Analogies and Differences Between the Particle' Model Used in a Cold

Physics & Astronomy International Journal

Opinion Open Access Analogies and differences between the particle’ model used in a Cold Genesis Theory and those used in the Standard Model

Abstract Volume 5 Issue 2 - 2021 The main particularities of the vortexial model of particles resulted in a cold genesis Arghirescu Marius theory of the author (CGT) are compared by those corresponding to the Standard Model State Office for Inventions and Trademarks, Patents Department, of particles. It is argued that the interaction mechanism by intermediary Z–boson and Romania respective– by ‘color’ charges and gluons, considered by the Standard Model for the weak and the strong and nuclear interactions, is semi–formal, a more natural explanation for these Correspondence: Arghirescu Marius, State Office for interactions being given in CGT by a multi–vortexial model of proton– resulted in CGT as Inventions and Trademarks, Patents Department, Romania, −+ non– destructive collapsed clusters of paired quasi electrons ( ee**) and by its resulted Tel 0040745795507, Email vortexial field, which imply also a specific “bag” model of inter–quarks interaction, a Received: June 27, 2021 | Published: August 16, 2021 “dynamide” model of neutron, with degenerate negatron rotated around the protonic center and a preonic model of quark, with quasi–crystalline kernel formed by kerneloids of me –preons of 34 me . A vortexial potential with repulsive kernel of ‘sombrero’ type can be proposed as general genesic potential, which can explain also the cold genesis by chiral quantum fluctuations.

Keywords: elementary particle, vortexial field, cold genesis, standard model, sombrero potential

Introduction volume, in the de confinement phase they are much suppressed.2 Also it has been shown that the string tension vanished upon removal of In the quantum mechanics, if ψ j is the complete set of eigen center vortices from the simulations.3 functions of the Hamiltonian, determined by the potential and boundary In a Cold genesis theory of the author, (CGT4–6), it is argued the conditions, the field operator can be defined asψψ=∑× c jj, where vortexial nature of the particles’ intrinsic energy E= mc2 , which– in c are destruction operators and ψ are field modes or eigen functions p j j the electron’s case, results as bosonic condensate of ‘cold’ photons, of the Hamiltonian. If | n〉 is the state of n particles in mode ψ , − j j with a super dense centroid m with the radius of ~ 1018 m – the single–particle state is reduced to its wave function ψψ:|1〉= 0 jj jfor the electron, which sustain a stable etherono–quantonic vortex: Operating on a one–particle state with a destruction operator, we Γ (r) = 2π rc = ΓΓ( r)() + r> r , of ‚heavy’ etherons (m ≈ obtain the vacuum: c .1〉=| 0. 〉 Operating on the vacuum with a µ µ µµ B µ s i i 10–60 kg)– generating the magnetic potential A and of quantons creation operator: c † |0〉=〉 |1 results in a particle in mode j , i.e.–if ij ()m=×= h 1/ c2 7.37 x 10−51 kg − generating the particle’s magnetic 〉 † h the single–particle state | a is empty, the creation operator c j will moment ξ and vortex–tubes ξ that ‘materializes’ the B–field lines ψ B B fill the state with a fermion. The eigen function j for this particle, is of the magnetic induction, but also the particle’s spin S = ½ħ given obtained from the field operator Ψ :0 〈|| Ψ 1 〉=y i i by a spinorial mass mmµ ≈ p of light photons vortexed with the light’ The second quantization approach exposes the fact that there is speed in the volume of Compton radius rl= ħ / mc pm = r,which do not contribute to the electron’s mass m – which results in CGT from zero–point energy for every field mode jψ , by writing a symmetric e † Hamiltonian in terms of field operators : H =∑+ii E( cci. i ½), 0 confining ‘cold’ photons with rest mass m f –half of their relativist where E is the eigen value of the eigen function Ψ , the second i j mass (m02= ½ m = ½/ hn c ) ,6 as saturation value given by the term showing that even in the absence of particles there is an energy ff ½E associate with every field mode ψ , forming the ‘zero point’ i j relations: m c22≈≈½ εε E dV( r) ½ µ H 2 dV( r) = e 2 / 8. a ; energy of the vacuum, confirmed by effects as the Casimir’s effect, e ∫∫00 0 the Lamb’s shift and the spontaneous emission, which consists also of 2 E = c . B = cµ H ; (r <= r r ; a = 1.41 fm) (1) intrinsic energies mc of virtual particles that have a brief existence, 0 m λ called ‘vacuum fluctuations’, which may be related also to the so– s = ½ħ = ½m cr .≈ π ½ mcr .; r= ħ / mc (2) called ‘cosmological constant’, used in cosmology.1 ml el λ e It is known that in the quantum vacuum, at specific energies of Γ which show that without µ –vortex, the me–particle cannot be excitation, particle–like states can be generated as chiral (spinorial) created. It may be argued that this model of electron is compatible with excitations, individually or in pairs. It was argued also that the vortices the interpretation given by Giovanni S., Erasmo R. and co–workers7,8 play a crucial role in the confinement process, and that condensation 2 of such vortices may be the long–sought confinement mechanism: to the Bohm’squantum potential9: Qm = (ħ /2 )( ∆ ρρ/ ) in the confinement phase vortices percolate and fill the space time identified with the kinetic energy

Submit Manuscript | http://medcraveonline.com Phys Astron Int J. 2021;5(2):60‒71. 60 ©2021 Marius. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and build upon your work non-commercially. Copyright: Analogies and differences between the particle’ model used in a Cold Genesis Theory and those used in 61 the Standard Model ©2021 Marius

of the internal motion (“zitterbewegung“) associated with Conform to eqns. (1)+(4), the inertial mass of a lepton like the the spin S of a spin −½ particle, (ρ = R2* =ψψ ; ψ = Re. −iS /ħ ; electron is formed around a material center of a quantum (etherono– Γ S = m cx . ; x ⊥ r ) , in accordance with the Schrodinger’s equation, quantonic) vortex µ only by attraction of lighter leptons (photons) µ Γ written in the form: with non–null volume, i.e–with inertial mass, the µ –vortex without the mass of attracted leptons being the classic equivalent of a so– 2 2s -S/  named ‘virtual particle’. - ∆Ψ= E Ψ ; Ψ= R ⋅ e ; s = (3) m2 In CGT is possible also to deduce a quark model of cold formed particles with effective (constituent) mass of quarks, which gives the The CGT’s generalization of the relations (1), (2) for the case of the particle’s mass by the sum rule, considering as fundamental stable sub– vector photons4–6 is in accordance with the Esposito’s generalization 0* * of the Giovanni’s interpretation of the Bohm’s potential from matter constituent the basic preon z= 42 mmee≅ 34 , (mmee≅ 0.81 – the particles to gauge particles, in particular– to photons.10 mass of quasi electrons), which can form derived “zerons”, (preonic neutral bosons: zz3 0 ; zz4 0 ; zz6 0 , etc.) and two preonic The attractive interaction potential VΓ given by the vortexial field 1 ( ) 2 ( ) m ( ) of superposed vortexes: Γ=Σ(Γµ (r) results in CGT by the quantum 0 0 bosons: zz2 (4) = 136 me ; zzπ (7) = 238 me , which form the light 2 dynamic pressure Pcdc= ½ρ , in an eulerian expression: 2 and semi–light quarks (mq c< 1 GeV ) . V ( r) =−=− uP ½ uρ c2 ( 4) Γ kd k c According to the model, the quasi–crystalline structure of the

in which: ρc –the density of vortexed quanta, given by a single preonic kernel of the quark is given by electronic centroids and vortex– for the vector photon and for electron and by superposed ‘naked’ heavy photons (corresponding to X–rays and γ–rays– which * can be emitted at nucleon’s vibration) and can explain the values of vortexes Γ of quasi electrons (degenerate electrons with degenerate m the masses of cold formed quarks, mesons and baryons by a quasi– * *2 * mass mmee≈ 0.81 , charge ee= ± /3 and magnetic moment µ ) − crystalline model of quark, with its current mass with quasi–crystalline for particles heavier than the electron, uk being the impenetrable arrangement of preonic kernels and with the electronic centroids inter– quantum volume of the attracted particle, named ‘kerneloid’ in CGT.11 distanced by a small repulsive field generated by internal photons’ destruction by zero–point vibrations of the electronic centroids. −1 The equation (4) results from the Euler equation: ωω=ρ fs.P ( − The particle’s mass results in the approximation of the sum rule, as ρ − the thermodynamic work per unit mass; f the fluid’s density; Ps consequence of the quantum fields’ superposition principle applied to –the static pressure of the fluid) by the Bernoulli’s law considered in the the particle’s cold forming as sum of degenerate electrons, whose total simplest form: 12 vortexial field Γv can explain also the nuclear force. 0 02 Prsd( ) += Pr( ) Prvc d( ; ===) ½ρc( rcct) ., (5) –The particles cold forming by clusterizing may result– according to CGT, in a “step–by–step” process13 consisting in: ∇=∇VΓ ( w.ρ f .) u k =∇=∇ L f (.) uP ks =×∇ u k P s; –quark pre–cluster forming, as quasi–crystalline Bose–Einstein 2 2 ∇P = −∇ P ; ⇒ VΓ =− uP. =−½ uρ v (6) condensate of gammons or of preons, at E= ½ mv → µ , ( E the s d kd kf kcγ k kinetic energy, µc –the chemical attractive potential); Conform to the “bag” model specific to CGT, even if P0 ( rv;0= ) have different values for different radial distances – quark (cluster) forming, as non–destructive collapsed quark pre– s cluster; (at E= ½ mv2 ≤ µ ) and: r , the Bernoulli equation (5) is applicable for each vortex–line kcγ

lrΓ = 2π and for two diametrally opposed points : xr1 = i , xr2 = − i – elementary particle/dark boson forming as confined cluster , positioned to the surface of the impenetrable quantum volume of quarks with the current mass in the same baryonic impenetrable

uk1 of the attracted particle m1 , the supplementary dynamic quantum volume and completed with a shell of ‘naked’ photons; a 2 small impenetrable volume of quasi electrons /preons and a repulsive quantum pressure: δ Pdrd1()−= i ½ vρ fi () dr −, respective: field of zeroth vibrations impede the destructive collapse. The known 2 possibility to produce bosons and quarks ( ()qq− pairs) by high δ Pdrd2 ()+= i ½ vρ fi () dr +, introduced in the points x1 and x2 by −+− the vortexial field of an attracting particle m2 positioned at the distance energy (ee) interactions sustains the model. ‘ d ’ from the center of m1 will determine– according to eqn. (5), a pressure difference: Analogies and differences related to the ∆P( xx) = −∆ P( xx) = −(δδ P − P ) , particle’s creation from the quantum vacuum s12 d12 dd1 2 which will generate a force: Related to a real process of leptonic particle creation

22 † F≈∆ππ. r P( xx) = −× r∆ P( xx ), The creation operator: c j used in Q.M. can have a classic 1,2 is12 id12 equivalent, dependent to the impulse density of the Γµ –vortex’s F so– an attractive force toward 2,1. † quanta: cjf~ p( a) = = ρ f( ac) , which– reported to a reference Similarly, the particle m will generate an attractive force F e 1 2,1 value, specific to the electron, for example, ()ψψj = , gives a toward the particle m2 . Conform to the model, at equilibrium, for a creation operator, 00 212 free m–particle, we have: Psii( r) = P dii( r) ≈ ½ρ pi( rv) , † ckjj=+=÷(1 ) 0 2, (ρ pi(r ) − the local particle’s density), with vc = .

le ( k j –creation/destruction factor): If ()()(ρρa= f a = ρ ea) , ⇒=k j 1 and the initial electron is

duplicated. If k j → −1 , then: † e † e ckjj=(1 + ) ; kjf= [ρρ( aa) / f( )] ; ψ j=|.kc 〉= jjψ 2= †2 2→ † Rs( cR je ). 0, , so the electron is partially or totally , (−≤1 kjj ≤1; c =÷= 0 2 ;a 1.41 fm (7) le e destroyed: ρce(aa) / ρ0 = − δρ( ) / ρ 0 , Because in eqn (1) , we have: ()δρ ≤ ρ (a) being a loosed density. 2 2e 22 ea e ε00E( a) =µρ H =fe( ac) = ρ( ac) , it results that: † The expression (7) of the creation operator c j is different from el kjf= []ρρ( a) / f( a) = ρρ c( aa) / e( ) , the density ρ f (a) † those used by QM because while in QM the c j − operator adds a of the H–field’s quanta being equal with the particle’s surface density fermion to the system, the form (7) of CGT increases or decreases l 3 0 ρc (a) , conform to CGT, (ρe (a) being the density in the electron’s the density and the mass of a fermion. It is observed a similitude surface). with the expression of the quantum expectation value used by D. Böhminconcordance with the Q.M.: In this case, the values: 0 <

†2 and: S=∫=Γ δ mcdx.. 2 pδ mcr .. , 〈=∑ρ (r)〉 () crρ ( ) , (10’’) r ij i † at quantum equilibrium, when: The c j − operator explaining in this case, in CGT, the fact that the * 12 mass of the protonic quasi electron ()mmee≈ 0.81 is lower than the ek/Bh=×= k S /ħ r/η , † mass of the free electron, (kcjj<< 0; 1) Similarly it is explained (. S = 2π mc ×= rm ; h./1 c2 ) , we can take: hh h the γ -quanta spectrum of vibrated nucleons of a specific nucleus, (photons losing by the Γ -vortex’ disturbing and the decreasing of Re = −−ek/2 = e rh /2 (ε(r)-the internal entropy) and– in a µ ρ (a) ). determinist expression, we will have: 6 f

R22=||Ψ =ρρ( re) / = −r /η , (8) Related to the total interaction potential c 0 Resulted by attraction in a total vortexial field, the expression (4) ()ρρ=(r); ρρ = ( 0.) cc0 c of the vortexial potential becomes: 1 − η For example, supposing that close to the super dense centroid m0 V r =−=−=−=− uP ½ uρψ c2 V.| | 2/ Ve . r with: 21 Γ ( ) kd k c o o of an electron was placed another centroid mm00≤ , with a vortex ’ = ρ 2 Γµ around it, a new leptonic mass mmle≤ will be formed, according Vok ½ uc0 (11) −iSž / to eqns. (1), (4), with an associated wave function: Ψll= Re. , with: However, because the non–null value of the kerneloid’s volume υk and the ‘zeroth’ vibrations of the particle’s centroid m0 , we must R22=||ψ = ρρll(r) /= kR.2, take into account and a small repulsive potential, which– for the l l c 0 je interaction between two electrons at distances r <ηe ≈ 0.96 fm , it the electron being ‘supplemented’, the amplitude of the associated has the expression: 13 wave function , Rs being given by: V r = 2π d3ρ or ce 2/− η (12) 2 r( ) ie 2 †2 22 er− /η 6 Ras( ) = ( c je) . Ra( ) , (Rsss= ||ψ =ρρ( re) /0 = ) , o 12 3 4–6 −2 with: ρρee=(0) = 2.22x 10 kg / m and di ≈ 2 x 10 fm – 2 22† e the equilibrium inter–distance between the attractive magnetic–like Ree=||ψ ; (c j) = 1 + [(ρρc ) / ( fa )] (9) force and the repulsive force: Frr= −∇ Vr( ) at ordinary temperature For the same expression of the action: S = prx( ) , ()xr⊥ , we ≈ 0 −iSž / of the kinetized particles ()TC20 . have ψ ss= Re. and (7), (8) + (9) gives: For the total potential between two vectorial photons, by 2 2 2 el e 22 Rs( a) = (.) Re++ kR jea=ρρρ e( a) /00 + ( c(a) / ρρρ e( a))( e( a) / ) ≈ Re R l similitude with the electron’s case, it may be taken a similar attractive ( )a and repulsive potential. But the form (11) of the attractive vortexial ; Ra2 ( ) ≈ ρρle( a) / (10) potential allow also a semi–formal expression of the total potential lc0

If –for the system of two electrons with anti parallel magnetic V qi= ½υ ρ 0⅓ 0.9m / m*2 c≈ 1.73 MeV , −2 0 qe( p e) moments, we have as in CGT: di ≈ 2 x 10 fm andηe ≈ 0.96 fm , it results 2 2 i = 3 that: | Ψ | e = KK12/ = 0.9794 , ⇒=KK21 /||Ψ e = 1.021 ×V0 , the With uq (0.21 fm) 0.03877 fm and: eqn. (13) becoming: qq’ V00≈ 2 V= 3.45 MeV − for the vortexial interaction between a 22 2 couple of two nucleonic quarks and a third nucleonic current quark. With Vr1,2 ( ) = −× V0 ||Ψ ( 1 − kr .|Ψ | ) with: KV10= = ½υk ρ 0 c; 12 q 2/−r η the value: h= 0.8 fm and considering thatV( rq =0.21 fm) = 0 , kr = KK21 / = 1.021; ||Ψ =ρρc (re) /0 = (14) It is observed q the eqn. (14) gives: V0 (0.45 fm) = 0.5 MeV − much less than the that for r >= dVi ( 1,2 0) , the potential Vr1,2 ( ) is attractive. The 12 relation (14) even it is semiformal, it may explain the cold genesis of value Td = 2 xK 10 , obtained in CGT for the confining potential heavier photons from light photons resulted from chiral fluctuations of current nucleonic quarks by a specific “bag” model– which of quantum vacuum (as etherono–quantonic vortexes in the flowing explains the quarks’ cluster deconfining at a very high temperature, of the primordial dark energy) by forming of super dense centroids T= 2 xK 1012 . This result is explained by the fact that the strong from confined quantons.15 The quanta density and the intensity of d force which maintains the current quarks inside the impenetrable the stabilized etherono–quantonic vortex Γ depends on the size of µ nucleonic volume is of “asymptotic freedom” type and is given by a the formed centroids m considered in CGT with a possible chiral 12 0 repulsive shell (surface) of a “bag” with the radius rb ≈ 0.6 fm , (as (spiraled) shape. Because the resulted potential Vr1,2 ( ) not contain in the Toki & Hosaka bag model). any term dependent on the kinetic energy of the particles, (i.e. –on the particles’ temperature, T= ⅓ mv2 / k ) , it is understood that For a generalization of the eqns. (13), (14) for the potential p pB of qq− interaction, we may propose a generalized potential of the potential (13), (14) is usable for temperature lower than the Bose– “modified sombrero” type, based on the equation (8), in theform: Einstein temperature: TT < BE , for the case when the kinetic energy 24 2 of the particles tends to the value of the chemical attractive potential: Vr1,2 ( ) =−× K1 ||Ψ + K2 ××()η / r| Ψ | with: KV10= = ½υk ρ 0 c 2 Ekg= ½ mv → ()µ c, the chemical potential being the total potential 2/−r η ; ||Ψ=ρρc (re) /0 = (16) of interaction by fields: ()µc = VrVrVr1,2 ( ) ++ em( ) ( ) , and show that even if the electric and the magnetic potentials are of null re/η which– withVr1,2 ( e ) = 0 , gives: K21= Kr()e /η × e , = = << − value ()Vrem( ) V( r) 0 , at TTBE the pre–cluster of BE obtaining the form: condensate can collapse until a value of the inter–distance di given re 2 η  re  2 2 2  ρ c (r)  -r/ η by: Vr 1,2 ( ) = 0 , i.e. in a non–destructive way, with the cold forming V (r) = - V Ψ (1 - e ⋅  ⋅ Ψ ); Ψ = R =   = e ; 1,2 0 r  ρ  of a bosonic or pseudo–bosonic particle.    0  S ϑ -i m = ki ρ 2 Ψ = ⋅  ρ = k ρ e = ρ e * ≈ ρ e = 13 3 V 0 0 c ; R e ; 0 n 0 0.9 * 0 ; m e 0.81 m e ; 0 22 .24 x10 kg / m It results by eqns. (13) and (14), a relative similitude with the 2 m e genesic mechanism considered by the Standard model, which use the (17) sombrero potential for describe the spontaneous symmetry breaking and the Nambu–Goldstone bosons,14 for example, in the form: Which –for the interaction between nucleons (n–n), with n 24 V1,2 (0.6 fm) = 0 ; V0 = 115 MeV and η = 0.8 fm ,12 gives: V()φ) =−+=− 5φ φ 25 ee−−22θθ(1 − with: θ =5 × eiθ V1,2 (2 fm) = − 8.93 MeV , and for the interaction between θ = ÷ π , (( 0 2 )) . (15) q two quarks (qq− ) , withV0 = 1.73 MeV , V1,2 (0.21 fm) = 0 which gives an infinity of quantum vacuum excited states.16 and h = 0.8 fm , 12 gives: V1,2 (0.45 fm) ≈ − 0.645 MeV and It is observed that the form (14) of the vortexial potential Vr1,2 ( ) V1,2− 3 (0.45 fm) ≈ −− 1.29 MeV for the vortexial interaction between is similar to the form (15) specific to the SM, and– by pes cific values a couple of two nucleonic quarks and a third nucleonic current quark– k 0 ofV0()υρk 00 Vn≈ ( υ ke; ρ ) andη , it may be generalized for the close to the value obtained by the ‘bag’ model specific to CGT, interaction between photons ()k=−∈1; nN or between mesons and (1.56 MeV 12). * k * 12 η baryons with mass m = nm. e , (k= +1; n≈ 0.9 mm / e ). The fraction ()/ r in the expression of the repulsive potential may be justified by the flux of radially reflected ‘naked’ light photons

For example, for the interaction between nucleons, with the on the surface of the impenetrable quantum volume υii(r ) of the i 3 values resulted in CGT: un = 0.9 fm ;ηn = 0.8 fm , a value attractive m–particle, corresponding to a repulsive scalar field. For m >= = n n mue; kI ur i( i ) we can approximate in eqn. (11) that: Vr 1,2 ( i ) 0 VΓ ( d=2 fm) = 8 Me V is obtained with V0 = 115 Me V

According to CGT,13 the quarks of the light and semi–light astro , because ukI represents the value of interaction by vortexial field, particles (including the baryon Ω(1627) ) have similarly a kernel with which have a radius r higher than the mechanical radius, rr> ; i i mi low mass ()~8MeV / c2 and a photonic shell (of ‘naked’ photons) for example, for nucleon, ri ≈ 0.6 fm and rmi ≈ 0.45 fm –according + instead of gluonic one, but it is composed of light quarks ( m1 16 δ = − to the scattering experiments, the difference ri ( rr i mi ) ; m2 , with a mass of ~ 135me ; 1 37.5me ) magnetically attached to representing the thickness of a repulsive shell given by brownian a neutral cluster formed by preonic bosons: zz40 = 136 m and ‘naked’ light photons kinetized at the surface of the impenetrable 2 ( ) e 0 12 zzπ 7 = 238 m, i.e. – with the kernel formed by preonic kernels quantum volume urmi( mi ) , conform to the CGT’s model. ( ) e 11 0 (‘kerneloids’, CGT ), of zm(34 e ) – preons (pre–quarks)–predicted According to CGT, the impenetrable quantum volume υqi(r q ) in CGT in 2005–20064 and experimentally evidenced in 2015 by a 20 of nucleonic quarks which –for concordance with the experiments,17 team of Hungarian researchers from Debrecen but considered as being a quantum of a fifth force, of lepton–to–quark binding.21 is considered with a radius rq ≈ 0.21 fm , [6, 12] and of value:

−23 18 υ qi ≈ 3.87x 10 fm , may be obtained by a semi–empiric equation: The quasi–crystalline structure of the current

 m   m  quarks in CGT −  − k ⋅   − k  K 1 k  1   m p   m p  3 ϑki =ϑni ⋅ e ; k = e ; K = 8.97; ϑni (m p ) ≈ 0.9fm ; m p ≈1836 me According to CGT, the electron’s mass is given mainly by the (18) inertial masses of a number of ‘nakes’ photons (virtually reduced to their kernel, i.e. with loosed evanescent part) attracted by the in which the factor ‘ k ’ take into account the fact that– inside the vortexial field of the electron’s magnetic moment, given byan υ e ee quantum volume of a bigger particle, the value ki of a smaller particle etherono–quantonic vortex: Γµ =ΓBc +Γ , given by a vortex of increases proportional with the local density, as in the case of quarks. ‘heavy’ etherons ( ~ 10−60 kg ) which explains specific effects (like the > = For (quasi) free mk particles or with mmkp, we have: k 1 . Aharonov–Bohm effect) of the magnetic potential A and by a vortex − e −2 of ‘quantons’ ( m= h .1/ c2 = 7.37 x 10 51 kg ), which generates For electron, it results: ri ≈ 3 x 10 fm . h quantum vortex–tubes of the magnetic induction’s field lines ξB . The saturation value of the number of bosons attracted in a In CGT is considered also a small impenetrable quantum volume volume of fermionic radius around the attractive particle ‘ m ’ by its υI not only for nucleons and quarks, but also for the electron and for vortexial potential VrΓ ( ) is given by the eqn. (1). The equilibrium 0 −2 13 z –preon, with a radius: 3x 10 fm –for the free electron, respective: value re is proportional with the particle’s temperature: rTei~ , −2 0 but for stable baryons, like the proton, the main contribution to the 3.5x 10 fm for the z –preon– values given by the eqn. (18),18 particle’s stability is given by the potential of “asymptotic freedom” type, resulted from the repulsive pseudo–charge of the scalar shell Even if these ‘impenetrable’ quantum volumes υI (“kerneloids”) of the particle’s impenetrable quantum volume, urii( ) , which –at can be penetrated by photonic or electronic super–dense centroids, moderate vibration energy of the current quarks, gives a force of (fact evidenced in experiments of X–rays scattering on electrons and quarks retaining: FNq ~− 1029 , conform to the “bag “ model of electrons scattering on nucleons), they impede the particle’ destroying quarks confining resulted in GTC .12 by quarks/quasielectrons collapsing, with the aid of a small repulsive field of quantum perturbation given of ‘zeroth’ vibrations ofthe The previous results show that the eqn. (17), of modified ‘sombrero’ particle’s centroid(s), which is increased at high intrinsic quantum type, may explain the experimentally obtaining of B–E condensate of temperatures. photons19 and sustain the conclusion of the cold magnetic (vortexial) confining also of ‘gammons’ f oro z0 – preons and of quarks or In concordance with the equation (1) a similar kerneloid may even of mesons,13 with particle–like cold cluster forming by non– ± 2 be considered also for the ‘quarcins’ cm0 ≈ 17 e ( ~ 8.7 MeV/ c ) E=½ mv2 < m =2 < destructive collapsing, at kgc, when Ekgc½ mv m considered in CGT as last sub–components of the quarks. ; ( µc –attractive chemical potential). By comparison, the problem of the particle’s non–collapsing by inter–quarks attraction was solved Also a problem of the SM’s model of quark is the explaining of the in the Standard Model by considering an inter–quarks potential of repartition of the mass of gluons (and ‘sea quarks’ resulted as virtual “asymptotic freedom” type, which decreases at quarks’ reciprocal ( qq ) pairs of split gluons) to the valence quarks, at the quark’s/ approaching, effect explained in the SM as anti–screening of the baryon’s transforming. quark’s color charge by polarization of virtual gluons in the quantum vacuum. In CGT, the similar problem, of explaining the retaining and transporting of a mass of “naked” photons of the particle’s quantum Related to the particle’s structure volume proportional with the current mass of the quark in strong interaction, is explained by the vortexial field of the quark’s kerneloid, It is known also that the quark model used by the Standard model given by the sum of quantum vortexes Γ * of the degenerate supposes the existence of an un–structured quark’s kernel of current µ magnetic moments of its preonic quasi electrons, in accordance with ÷ 2 mass: 2.3 4.8 MeV / c –for the nucleonic quarks, having a ‘color’ the superposition principle of the quantum mechanics. Also, a quarcic charge of strong interaction, surrounded by a shell of gluons and shell of “naked” photons, i.e.–penetrable by other particles, explains quark–anti quark pairs having ‘color’ charges of opposite ‘colors’. the possibility of elastic interaction between nucleons better than a Even if the gluons are considered in the S.M. with null rest mass, shell of gluons, considered by the SM and the value of the proton’s they are the majority contributors to the quark’s effective (constituent) radius experimentally determined, ( 0.84÷ 0.87 fm ). Because these mass by the coupling to the Higgs field which gives them rest mass, electronic/quarcinic/preonic kerneloids, by their (quasi)electronic according to the Higgs’ mechanism considered in the S.M. e vortex(es) of the magnetic moment(s) Γµ , attract and retain in their

m0 on the radial direction, the length of the preon resulting of value: of ‘naked’ photons upon the surface of the impenetrable quantum −2 volume of the nucleon, which gives a static repulsive shell of radius lzi= 6 × d≈ 0.12 fm . The previous value: di ≈ 2 ×10 fm , is in * = ≈ concordance with the value of the root–mean square charge radius of rii a0.6 fm , according to a ‘bag’ model of strong interaction resulted in CGT,12 more probable being the rotation of the cluster of the free electron: re = 0,0118 fm , resulted from calculations made by Storti and Desiato,22 and to some high–energy scattering experiments quarcic kerneloid, generated by the magnetic moment’s vortex Γµ , reported by Milonni23 which gave a value: r= 0.01 fm – which is the in CGT. Also, because the fact that the magnetic moments of quasi e 0 11 electrons of the z –preon are axially coupled on the axial direction, electron’s kerneloid mechanical radius, conform to the CGT’s model * * forming a common vortex–tube Γµ , the central, un–paired Γµ – and justfy the approximation Vr1,2 ( i ) = 0 used for eqn. (17) in which vortex–tube gives the preon’s magnetic moment and similarly– the υυ kI= i(r i ) represents the value of interaction by vortexial field, with central un–paired preon gives the magnetic moment of the pseudo– r obtained by the eqn. (18), ( re = 0.03 fm –for the electron). i i quarcic neutral cluster of preonic bosons which– by an attached un– Because the quasi–crystalline structure of ( u , d )– quark kerneloid paired quasi–electron, gives the cold (quasi–crystalline) quark. have three layers– in CGT, ( m1;2 ; zπ ; zπ –Figure 2) with (4; 7; 7) 0 13 At ‘hot’ formed quarks, a similar quasi–crystalline re–arrangement z –preons, it results an approximate length of the ( u ; d )– quark of preonic kerneloids may result by internal re–arrangement of the kerneloid: lqz= 3 l≈ 0.36 fm , the minimal possible radius resulting common preonic cluster of quarks, by transfer (changement) of 0 kerneloids of preonic bosons ( z0 , zz3 0 , zz4 0 , zz6 0 , of value: rqz=×= 3 r 0.105 fm , value which is the radius of 1 ( ) 2 ( ) µ ( ) mechanical interaction and which– compared with the resulted radius 0 zzπ (7 ) ) from a quarcic kerneloid (internal or resulted by interaction value of the quark’s current mass: r≈ 0.21 fm ,17 of interactions by q with other particles or with bosons of the quantum vacuum) to vortexial field– in CGT, indicates a small vibration liberty lv of the 0 another cuarcic kerneloid, with the aid of the vortexial attractive field z –preons inside the quark’s kerneloid. The mass of the current of a kerneloid upon the impenetrable quantum volume of another quark results approximately as total mass of its preonic kerneloids. kerneloid, (similar to the case of the nuclear interaction between nucleons –conform to CGT4–6). These bosonic kerneloids are mechanically similar with the gluons considered by the SM, a higher similitude being given by the fact that the resulted composition of the z0 –preon, as aquarcinic pair: + +* * ()cc0 0 ()~ 2× 8.7MeV , is similar to the composition of gluons of the SM considered as pairs ()qq , of quarks with current mass, with the main difference that in the SM, the nucleonic current quarks Figure 1 The generating of the attraction force by a vortex field.

However, some high energy gamma–quanta, of 1÷ 100 MeV , emitted at nuclear de–excitation, as in reaction (1), may be explained in a Galilean relativity as In CGT, as clusters of gammonic kerneloids, 0 particularly– kerneloids of zz−, k – preons, (k ≥ 1) , emitted either by the vibrated (excited) quark’s kernel or from the quantum shell of the nucleon’s quantum volume, at the nucleon’s vibration, by the force of dynamic quantum pressure of the Γµ –vortex of the proton’s magnetic moment. Conform to CGT, at their releasing, Figure 4 The vortexial electron model (CGT); (v- -vecton; w- -vexon). these clusters re–obtain a photonic shell of mass proportional with the number of quasi electrons’ kerneloids which compose the preonic boson’s kerneloid, i–e– corresponding to boson’s effective mass, by the negentropy of the quantum vacuum given by etherono–quantonic winds (fluxes) which explains also the constancy of the magnetic moment of the free charged particles.4–6 A similar conclusion, of a quasi–crystalline arrangement of quarcic gluons, results also for the quark model of the SM, because the strong interaction between quarks and gluons, given by the so–named “color” charge of quarks and a resulted interaction potential of “asymptotic freedom” type. It may be argued also –in CGT, that the e± –charge is given by an electron also in the case of the proton (whose charge is given by a positron4–6), the E–field’ quanta (vectorial photons, “vectons”–in CGT) resulting from pseudo scalar quanta of background radiation of ~ 2.73K and having a cylindrical density variation inside the electron (which is generated by the vortexial energy of the electron’s magnetic moment and as consequence of its barrel–like vortexial form), ≥ transformed into spherical distribution for ra, as consequence of Figure 5 The neutron’ model. the spin’s precession movement (Figure 5):

00 0 2 The electron’s kerneloid, with a radius of mechanical interactions, ρρv(r) = vv( rr/ ) for rv <≤ ra; ρρve(r) = ( a) · ( ar/ ) resulted of value rε = 0.01 fm in CGT [11], ensures the forming of for ra > , a etherono–quantonic vortex Γµ around it and implicitly– also a vortex of vectons (which can escape from the level of the surface of 0 0 0/−r η 0 ρρve= (a)· ( a/ r v) = ρ e. e⇒ r v= 0.64 fm (19) 0 radius rv =0.6 ÷ 0.64 fm –Figure 5 more dense thanin the case of a

vectorial photon as consequence of a bigger superdense centroid m0 which sustain and stabilize the Γµ –vortex, conform to CGT. Also, 0 the cylindrical density variation inside the electron for rv <≤ ra , suggests a fusi form centroid, with the length sensible bigger than

its diameter , considered with chirality ζ 0 = ±1 (of spiral form) in CGT,6 the electron’s charge being given by quantum vortex–tubes

with ζζw = − 0 .

If the pairs of electronic centroids with opposed chiralities gives 22 electronic neutrinos of Majorana type and mass mv ≈ 10 eV / c – conform to CGT,4–6 it is possible that similarly – a quantity of photonic centroids of sensible lower mass, of thermalised photons of the quantum vacuum can form pairs with opposed chiralities which corresponds to a quantity of pseudo–neutrinos of ‘dark matter’ which includes the so–named ‘axions’, with a rest mass of Figure 3 The cold forming of a baryonic kerneloid (CGT). 10−−53÷ 10eV / c 2,26 the electronic superdense centroids resulting

Citation: Marius A. Analogies and differences between the particle’ model used in a Cold Genesis Theory and those used in the Standard Model. Phys Astron Int J. 2021;5(2):60‒71. DOI: 10.15406/paij.2021.05.00235 Copyright: Analogies and differences between the particle’ model used in a Cold Genesis Theory and those used in 67 the Standard Model ©2021 Marius in this case from confined pseudo–axions which in turn results from In the case of the photon, the purely Brownian motion of the vortexially (magnetically) confined quantons, conform to CGT. The quanta and sub–quanta of the “quantum vacuum” would prevent the large mass spectrum of these photonic centroids (pseudo–axions) generation of vortices around the super–dense centroids of photons, results theoretically from the large spectrum of photons in accordance even and their c–velocity (the speed of light in vacuum), which would with the vortexial model of pseudo–scalar photon, composed by two make inexplicable the dualistic, wave– particle character of photons, magnetically coupled vectorial photons (“vexons”– in CGT6), as in because the electromagnetic wave property involves both electric field the Munera’s model of photon, but with the diameter lw /2 ( lw –the vectors E and magnetic field vectors, H– vectors that can be explained length of the pseudo–scalar photon)dimensioned like in the Hunter– only by the quantum–vortex character of the magnetic field lines ξH Wadlinger’s model of photon and considered a vortex of heavy (vortex–tubes of etherons and quantons –conform to CGT4–6). – In the 6 −60 etherons (“sinergons’– in CGT, ms ≈ 10 kg ) around the quanton’ case of the electron, because the Brownian motion does not generate mass, m= hc/ 2 and a density ρρ(r) = 0.( rr/ ) of Brownian vortices, by pure Brownian kinetics of the sub–quantum and quantum h s sw environment neither the electric charge nor the perpetual magnetic sinergons (but also a sinergonic vortex Γs with a similar variation of moment of the electron could be explained micro physically; its density) around the kerneloid of the vexon’s inertial mass, mr. ww( ) In the case of nucleons, if the quantum and sub–quantum medium were only brownian, without vortices, and if the quarks would be For: l /2≈ λπ / , the dynamic equilibrium for the vortexed −18 w 0 with a radius of approx. 10 m (according to the conclusions of quantons or clusters of quantons inside the Compton radius: quantum mechanics), to keep the quarks together inside the nucleon, r = λπ/2 , is given by a magneto–gravitic force of Magnus type λ 0 a pressure on them from the outside would be necessary, as in the generated by the sinergonic vortex of the quantons rotated with vc= case of the “bag” model of nucleon with quarks held together by = π Γ ρ to the vortex line (circle) lrr 2 by the s –vortex in the s (r) an external pressure. The explanatory problem that arises is that– –density of sinergons, in the form: at a relatively small distance of the nucleonic quarks from each 22 0 2 other, (at distances of maximum 1fm), the static quantum pressure F=2 r.. Γ( r) ρ( r) ×= c4 πρ r.. c.( r/ r) = m c /; r r ≤ rλ = h /2π mc sl c c c s c s w h generated by the pseudo–Brownian motion of the quanta with which (20) the quantum and sub quantum medium of “zero” point energy, that by the resulted condition: 4/πρr20.. r= m = hc2, with: intervenes in the space between quarks, it would generate a greater c sw h rejection between them, increasing the inter–distance between quarks 0 Γcc(r) = 2π rc c. ; rc − the quanton radius; ρs − the density of which are eclipsing each other. Or– the experimental data showed sinergons at the vexon’s inertial mass surface of radius raw ≤ ; mh that –apparently paradoxical, over short distances, below 1fm, the force of their reciprocal approach increases with the inter–distance – the quanton’ mass; Γcc(r ) − the circulation of sinergons at the quanton’s surface. It is observed that –because the generating of a (“asymptotic freedom” effect). It results that the hypothesis a) is not magneto–gravitic (Lorentzian) force of Magnus type by the sinergonic in concordance with the experimental observations on the properties of elementary particles. vortex of the quantons and the ρs (r) –density of sinergons, the vector photon and the electron seems to be a micro–black hole but In the case of the atoms, by pure Brownian kinetics of the sub not because the gravitational force (which is neglijible in this case). quantum and quantum medium cannot be explained micro physically For a heavier particle, formed as non–destructive collapsed cluster neither the magnetic moment of the nucleons and of the nucleus and of quasi electrons, it results that at very low temperatures, ( TK→ 0 implicitly– nor the perpetual motion on the orbital of quasi–constant 2 mean radius of the atomic electrons, with angular velocity ω = vr/ , Ekc= ½ mvγ → µ ), the force Fsl canensures the maintaining of quantons inside the particle’s volume if the quasi electrons are – quasi–constant, (in the case of the Bohr atomic model), case in coupled in pairs with anti parallel magnetic moments– maintained which – according to the laws of the classical electromagnetism, the at a diminished (degenerated) value, in accordance with the fields electrons should gradually lose kinetic energy by radiative emission superposition principle. This fact can explain the detection of cosmic and eventually fall on the nucleus– fact that does not take place, phenomenon well explained only in the case of the atomic vortex ultra–heavy particles (of “oh–my–god” type ]xx]: mc2≈ 10 20 eV , −16 model; according to quantum mechanics, the orbital motion of atomic ()~ 5× 10 kg , without the Einsteinian relation of speed–depending electrons without radiation emission and without diminution of their mass variation. kinetic energy is only postulated, not explained. Other theoretical arguments for the vortexial In the case of nuclear interaction, between two or more nucleons, model of particle the standard model of quantum mechanics considers (in the quantum “chromo dynamics” theory) the existence of residual gluons of the There are at least three hypothetically possible situations regarding nuclear field, for explain the interaction between nucleons, being the action of some bosons (in particular – radiation quanta) on the postulated the existence of a so–called “color charge” of nucleonic/ surface of the nucleonic volume: gluonic quarks, (similar to electrical charge but of significantly higher value), but without a plausible explanation for the microphysical I. The pressure on the surface of the nucleonic ‘bag’ is given by nature of this “color charge”. Brownian kinetic quanta, (such as molecules); Also, is not clear in the SM how in the case of a baryon like II. The pressure is given by the quanta of some quantum “winds”; Λ0 (1116)– which is considered with the structure ( u d s ) and is III. The pressure is also given by Brownian kinetic quanta and Λ→0 +−+ π Λ→0 00+ π quantum winds; transformed by a reaction: ()p or: ()n , the losing of a π – meson from the s–quark (whose current mass In the first case, a), the explanatory problems that appear regarding is considered elementary, without structure) take place by the losing the particles consist in the following: of a couple of ( u d )– or ( d d )– of valence quarks with the same

0 17 3 current mass as those of the nucleons but carrying a considerable in which: µN –the nuclear magneton; ρn = 4.68x 10 kg / m –the lower but exact mass of gluons, ( ~ 68 MeV/ c2 per quark, compared ρ * 2 maximal density of the proton; ne(r ) –the proton’s density at the to ~ 310 MeV/ c per quark –in the case of the nucleon). * mean distance re resulting that: In the hypothetical variant a) or c) we could imagine a model of nuclear interaction similar to the Fatio/LeSage model of gravity: with µ L ≅ −0.156µ ; µµS ≅ −4.55 ; eNeN attractive force given by difference of pressure generated by Brownian n quanta or by quantum winds, pressure difference generated by the Se = 0.0025 ħ , ()ħ = h / 2π , the position of the protonic positron reciprocal eclipsation of the nucleons in report to the action of the being: r+ = 0.96 fm , [4–6]. quanta on their surface; but because the nuclear force is about 1040 times stronger than the gravitational force and because the tendency The attractive vortexial potential Vre * given by the eqn. towards equilibrium of the quantum medium, that would homogenize Γ ( e ) the values of density and pressure of the quanta, to explain the value −−2 43 (4) with:υυk= ei (3x 10 fm) ≈≈ 1.13× 10 fm , results of value: of nuclear force by static quantum pressure difference generated without vortices would be necessary a considerable quantum density, e * ≈ VΓ ( rec) ≈ 3 keV>> E , the maintaining of the negatron’s orbital close to the density of the nucleon, ~ 1017kg / m 3 ). with the mean radius r * being explained by a vibration energy Or such a value of the density of the quantum medium e e * 12 corresponding to the “zero” point energy, even if it may be supposed Erlv ( ev; ) of the neutronic negatron with an amplitude lv . as existent in the planetary and stellary space, it would produce an accentuated red shift effect of the spectrum of light radiation from So, by eq. (32), the model of CGT solve the classical problem distant stars by the effect of radiation “aging”, by a considerable of the nucleon’s spin and of the magnetic moment values, problem drag force at the photons passing through this quantum medium, which determined the abandonment of the classical nucleon models even if is taken into account also the d’Alembert’s paradoxe [28]– in presuming incorporate nucleonic electron(s). The continuous contradiction with the fact that we can observe through the telescope energy spectrum of the β radiation at neutron’s transformation, also the radiation of very distant stars. corresponding to a speed ve of the β –electron up to 0.7÷ 0.92c , is explained– in accordance with eq. (34), (35), through the acceleration It results therefore that the nuclear interaction between nucleons given to the β –electron by the vortex Γµ of the protonic µ p – cannot be explained naturally without the concept of ‘quantum magnetic moment, energy depending on the angle of the electron’s vortex’, the use of postulates such as the existence of the “color” initial impulse,θ ()pr, . charge of quarks being more formal than a natural explanation, (more β p hypothetical than phenomenological). The fact that– according to the neutron “dynamide” model, the protonic positron coexists with the neutronic negatron inside its Analogies and differences in the explaining of quantum volume until the neutron’s transformation, may be explained the weak interaction by the model through the hypothesis that the difference of approximate 2.53 m between the neutron mass and the proton mass is given by The mechanism of the beta decay is explained in the Standard e γ σ Model by the conclusion that a nucleonic down quark of a neutron a binding * –gammon called “ –gluol” in CGT, which has the 22 is changed into an up quark, converting the neutron into a proton intrinsic energy:∈σ = 2mee * c ≅≅ 1.74 m c 0.889 MeV , released by the emission of an an intermediary carrier: a virtual W––boson, at the σ –gluol’s transforming into an electronic (anti)neutrino ve 2 having a large mass (approximately 90 GeV/ c ) and a short lifetime, , resulted as coupled electronic centroids with opposed chiralities, in of under10−24 seconds, which has a very short effective action range CGT.4–6 −17 −16 (around 1 0 to 10 m [29]) and is transformed into an electron and The reaction of neutron transforming,15 : an electronic antineutrino, (which may explain the mass difference 01− 1 between the quarks d and u ). The explanation of the SM for the ner→ p+β ++ ve Q k(780 keV ) (22a) may be considered in large energy spectrum of the beta–electron is the conclusion that it share the W—boson’s transforming energy, Q , with an electronic the model, in this case as derived from a reaction having the form: + antineutrino (or a neutrino– in the β – decay). So, the consideredW +− (M * ++γσ0 ) → M* + e + e+∈ v + (889 keV ) —boson, resulted in the electro–weak theory, is essential in the weak n( ne) σ interaction’ explaining, for the S.M. + 1 0 ; (Menr* +=) p (22b) given by the dissociation of the γ – Acording to CGT,6 the neutron results in the theory conform to gammon, with the transformation of the σ –gluol. a Lenard–Radulescu dynamid model, (Dan Radulescu, 1922, 30) , as being composed by a proton center and a negatron revolving around It is observed that the couple: we−−=( +σ ) , named “weson” in * 6 – it with the speed vce ≈ 0.023. and with a kinetic energy Ec = 74 eV CGT , is a classical (real) equivalent of the W –boson used in the * S.M., it explaining the difference between the neutron’ and the proton’ , at a mean distance re ≈ 1.3 fm< a , (Figure 5), at which it has a S n S mass. degenerate µe – magnetic moment and Se –spin = µee.(me/ ) given by the equation: The energy∈σ (889keV ) , released as static quantum pressure

0 of quantons –conform to the model, compensates the electrostatic r S ρn * o - e µe = µN ⋅ ; ρn(r e )= ρ . e ηd ; ηd = 0,93 fm ; and the magnetic attraction energy between the remained proton ρ (r * ) n n e and the released negatron:Vaa ( ) , at the minimal inter distance: (21) di = a = 1.41 fm . This conclusion can be argued in the next way:

If we consider that the gamma–quantum with the energy m0 (like the electron, for example) as an energy resulted from the 22 Eγ = 2 me c = e / 4πε 0 a = 1.022 MeV is given by the electrostatic potential of a basic field (Higgs field): and the magnetic interaction between a negatron and a positron, aH. = mc2 , the rest energy of a particle being interpreted as a (which can be separate in the electric field of a nucleus), we have: 00 dynamical effect due to the interaction of the particle with the Higgs 22 2 field of minimal value H . Considering- in QM, a relativist mass Veµ+= V 2 mc e = e /4πε0 dγ + µ . B ; Veµ = /8πε 0 dγ , 0 variation with its speed, the relativist mass mv( ) will result by an ⇒=daγ 1.5 ; (d <= rµ ; B Ec/ ) (23) additional H-field:

2 aH.()0 += H m(v) c (any particle coupling with the Higgs field (because for: d <= rµ h /2π mce we have : gets then a mass just because it interacts with that field); reciprocally, 3 since the energy is conserved, any variation of the a H contribution to B = (µµ0 /2π )( /d) = Ec/ , it results that: the energy results in a change of the particle’s speed, conform to the µ = (½) ecd) . In consequence it results that: S.M. But the genesis of a particle supposes a broken⋅ symmetry, which is explained in the S.M. by the conclusion that the Higgs potential 22 Vaa ( ) = e/4πε a + e/8 πε 0 a, is unstable at the origin, so- by a quantum fluctuation in the Higgs field. The value: a.() HH0 corresponds to the rest energy of the Higgs

with εε≈ 5 0 –as consequence of the variation of the refraction boson. In CGT, the equivalent of the Higgs field is the ‘primordial d index n and of the electric permittivity : εε=0 × εr with the dark energy’, which is a field-like component U0 of the quantum vacuum energy (of the ‘zero-point energy) which- in contrast with local density of quanta: nl= cv/~ l≈ ερ rl, ( εr (1.5a) = 1 ; s the Brownian etherono-quantonic componentU0 , is in the form of 2 ε(a) = na( ) / n( 1.5 a) = ρρ( a) /( 1.5 a) = (1.5 a / a) ;⇒ ε( a) ≈ 5) omni directional etherono-quantonic winds (fluxes) of mean speed c r ll r . The high difference between the mass of an electronic neutrino and , which gives: an electron is explained in CGT by the hypothesis of a chiral form of e d the electron’s super dense centroid m0 which in interaction with U0 22 e V( a) =≈= e / 4πε a e / 20 πε a 205 keV ; will generate an etherono-quantonic vortex Γµ and a vortexial field: e 0 2 22 V( a) = m c = 511 keV , so: VrΓ ( ) =−= υυkd P −−½ kρ c c = V o.|Ψ | which - by the µ e attraction of ‘naked’ thermalized photons from the quantum vacuum, V a= V a + V a + V a≈ 716 keV+ 3 keV = 719 keV < Q <∈ ak( ) e ( ) µσ( ) Γ ( ) will generate the electron’s mass m in accordance with the eqns. . (24) e (1), (10), (10’’). So, the quantum fluctuation which generates the The mean attractive potential in the interval a ÷1 ,5a is: rest mass of the electron is a chiral (vortexial) one, generated by the e chirality of the electron’s centroid: ζ e ()m0 = ±1. The fact that the Va( d) =( V aa( a) + V(1.5 a)) / 2≈( 719 + 1022) / 2 = 871keV <∈σ . 4 electronic neutrino has a rest mass of at least 10 times lower than the electron is explained in CGT by the conclusion that it results by Taking into account also the centrifugal potential Ecf given by the the transforming of a σ-gluolby the loosing of its photonic mass when e Γµ of the protonic magnetic moment to the β –electron which– the centroids of its quasi electrons ()m0 of opposed chirality enter in contact forming a centroid of double mass but of null chirality: in the outside of the proton can attain a relativist speed vce ≈ 0.9 , 2 v e (E= ½ m v≈ 0 .23 MeV ) , it results that the attractive potential V ζζne()mm00 =∑() =+− 11 = 0 , which will not generate cf e a d etherono-quantonic vortex by interaction with the U0 –field. is compensated by the energy ∈σ (889keV ) released at the σ –gluol’s transforming and the centrifugal potential, conform to the CGT’s In the case of a pseudo-scalar photon, the generation of its relativist 4–6 2 model. mass mf = hv/ c can be imagined as resulted by the interaction of two super dense centroids of opposed chirality (initially un-separated) Also, the fact that for ddi <= γ 1.5 a, we have: Vµ ( di) > Vd ei( ) and of relative neglijible mass- compared with the electron’s mass , indicates the possibility of the particles’ cold forming as non– d with the etherono-quantonic U0 –field in which the generated destructive collapsed B–E condensate of ‘gammons’ (of degenerate chiral (vortexial) fluctuations will attract more quantons from the −+* ee pairs) by magnetic interaction between the quasi–electrons: s ( ) U0 component of the quantum vacuum, forming the pair of vectorial e*− , e*+ . photons of opposed spins and magnetic moments, in accordance with the eqn. (20), v-photons which compose the pseudo-scalar photon, in The relative correspondence of CGT with CGT. the Higgs field’s theory In concordance with the previous conclusions we may re-write the † As it is known, the basic idea in the hypothesis of the Higgs field expression of the creation/degeneration operator c j in the form: was the explaining of the intrinsic energy of a particle with rest mass

††=+== ζζ ζζ ρ ρ Ψ= 〉=Ψ≤e −≤ = cj 1 Kj ; K j () ef k j ()[ ef f(a) / e( a) ] ; j | K j c j . , ( 1Kj 1; a 1.41 fm) (25)

ζζ= ζ in which the Kj coefficient is creator if feand destructor chirality f attached to the electron’s centroid with ζ e –chirality ζ Γ f − ρ − if ζζfe= − (because the super dense centroid f with opposed will generate an opposed µ vortex of f (a) density which

In this context, it results that the interaction mechanism by e e will destroy the Γµ − vortex, as in the case of the electron’s m0 – intermediary Z–boson and respective– by ‘color’ charges and gluons, centroid internal vibrating. In the photon’s case, the large spectrum of considered by the Standard Model for the weak and the strong and light photons suggests- according to the model, a large mass spectrum nuclear interactions, is semi–formal, a more natural explanation for of vector photons’ centroids, because a bigger chiral centroid m f these interactions being given in CGT by a multi–vortexial model of 0 proton and by its resulted vortexial field, which imply also a specific d Γ − will generate by interaction with the U0 –fielda denser f vortex; “bag” model of inter–quarks interaction and a “dynamide” model of † the creation/degeneration operator c j can be written in this case in neutron, with degenerate negatron rotated around the protonic center. the approximate form: This conclusion is important also in the cosmology of matter’s genesis, because it shows that the mechanism of paired quarks forming c† =1+= KK ; = ()ζζ k () ζζ mmfr / ; and j  j j fr j fr( 00) from very “hot” radiation by quantum fluctuations, considered by being applied to the reference wave function ψr of the reference the S.M. in connection with the Big-bang cosmological model, is more formal than explanatory; (for example-it cannot explain how particle with centroid m r : 0 the radiation quantum, with null ‘color charge’, generates paired

† r frr quarks or/and gluons with ‘color’ charge, the same problem existing Ψ j=|K〉 j = c j .Ψ = [(1+Ψ ζζfr)( mm00/,)]. (26) at the explaining of the paired non-leptonic particles creation from

the quantum vacuum, by spontaneous symmetry breaking). Also, the It is possible that initially the quantonic vortex may be weaker than experimentally obtaining of bosons (even W, Z-bosons) and of q-q the etheronic vortex, the equality being attained by the forming of the pairs by (ee−+− ) or (ep−+−−) interactions30 sustains the possibility = fr fermion’s kerneloid of mk-mass , so: kmjk/. m k of quarks’/particles’ forming as clusters of “gammonic” pairs of degenerate electrons and the CGT’s model of nuclear interaction So, the real relation of the leptonic fermion’s centroid to the ground d (without the concept of ‘color charge’). Another experiments which field U 0 is in the form (1): sustains the theoretic model of CGT is the experimentally obtaining of a Bose-Einstein condensate of photons, (a “super-photon”), by a m. c22= b.() Uda+< U≈ ½ µ H dV( r); () r r (27) German team (2010,19), indirectly proving the existence of the rest 00∫ λ mass of photons, considered in CGT, as in the case of the ‘dark 4 photon’ theorized in the quantum mechanics). with H = B/µ01 = kρ f ( rc). , (CGT, ), the value of b depending on the centroid’s m r − mass/volume. The vortexial field results in CGT by a mono–vortex for 0 the vectorial photon and for electron and as field of superposed The additional genesic potential U a can be a vortexial field, as vortices – in the case of mesons and of baryons, resulted in CGT ad as non– destructive collapsed clusters of paired quasi electrons, (of those of a very strong (magnetaric) magnetic field, UU= or a ( ) **−+ disturbing (Brownian) field (UUas= ). ‘gammonic’ pairs of degenerate electrons, (ee ) ). Also, it results by CGT that all quarks are preonic, i.e.–composed sub particles, 0 r † ar with quasi–crystalline kernel formed by kerneloids of z –preons of Because Ψ ~ H, we have: cj=[1 + (ζζfr )(UU/ 0 )] , 34 me , this conclusion being sustained by the possibility to explain r 0 d 0 Um0 ( ) being the value of U0 -field necessary for the m - the mass spectrum of the astro–particles and of the ground states of particle’s forming. the heavy baryons and mesons, in concordance with the experiments The ‘virtual particle’ corresponds in CGT to a centroid without of bosons’ and quarks pairs’ forming by interaction of high energy −+− photonic shell (i.e- without vortex) and the transforming of a pair (ee) fluxes and those which determined the almost identical size order of the maximum radius of the scattering center inside the of virtual particles into a pair of real leptonic particles (possibility −18 considered by the quantum vacuum fluctuations theory) corresponds electron (with X–rays):10 m , with that of the scattering centers determined inside the nucleon: 0.43xm 10−18 (considered as quarks to the splitting of a centroid of ζ r = 0 into its components of in QM and as electronic centroids, in CGT ). A vortexial potential ζ = ± d f 1 which- by interaction with the U0 – field, will obtain a with repulsive kernel of ‘sombrero’ type can be proposed as general Γ f − vortex and implicitly- and a photonic shell; (i.e.- the conversion: genesic potential, which can explain also the cold genesis by chiral +− d ve → (ee− ) is possible in CGT, by the energy of theU0 –field). cuantum fluctuations. But-compared with the S.M.’s hypothesis, in CGT all particles Conclusion have rest mass, with the difference that the bosons with super dense It results from the above comparative analysis that a non– centroid of null chirality haven’t genesic vortex and cannot have postulated explanation (natural, based on cause–effect determinism) photonic quantum volume (as in the case of the electronic neutrino, of the known properties of elementary particles and of their magneto– conform to CGT). This potential can explain also the cold forming electric and nuclear interactions cannot be obtained by disregarding of the photons and of electrons- considered in CGT with quantum the concept of quantum and sub quantum vortex (etherono–quantonic), volume of classic radius a=1.41fm (with e-charge in surface) formed the most plausible explanatory variant indicating that the forces of the by ‘naked’ photons vortexially confined and e-charge given by basic interactions: gravitational, electric, magnetic, weak and strong/ vectorial photons. Implicitly, the possibility of paired (pseudo)quarks −+ 30 nuclear , can be generated as differences of static quantum pressure forming by (ee− ) interactions invalidates the gluonic model of –given by Brownian kinetic quanta and by quantum winds, and that– quark and the gluonictheory of the nuclear interaction, (by the lack for the etherono–quantonic winds and vortexes, the mechanics of of ‘color ‘ charge). the ideal fluid can be considered, the Bernoulli’s law, in the simplest A reaction that sustains the possibility of paired particles + +− form: Ps Pd = constant, being also valid. forming by ‘gammonic’ pairs (ee) is also the known reaction:

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