ) . At r = r 0 , using also Equation (18), it results that:

Taking a value: ρ s c ( r 0 ) < 0.49 × 10 17 kg / m 3 , for example: ρ s c ( r 0 ) = 10 16 kg / m 3 , it results: k c ≈ 2.3 × 10 − 8 , giving: v c 1 ≈ 6.9   m / s and: ρ s v c ( r 0 ) ≈ ρ s c ( r 0 ) k c / 2 = 1.63 × 10 8 kg / m 3 corresponding to a critical value: B c ( r 0 ) = k 1 ρ s v c ( r 0 ) w ≈ k 1 ρ s c ( r 0 ) k c c ≈ 5.27 × 10 7   T .

It results in consequence the next scenarios of the cold forming of centroids and kerneloids of vector photons and of electrons in the Proto-Universe’s forming period:

a) either from confined quantons of relativist mean speed: v c ≈ c , at high intensities of B-field corresponding to the formed etherono-quantonic vortex-tubes ξ B , ( B = B 0 ( r v k ) ) and to a sinergonic density higher than the critical value ρ s 0 ( r 0 k ) of case A;

b) or at densities of the sinergonic medium lower than the critical value ρ s 0 ( r 0 ) and at lower intensities of the B-field corresponding to the formed etherono-quantonic vortex-tubes ξ B , ( B < B 0 ( r v k ) ) , but from slowed vortexed quantons, having v c < c ;

c) or the cold genesis of centroids and kerneloids of vector photons and of electrons at densities of the sinergonic medium higher than the critical value ρ s 0 ( r v ) and at lower intensities of the B-field corresponding to the formed etherono-quantonic vortex-tubes ξ B , ( B < B 0 ( r v k ) ) , from initially slowed vortexed quantons, having v c < c , which finally, at: ρ s ( r v ) = ρ s 0 ( r v k ) and B = B 0 ( r v ) , were vortexed with mean speed v c ≈ c , this evolution being specific to a high mass of vortexed sinergons and quantons with constant impulse moment: L h = m h ⋅ r ⋅ v c ( r ) , which has a density of the sinergonic medium initially lower than the critical value ρ s 0 ( r v ) , and a high radius which is gradually decreased with the increasing of the ρ s 0 -density until the actual critical value ρ s 0 ( r v ) .

In our opinion, this c)-variant is more explanatory.

Conform to the model, the further increasing of the fermion’s centroid or of its kerneloid is impeded by a repulsive field/potential V r ( r ) ~ ρ s 0 ( r ) of short range, given by the kerneloid’s zeroth vibrations of spin precession [9][18], which determine the quasi-radial emission of sinergons and quantons from the kerneloid’ surface and which transform a quasi-cylindrical (barrel-like) electron into a quasi-sperical one, ( ρ s ~ r − 2 ) with specific variation of its field: ( B ( r ) = E ( r ) / c ~ r − 2 , for r ≤ r λ , this spin precession movement determining a exponential variation of the densities ρ s ; ρ s v 0 , at least inside the fermion’s kerneloid.

This conclusion corresponds to the Copenhagen-like conclusion [1][2] which considers a vortex-tube of magnetic H-field in the quantum vacuum as a fluctuation ρ_f of the vacuum value of the flux ϕ resulting from a Higgs-like potential: V ( ϕ ) = − c 2 | ϕ | 2 + c 4 | ϕ | 4 whose minimal value: | ϕ | = ϕ 0 = c 2 / 2 c 4 characterizes the vacuum-value of the field | ϕ | and gives an equation of motion:

(e—the electron’ charge, A μ —the magnetic potential), resulting that:

the value: κ = 1 / 2 representing the distance until the | ϕ | -field reaches its vacuum value ϕ 0 , but with the difference that the variation: | A | ~ r − 1 corresponds—by (13), to a variation: B ( r ) ~ r − 2 , characteristic to a < r < r λ and to a e-charge with precession movement, whose μ e -magnetic moment is similar to a magnetic vortex-tube ξ B but with: B ( r ) ~ r − 2 for r ≤ r λ .

Also, the first and the second terms of the Higgs—like potential corresponds in CGT to the gravito-magnetic potential

and to the mentioned repulsive potential V r ( r ) , i.e.:

But unlike CGT, the Standard Model considers that the formation of rest mass of elementary particles implies an exchange of a virtual Higgs boson between coupled particles, resulting in classical potentials of the form: V H ( r ) = m i m j m H 2 1 4 π r e − m H c ⋅ r / ℏ with a Higgs mass: m_H = 125.18 GeV/c², which gives an action range equal to the reduced Compton wavelength of m_H: 1.576 × 10⁻¹⁸ m, (of about 10¹⁸ times weaker than the weak interaction between two electrons).

In CGT, this explanation of the formation of particle’s rest mass results as speculative and unnecessary, as in the case of the Einsteinian relation of mass increasing by the particle’s speed contrary to the law of substance-energy conservation.

Also, the ‘vacuum catastrophe’ theoretic problem of the Standard Model, (a very high density of the quantum vacuum, which can impede even the atomic electrons’ rotation) is avoided by the previous model of the cold genesis of photons and electrons.