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Tphysicsletters/6981/10/1490/365787tpl/The Nature of the 1 MeV-Gamma quantum in a Classic Interpretation of the Quantum Potential
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The Nature of the 1 MeV-Gamma quantum in a Classic Interpretation of the Quantum Potential
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Abstract
By considering wave-particle dualism with an interpretation of the squared amplitude of the wave function R2(Y) compatible with the known Bohm’s equations, for a 1 MeV-gamma-quantum considered as ‘gammonic’ (e-e+)- pair of electrons having the phase speed of the associated wave equal to the group speed of passing through a low frictional component of the quantum vacuum, it results a value of the quantum potential Q equal to the particle’s kinetic energy, Qc = ½mv2 , for a classic model of electron composed by heavy photons, this value being explained by a generalized relation of quantum equilibrium of de Broglie type, with the associated entropy proportional to its action S, as representing a centrifugal potential given by a spinorial mass ms = nvmv » me resulting by nv -vector photons explaining also a half of the electron’s rest energy by considering and a dynamic component of the quantum vacuum- given by quantum and sub-quantum winds, which generates also a centripetal quantum force of Magnus type acting over the rotated vector photons and corresponding to a vortical potential Qa which maintains the centrifugal potential Qc , the spinorial energy of the vector photons contained by the electron’s shell explaining the second half of its rest energy and the Lorentz force- resulting of Magnus type, but in the Galilean relativity, the resulted interpretation indicating a rest energy at least for photons of gamma quantum, in concordance with the known relation for the red-shifted photon’s frequency in a gravitational field.
Introduction
It is known that- at the base of the wave-particle dualism, inserting the wave function ψ in polar form into Schrödinger’s equation, written – for simplicity, for a single particle of m-mass:
(V – classical potential; R, S - real-valued functions of space and time) and separating the real and imaginary terms were obtained the Bohm’s equations [1] :
If ρ = ψ×ψ* = R2 is interpreted as a probability density of particles distribution, Eq. (3) is the continuity equation, Eq. (2) representing the quantum Hamilton-Jacobi equation. In the Madelung’s form, R2 = ½Y½2 = rm/m, with rm –physical density of m-particles. It is also considered that the potential Q generates an additional quantum force F = −∇Q, of particle’s interaction with a sub-quantum fluid of the quantum vacuum . According to the de Broglie-Bohm causal interpretation, the particle’s path is deterministic, R2(x,t)dx representing the probability that a particle lies between x and x + dx, [1]. In an interpretation given by Giovanni S., Erasmo R. and co-workers [2] to the Bohm’s quantum potential: Q = -(ħ2/2m)(DÖr/Ör), it is identified with the kinetic energy of a rotation motion (“zitterbewegung”) associated with the spin s = ½ħ of the fermionic particle, (particularly –of the electron), in accordance with the Schrodinger’s equation written in the form: -(2s2/m)DY = EY, the internal zitterbewegung velocity being: V = Ñrxs/mr, (r = R2). It is known also that –using a complex velocity: vi = v + i×u, and a complex action, Si = Sp + iSR , in the scale relativity theory Nottale has shown that –expressing u in terms of the modulus of ψ = eiS/ħ , i.e.: u = DÑlnR2 , (R2 = |y|2), with the scale parameter: D = ħ/2m, the variation of the u –velocity introduces a new force: F = m(du/dt) = -ÑQ which derives from a quantum potential Q = -(ħ2/2m)(DR/R), [3], with: m- the particle’s mass. The fact that the 1 MeV- gamma quantum splits into a (e- -e+ )-pair in the E-field of a nucleus suggests the possibility of an electronic nature of the 1 MeV-gamma quantum. In such a case, their electro-magnetic properties must depend on the electron’s properties. So, it is raised also the question: how the Bohm’s quantum potential can explain the electron’s spin? Relating to the electron’s structure, it is known that the Quantum Mechanics considers the electron as being an almost point-like particle, with radius of at most 10-18 m, [4]. However, this electron model of QM cannot explain the origin of the electron’s magnetic moment, its electric charge and its spin s = ħ/2 as physical properties. Also, for an electron with radius < 10-18 m, i.e. with high density: re > 1023 kg/m3, it would be difficult to explain the e--e+ annihilation at v®c and the photon emission process. But these properties can be at least partially explained by a classic, Lorentzian model, of vortical type [5]. In a classic vortical model of electron [5], the radius of value ~10-18 m corresponds to the radius of a super-dense kernel of a quantum volume of photons with inertial mass mf confined around a denser kerneloid of radius ~10-17 m (corresponding to an experimentally determined electron’ radius reported by Milonni [6]) which give the electron’s inertial mass –equal with its electromagnetic mass : me = e2/8pe0ac2 , (a = 1.41 fm –corresponding to an e-charge contained by the electron’s surface. An interpretation of the Q-potential was obtained [7] by a classic model of electron with confined photons by considering a vortical structure with a relativist speed (v ~ r-3), of a vortexed quantum fluid, ([7], p.137) and by using the relations specific to quantum equilibrium obtained by de Broglie [8] , but in the form: e’/kb = iS0/ħ , (e’ -the associated entropy; S0 = òLdt –the physical action; kb –the Boltzmann’s constant; ħ = h/2p, h -the Planck constant), specific to the case of a stationary entropy: e’ = - kblnrp = - kblnR , resulting by Boltzmann’s relation:
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Conclusions
By considering the wave-particle dualism with an interpretation compatible with the known Bohm’s equations, for the electrons of a ‘gammonic’ (e-e+)-pair having the phase speed of the associated wave equal with the group speed, it results a value of the Bohm’s quantum potential Q equal to the electron’s kinetic energy, Ek = ½mv2 . For a classic model of electron composed by heavy photons, this value is explained by a generalized relation of quantum equilibrium of de Broglie type: e/kb ~ S/ħ , as centrifugal potential Qc given by the rotation with the same v-speed of nv – vector photons of inertial mass mv giving a spinorial mass ms = nvmv » me , determined by a vortex of circulation Gr = 2pr×v induced by the particle’s passing through a low frictional medium of fine quanta (etherono-quantonic, [5]), of density rb0 and maintained by a corresponding vortical potential Qa = -Qc generated in accordance with the laws of the ideal fluids applied to the considered low frictional medium of the quantum vacuum. But the necessity to explain also the electron’s spin and its rest energy mec2 also indicate the existence of a dynamic component, rv0, given by quantum and sub-quantum (etherono-quantonic) winds, which generates a vortical potential Qa = -Qc also at rest, the low frictional component rb0 generating a centripetal quantum force of Magnus type acting over the rotated light vector photons which give the electron’s spin and its intrinsic rest energy. The circulation of the heavy vector photons which give the electron’s inertial mass me - considered as contained in a volume of classic radius corresponding to the e-charge in its surface, can explain also the Lorentz force by a kinetics corresponding to a multi-vortical lepton, with secondary vortices of light vector photons rotated with c-speed around the inertial mass of heavier vector photons contained by the electron’s surface, which gives also the electron’s charge. The forming mechanism seems to be similar to the multi-vortex tornado phenomenon. The value of ~ 10-18 m of the electron’s radius indicated by some experiments [4], is explained by the conclusion that it represents the radius of an electronic super-dense kernel, which ensures the stability of the electron’s vortical structure [5]. This vortical electron model explains the electron’s spin ½ħ in concordance with other theoretical observations [45] showing that the electron’s spin can be explained by a non-relativistic theory based on the Galilean relativity, that allows nonrelativistic wave equations for any spin, in concordance with Galilean electromagnetism and invariance. Extrapolating the conclusions resulted from the used electron model to the vector photon of a pseudo-scalar g- photon considered in a revised Munera model of pseudo-scalar photon [20] leads to the conclusion that the considered quantum/sub-quantum (etherono-quantonic) winds give similarly rest energy and a rest mass also to g- photons, this conclusion being non-contradictory in the Galilean relativity and explaining the conclusion of the quantum mechanic that at 0K the stationary particles as the leptonic fermions have a non-null energy: ½hn = ½mc2. Even if this conclusion is in contradiction with conclusions of quantum-relativist mechanics, it is in concordance with Minkowski’s expression of the momentum of a refracted ray: p = En/c = m×v, and with the experimentally evidenced possibility of obtaining a Bose-Einstein condensate of photons [11]. Also, the revised Munera model of photon is more plausible than the Hunter-Wadlinger model (supposing a vortex parallel with the photon’s impulse [46]) as pseudoscalar model, because it explains also the light’s polarisation and the Faraday effect, of light’s polarisation plane rotation in a magnetic field, but in the Galilean relativity, because it cannot be used in the Einsteinian relativity in which a vortex G = 2prc of a particle having a speed v » c and G ^ v is canceled by the Einsteinian relation of speeds composing. The use of the Galilean relativity also for photons was argued as natural way and by the possibility to explain the Lorentz force as a Magnus type force and the maintaining of the electron’s magnetic moment and its e-charge with constant values also to electrons deviated by a Lorentz force in a magnetic B-field, conform to a vortical model of electron and of magnetic moment, (the same explanation not being possible in the Einsteinian relativity because the conclusion of spin’s cancelling at v ®c, for electrons and vector photons with the spin rectangular to impulse, s^ p, in the special relativity). Because the considered dynamic component rv0 of the quantum vacuum can explain also the e-charge’s magnetic moment as etherono-quantonic vortex [5], by its etheronic part, it results that the nuclear magnetic moment can also explain the perpetual rotation of the atomic electrons around the atomic nucleus [5]. Relating to the discrepancy between the density of the vacuum energy of the free space resulting from the upper limit of the cosmological constant: ~10-26 kg/m3 and that estimated in quantum electrodynamics: 1094 kg/m3, [47], it can be observed that supposing a quark model formed as cluster of degenerate electrons (i.e. as Bose-Einstein condensate of “gammons”, [5]), the resulted model supposing etheronic and photonic vortices generated by the quantum vacuum’s energy do not imply the necessity of a density of the low frictional medium of the quantum vacuum (resulted as preponderant etheronic) higher than that of the nucleon, the value of ~10-26kg/m3 specific to the cosmological constant representing in this case only an un-compensated dynamic component that generate the cosmic expansion, (whose pressure is not compensated by an opposed pressure of another component, [5]). This is a logical conclusion because it is plausible that the gravitational field’s energy is given by similar quanta as those of the ‘dark energy’. Also, it is known that it resulted experimentally the absence of time delays associated with forces of the magnitude needed to explain the phase shift observed in the Aharonov-Bohm effect to an electron that pass through a zone with null magnetic B-field but non-null magnetic potential A [40] . The existence of a quantum force, predicted in 1990 as physical explanation for the Aharonov-Bohm effect [41], was evidenced in an experiment [42] as transverse force derived from a potential of Bohm type: Q = -(ħ2/2m)(Ñ2R/R). Qualitatively, this result corresponds to the obtained physical interpretation of A-potential, of Qc and of Qa , by the conclusion that A-potential is given as (pseudo)vortex of etherons induced around elementary particles by etheronic winds which penetrates the atoms and which can exists also around a magnetically shielded solenoid [5], the Qa-potential resulting as given by a quantum force of Magnus type, conform to Eq. (40), produced by an etheronic vortex formed around a chiral (spiral) electronic centroid. Also, the conclusion of photon’s speed and energy attenuation also in vacuum, depending on the photon’s mass, as in Eq. (72), is in concordance with the experimentally observed Lorentz-invariance of the photon’s mass of a very large but finite numbers of non-collinear photons of light pulses propagating in vacuum whose velocity was a little lower than the light speed in vacuum, the resulted difference being related directly with the invariant mass of a pulse, [48]. These arguments sustain a particles cold genesis scenario supposing vortices in a quantum and a sub-quantum (etheronic) medium generated as effect of chiral fluctuations at high densities of this medium, comparable to those of a magnetaric magnetic field, the considered etherono-quantonic vortical nature of the magnetic field being concordant with the basic laws of electromagnetism [5] but also with the observations regarding the generating of quantized vortices in a superconducting thin film of Nb, [18], which reported the observing of vortices and anti-vortices which annihilate each other, generated when a 100 Gs magnetic field applied to the thin film of Nb is suddenly reversed and its magnitude increases (generating the anti-vortices). The concept of ‘etheronic medium’ used in the paper is compatible with the concept used in other similar approaches such as those used in Ref. [36] and with the field-like nature of the ‘dark energy’, evidenced also by some astrophysical observations [49] . The super-fluidity of the considered etherono-quantonic component of the quantum vacuum is in concordance also with the fact that the vacuum is a dielectric medium, in which the displacement current (∂D/∂t) does not vanish. The conclusion of the creation of etheronic vortices in the quantum vacuum corresponds indirectly to the conclusion of superluminal propagation of the quantum potential, introduced in the Vigier’s model [50], which considers that the quantum potential is a real interaction among the particles and the sub-quantum fluid polarized by the presence of these particles [51] and therefore is considered to be a true stochastic potential [52]. Mathematically, the resulting interpretation of the quantum potential does not exclude other interpretations corresponding to other premises and values for R, for example- as in the case of the interpretation of Perelman [53] which correlated the quantum Bohm potential with an antigravitational potential Vg , possibly implied in the Universe’ expansion. The obtained interpretation is in concordance with the fact that the previous attempts to explain the spin and the magnetic moment of the electron implied the conclusion of its mass and charge rotation with the light’s speed [54] . An argument for the conclusion that the photons can form vortical clusters is also the experimentally evidenced possibility to create optical vortices by light beams twisted around their axis of travel, [55]. Another argument is the experimentally evidenced possibility to “freeze” photons inside a crystal for up to a minute by the technique of electromagnetically induced transparency, the trapped photons inside the opaque crystal being converted inside the crystal (having controlled transparency) into atomic spin excitations ("spin waves") which thereafter were turned back into photons of emitted light, [56]. It was also argued that the electromagnetic properties of a single photon of a gamma quantum are given by antiparallel magnetic moments mf of the coupled vector photons that induce an electric field Ef , this explanation of its transversal (electromagnetic) wave being sustainable (only) in the Galilean relativity. Also, the conclusion that the electron’s e- charge is contained in its surface shell was argued and by other studies [57] and a value for the electron’s radius close to the classical radius of the classic electron’ model used in the paper was already experimentally determined [58]. By a classic expression of the gamma quantum’s energy based on the obtained theoretic model, the expression of the gravitational redshift is retrieved, but with the observation that in the case of a gamma-quantum considered as relativist ‘gammonic’ (e*-e*+)-pair of degenerate electrons, by the Galilean relativity it results a value of 2/3 from that given by the known relation, this difference being caused by its rest energy E0 = 2me*c2, resulted by adding the spinorial energy of the electron’s heavy vector photons to the vortical energy ½Smsc2 = ½mec2 of the electron’s spinorial mass- resulted as equal with its inertial mass but without contributing to its value, conform to the resulting model. The applicability of the Galilean relativity also to relativist speeds for the deducing of the real energy of a gamma quantum (given by its effective material mass) can change the conclusion relating to the physical nature of some gamma-quantum. For example, in this case, the gamma quantum with the energy of 17.2 MeV emitted in a reaction:
Li + p ® 2a + g(17.2MeV)
can represent- by the Galilean relativity, the neutral boson X17 experimentally evidenced by a team of Hungarian researchers by the de-excitation of a nucleus of Be formed by the reaction [59], [60]: Li + p ® Be* + X(17). Also, the gamma quanta produced by the reaction: p0 ® 2g can represent- in the Galilean relativity, a pair of preonic bosons: z2(136 me) identified as constituents of preonic quarks in a Cold genesis theory of particles, [5], [61]. The possibility to explain some basic magneto-electric and kinetic properties of the electron by the hypothesis of a main composition of the quantum vacuum given by a low frictional component, by the resulting vortical electron model also argues a fractal mechanism of the electron’s forming and an etheronic or etherono-quantonic nature of the “dark” energy.
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