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A new semiclassical model of the electron with helical solenoid geometry is presented. This new model is an extension of both the Parson Ring Model and the Hestenes Zitterbewegung Model. This model interprets the Zitterbewegung as a real motion that generates the electron’s rotation (spin) and its magnetic moment. In this new model, the g-factor ap...
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Effects related with the interference of electron waves around a magnetic point defect in two-dimensional electron gas with the combined Rashba-Dresselhaus spin-orbit interaction in parallel magnetic field are investigated theoretically. The influence of the magnetic field on the space distribution of the local density of states and the local densi...
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... Therefore, amidst ongoing efforts to comprehend the structure of quantum particles in atoms, many authors have devoted time to understand the intricacies of the electron's behavior. Notably, after Schrödinger coined the zitterbewegung term in 1930 [1], many authors have devoted attention to it [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. One of the most interesting interpretation is due to David Hestenes [12][13][14][15], which has led many researchers to develop semiclassical models, where the electron and other particles have structures and substructures [3,4,[10][11][12][13][14][15][16][17][18][19][20]. ...
... Notably, after Schrödinger coined the zitterbewegung term in 1930 [1], many authors have devoted attention to it [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. One of the most interesting interpretation is due to David Hestenes [12][13][14][15], which has led many researchers to develop semiclassical models, where the electron and other particles have structures and substructures [3,4,[10][11][12][13][14][15][16][17][18][19][20]. ...
... In some of these models, the center of mass and charge of the electron are located in different positions; the electron charge travels at the speed of light around the center of mass, on a circular orbit of Compton radius (Compton wave length over 2π) [3,4,18,19]. This idea has been supported by the helical motion of the electron when it is ligated, for instance, in the Bohr atom [17][18][19]. ...
This work deals with the origin of the force which maintains the Schwinger electromagnetic wave traveling around the electron mass in the toroidal electron model. The linear momentum exchanged between electron charge and electron center-of-mass suggests that the interaction force forms a long-distance action-reaction pair, as predicted by Newton's third law. The results show that the propagation of the Schwinger electromagnetic wave, responsible for the electron charge, induces oscillations in the electron center-of-mass with the zitterbewegung frequency. Furthermore, a restoring force is demonstrated to describe the oscillation of the electron center-of-mass. A unification of the centripetal, Lorentz, Schwinger, and restoring forces is also reported.
... In ordinary Maxwell equations, at time scales much larger than Zitterbewegung period T ≃ 0.81 · 10 −20 s , the currents generated internally by the Zitterbewegung motion of electron charges can be safely ignored and only the averaged macroscopic currents generated by the motion of many particles are usually considered. This Zitterbewegung electron model follows an old research stream that started from the rst decades of the XX century [27,2,18,19,20,12,5,11,6,17,26]. ...
This paper proposes the possibility that the formation of coherent charge clusters in nanometric gaps may have a role in the generation of Ultra Dense Hydrogen, Compton Scale Structures and in the catalysis of Low Energy Nuclear Reactions. This hypothesis is strictly related to a simple and intuitive theoretical framework that, in agreement with Occam's razor principle, proposes a common origin of fundamental physical properties as charge, mass, relativistic mass, spin and magnetic moment. This approach needs a particular Zitterbewegung electron model derived by a purely geometric/electromagnetic interpretation of Maxwell-Proca, Planck, De Broglie, Schrödinger, relativistic energy momentum and Aharonov-Bohm equations. Starting from this Zitterbewegung model a realistic hypothesis may be formulated on the structure of exotic vacuum objects (EVO) and dense charge clusters seen by Shoulders and other researchers in their experiments. key words Aharonov-Bohm equations, aneutronic and many-body low energy nuclear
... Oliver Consa presented a new semiclassical model of the electron based on the Parson Ring Model and the Hestenes Zitterbewegung Model [28,29]. In this model, the Zitterbewegung is a real motion that generates the electron spin and its magnetic moment. ...
... 95 constant, mass of electron and velocity of light respectively [29]. When = 0, i.e., = 1, this equation reduces to ring electron model and rotational period will be = ℎ 2 = 8.0932997857 × 10 −21 sec (54) ...
Maharishi Vyasa based on a Patanjali Yog sutra defined a universal, natural, indivisible, exceedingly small quanta of time known as kshana or moment. According to him time kshana is not a particle. It is a creation of the mind without mass. It is the time taken by an elementary particle to change its direction from east to north. For the elementary particle such as a spinning electron, the calculated value of a kshana in sec with different models of electron is of the same order magnitude as calculated for zitterbewegung which is equal to ten to the power minus twenty-one sec and is a constant. We found that the number of kshana in a second is inversely proportional to the radius of the spinning electron and independent of mass of the electron. Smaller the radius, small is the value of a kshana. Based on this definition of kshana, calculated value of the radius of an electron is equal to the reduced Compton wavelength.
... Oliver Consa presented a new semiclassical model of the electron based on the Parson Ring Model and the Hestenes Zitterbewegung Model [24,25]. In this model, the Zitterbewegung is a real motion that generates the electron spin and its magnetic moment. ...
... the rotational velocity of electron), Planck constant, mass of electron and velocity of light respectively[25]. When v = 0, i.e., γ = 1, this equation reduces to ring electron model and rotational period will beT o = h mc 2 = 8.0932997857 × 10 −21 sec(54)which is same as found in the equation 17. ...
Maharishi Vyasa based on a Patanjali Yog sutra defined a universal, natural, indivisible, exceedingly small quanta of time known as `kshana' or moment. It is the time taken by an elementary particle to change its direction from east to north. For the elementary particle such as a spinning electron, the calculated value of a kshana in sec with different models of electron is of the same order magnitude as calculated for zitterbewegung which is equal to ten to the power minus twenty-one sec. The value of kshana is dependent on the radius of the spinning electron. Smaller the radius, small is the value of kshana. Based on this definition of kshana, calculated value of the radius is equal to the reduced Compton wavelength.
... Refer to Figure 2. In Physics, it is called spiral torus [8,10]. The 2-dimensional representation of Villarceau torus is shown in Figure 3. (4,5). One is a cyclic rotation of the other. ...
... The electrons move on helix trajectories in a uniform magnetic field. It is called Helical Toroidal Electron Model [5,28]. Refer to Figure 9 (a). ...
Villarceau torus is a discrete graph theory model of spiral torus which is called Helical Toroidal Electron Model in Physics. It also represents the double stranded helix model of DNA. The spiral torus or toroidal helix in Physics and Molecular Biology is continuous whereas the Villarceau torus is discrete. The main contribution of the paper is the identification of cycles which are equivalent to toroidal helix in spiral torus. In addition, the poloidal revolution and the toroidal revolutions of Villarceau torus are computed. The paper identifies some striking differences between ring torus and Villarceau torus. It is proved that Villarceau torus does not admit any convex edgecuts and convex cycles other than 4-cycles. The convex cut method is extended to graphs which do not admit convex edgecuts. Using this technique, the network distance (Wiener Index) is computed, Also an optimal congestion-balanced routing for Villarceau torus is designed.
... One possibility for doubling the spin-field interaction energy in Eq. (3.12) so that it is consistent with Dirac's theory is to introduce further "hidden" components of the spin motion. For example, Consa [11] has suggested a toroidal solenoid spin model so for a free electron, the rest-frame circular spin motion presented here is replaced by a rest-frame toroidal motion of the electron moving at the speed of light. There are then two additional model parameters: the radius r of the circular cross-section of the torus and the number N of windings around the torus. ...
... The linear independence of the set of functions {1, cos(N ), cos(2N )} in the expression for the electron's speed (Eq. (36) of Consa [11]) means that this constraint implies that r = 0 , so the toroidal spin model collapses to the circular one used in this work. ...
In this work, a neo-classical relativistic mechanics theory is presented where the spin of an electron is an inherent part of its world space-time path as a point particle. The fourth-order equation of motion corresponds to the same covariant Lagrangian function in proper time as in special relativity except for an additional spin energy term. The theory provides a hidden-variable model of the electron where the dynamic variables give a complete description of its motion, giving a classical mechanics explanation of the electron’s spin, its dipole moments, and Schrödinger’s zitterbewegung, These features are also described mathematically by quantum mechanics theory, of course, but without any physical picture of an underlying reality. The total motion of the electron can be decomposed into a sum of a local spin motion about a point and a global motion of this point, called here the spin center. The global motion is sub-luminal and described by Newton’s Second Law in proper time, the time for a clock fixed at the spin center, while the total motion occurs at the speed of light c, consistent with the eigenvalues of Dirac’s velocity operators having magnitude c. The local spin motion is an inherent perpetual motion, which for a free electron is periodic at the ultra-high zitterbewegung frequency and its path is circular in a spin-center reference frame. In an electro-magnetic field, this spin motion generates magnetic and electric dipole energies through the Lorentz force on the electron’s point charge. The electric dipole energy corresponds to the spin-orbit coupling term involving the electric field that appears in the corrected Pauli non-relativistic Hamiltonian, which has long been used to explain the doublet structure of the spectral lines of the excited hydrogen atom. Pauli’s spin-orbit term is usually derived, however, from his magnetic dipole energy term, including also the effect of Thomas precession, which halves this energy. The magnetic dipole energy from Pauli’s and Dirac’s theory is twice that in the neo-classical theory, a discrepancy that has not been resolved. By defining a spin tensor as the angular momentum of the electron’s total motion about its spin center, the fundamental equations of motion can be re-written in an identical form to those of the Barut–Zanghi electron theory. This allows the equations of motion to be expressed in an equivalent form involving operators applied to a state function of proper time satisfying a neo-classical Dirac–Schrödinger spinor equation. This state function produces the dynamic variables from the same operators as in Dirac’s theory for the electron but without any probability implications. It leads to a neo-classical wave function that satisfies Dirac’s relativistic wave equation for the free electron by applying the Lorentz transformation to express proper time in the state function in terms of an observer’s space-time coordinates, showing that there is a close connection between the neo-classical theory and quantum mechanics theory for the electron’s dynamics.
... The first serious approach to a physical theory of the electron, published in 1990 by Bergman and Wesley [1] is based on a toroidal ring with uniformly distributed charge. In 2018 Consa [2] used the same principle for a modified and extended electron model. The presented article is based on an independent publication of the author [3] that is hidden in the web since 2014. ...
... The model of toroidal electron is common with many classical models (2,3,4,5,6,7) and semiclassical models (8,9,10,11) . These models are based primarily on the laboratory experiments of Compton 1919 (12,13) and Bostick 1956 (14, 15) . ...
Regardless of the nature of gravity, it has been proven that light behaves according to the laws of optics within the gravitational field. This fact proves that we can consider the gravitational field as a medium with a refractive index of which light transfer through. This paper explained the meaning of the inertial mass and the accompanying gravitational field, according to the results of the previous two papers (1 and 16). Accordingly, we showed the possibility of generating a gravitational field and designed a method to measure it. The required magnetic field and the sensitivity of the detection device are calculated carefully. It turned out that it was not possible to generate a strong enough gravitational field to be sensed and measured with the devices and capabilities currently available.
... The conclusion though is that " the only dynamics of a charged quantum system which has an interpretation consinsent with relativity is the Zitterbewegung" [6]. Readers that are interested in electronic internal structure can also review the paper of Consa that discusses the helical solenoid model of the electron [7] and even the work of Hu [8]. Probably the most known researcher in the field of Zitterbewegung is Hestenes, who in a series of papers has laid down the mathematical framework of the Zitter electron model [9] and also attempted to explain the experimental results of electron channeling in crystals performed by Catillon et al [10]. ...
... If equation (11) is valid then it should in principle reproduce known results for the total energy radiated during acceleration. In order to check this, instead of adopting Hestenes's equation for the zitter angular frequency which involves the so called Spin-Zitter interaction energy, one can use the results presented by Consa [7], who by simple geometric and physical arguments has derived the following relationships for ω z and L, which will be assumed to be valid for the accelerated case as well. ...
In this work, starting from the Larmor equation and using Zitterbewegung theory it is shown how to derive an energy output equation which is identical to the one given in Landau and Lifshitz. An attempt to semi-qualitatively describe how this model leads to photon energies in agreement with QED is also made, under the assumption that the internal electron clock has to be ''minimally disturbed''.
... The Zitter model for the electron postulates that the electron has an internal structure consisting of a subelectron particle with mass and charge that is rotating about a center of mass [2], [1], [8], [3], as depicted in figure 1. It is important to realize that while useful, the mental image of a point particle following a path is not very accurate. ...
This paper presents an approach to special relativity which is more in line with electrical engineering , namely as the time-harmonic analysis of a linear system. The approach is derived from Hestenes' Zitter model for the electron[1], [2], which assumes an internal structure of a light-like helix in spacetime. A time-harmonic model is constructed and combined with classical physical arguments to produce several fundamental multivector equations. In addition, the grade (dimension) of the quantities involved match their units. The Zitter model is then extended to a nested helix, as suggested by Consa[3], and attempts are made to derive the fine structure constant, and vacuum constants µ0 and 0. Since the models presented are based on a classical physics, they are 'local hidden-variable' theories which are not consistent with Bell's theorem.
