Starting from a probabilistic model of the electron, which explains spin and spin measurements in terms of a probability density distribution resulting from a rapidly changing angular momentum during an extended Zitterbewegung EZBW, a “light-like” model of the electron and other spin-1/2 particles is formulated. This model describes individual particles in terms of paths of a moving quantum. It is shown that this description allows one to reproduce observable properties as path-averages over a period of the fast EZBW in elementary calculations. The general topology of the paths may be described as a helical path, with a helix axis forming a circle around a fixed point in space. The radius of the helix and of the circle is equal and given by half the reduced Compton wave length of a photon of energy equal to the rest energy of the particle described. The paths depend on the relative velocity between the described “entity” and the observer, and represent the De Broglie wave. The merits of the proposed model are summarized and its role in relation to the established description by quantum mechanics is discussed. It is concluded that it supports the existence of the proposed EZBW, and offers a description of quantum behavior without quantum mechanics.
Starting from a probabilistic model of the electron, which explains spin and spin measurements in terms of a probability density distribution resulting from a rapidly changing angular momentum during an extended Zitterbewegung EZBW, a “light-like” model of the electron and other spin-1/2 particles is formulated. This model describes individual particles in terms of paths of a moving quantum. It is shown that this description allows one to reproduce observable properties as path-averages over a period of the fast EZBW in elementary calculations. The general topology of the paths may be described as a helical path, with a helix axis forming a circle around a fixed point in space. The radius of the helix and of the circle is equal and given by half the reduced Compton wave length of a photon of energy equal to the rest energy of the particle described. The paths depend on the relative velocity between the described “entity” and the observer, and represent the De Broglie wave. The merits of the proposed model are summarized and its role in relation to the established description by quantum mechanics is discussed. It is concluded that it supports the existence of the proposed EZBW, and offers a description of quantum behavior without quantum mechanics.
The spherical model of electron cannot explain Bohr magneton, de Broglie wave, etc. To explain these properties physically, we propose that spin, one core concept of quantum theory, is a reality, and introduce this alternative solely based on experimental findings, Planck’s, Einstein’s, and Dirac’s insights, and follows classical laws, that an electron is an electrical wave with a literal 21 spin (Dirac), i.e., spins two circles in one cycle, both angular momentum are ℏ. Its wavelength is determined by E=hνm0=λm0hc=m0c2 (Plank and Einstein), λ m 0 is the Compton wavelength. As E⃗ ⊥ c⃗ for a transverse wave, it has a net electricity due to the first spin, f(Eq)=21E0(1−cos(2ω0t)), half of its cycle, i.e., the minimal meaningful unit as F = E q , is related with its charge, q = E q ϵ 0 . Moreover, an electron has a ring shape due to the second spin, 2 π R 0 = λ m 0 , λ m 0 is the electron-impact cross section. As ℏ=λm0h2πλm0=m0cR0, it has a quantized classical angular momentum, with a speed of c . The Bohr magneton, μB=2m0qℏ, g -factor is 2. Critically, the full Dirac’s equation of an electron with a constant velocity is mc=ℏ⊥+p⊥+ℏ//+p//, and its electromagnetic properties due to charge are f(Eq)=f(Eq)cc2−v′2+f(Eq)cv′=Enet//+Eq⊥, v′//ℏ⊥ or v′//ℏ//, and v′//Enet. Assuming heavy charged particles have equivalent though shall not identical mechanisms, mathematically this model is equivalent to Special Relativity, and supports ALL its formulas, i.e., v < c , E = m c 2 , direction-insensitive m = γ m 0 and t=γt0; Moreover, the net electricity Enet// and Bohr magneton is orientation-quantized, direction-sensitive and follows Lorentz transformation, leading to Lorentz transformation of length contraction; while following Relativity, magnetism can be defined by f(B)=f(Eq)c2v′, which is not circularly symmetric and self-evidently does not follow Lorentz transformation. The temporospatial averaged magnetic intensity of a current is relativistic, Bˉ=∑f(Eq)c2Δv=2πϵ0c2I=2πμ0I, and μ 0 ϵ 0 c 2 = 1, supporting Maxwell’s equations. Further implications include chirality therefore magnetic spatial quantization, de Broglie wave, etc. The spherical model should be just an observation due to orientation quantization of Enet. We conclude this model of electron may provide one step further to the ultimate Quantum Theory in a nonrelativistic spacetime.
A recently proposed model of the Dirac electron, which has been shown to describe several observed properties of the particle correctly, is in the present paper shown to be also able to explain quantum interference by classical probabilities. According to this model, the electron is not point-like, but rather an “entity with structure”, formed by a fast periodic motion of a “light-like object”, whose momentum (p) causes the angular momentum responsible for the spin, and whose energy (E = pc) is equal to the energy of the electron, mc2. A qualitative description of the model is given, together with the quantitative formulae that allow to discuss interference. Applied to the experimental situation of the “two-slit” experiment, the formulae yield the same time dependence of the detection probability as the quantum mechanical treatment, and hence the same interference pattern. In contrast to quantum mechanics, the pattern is due to “particle interference” rather than to “wave interference”. No wave-particle paradox arises. The merits of the model are summarized, and its physical content discussed.
A theory employing the vortex shape of the electron was presented to resolve the enigma of the wave-particle duality. Conventions such as “particle” and “wave” were used to describe the behavior of quantum objects such as electrons. A superfluid vacuum formed the base to describe the basic vortex structure and properties of the electron, whereas various formulations derived from hydrodynamic laws described the electron vortex circumference, radius, angular velocity and angular frequency, angular momentum (spin) and magnetic momentum. A vortex electron fully explained the associations between momentum and wave, and hydrodynamic laws were essential in deriving the energy and angular frequency of the electron. In general, an electron traveling in space possesses internal and external motions. To derive the angular frequency of its internal motion, the Compton wavelength was used to represent the length of one cycle of the internal motion that is equal to the circumference of the electron vortex. The angular frequency of the electron vortex was calculated to obtain the same value according to Planck’s theory. A traveling vortex electron has internal and external motions that create a three-dimensional helix trajectory. The magnitude of the instantaneous velocity of the electron is the resultant of its internal and external velocities, being equal to the internal velocity reduced by the Lorentz factor (whose essence is presented in a detailed formulation). The wavelength of the helix trajectory represents the distance traveled by a particle along its axis during one period of revolution around the axis, resulting in the same de Broglie wavelength that corresponds to the helix pitch of the helix. Mathematical formulations were presented to demonstrate the relation between the energy of the vortex and its angular frequency and de Broglie’s wavelength; furthermore, Compton’s and de Broglie’s wavelengths were also differentiated.
A spatial model of a free electron (or a positron) is formed by a proposed superluminally circulating point-like charged superluminal quantum. The model includes the Dirac equation’s electron spin 12 and magnetic moment / 2e m as well as three Dirac equation measures of the electron’s Zitterbewegung (“jittery motion”): a speed of light velocity c, a frequency of 2 202 / 2.5 10mc h hz, and a size of 131 2 / 1.9 10mc m. The electron’s superluminal quantum has a closed double-looped helical trajectory whose circular axis ’ double-looped length is one Compton wavelength h/mc. In the electron’s rest frame, the equations for the superluminal quantum’s position are:
A neo-classical relativistic mechanics theory is presented where the spin of an electron is a natural part of its space-time path as a point particle. The fourth-order equation of motion corresponds to the same Lagrangian function in proper time as in special relativity except for an additional spin energy term. The total motion can be decomposed into a sum of a local spin motion about a point and a global motion of this point, called the spin center. The global motion is sub-luminal and obeys 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 corresponds to Schrödinger's zitterbewegung and is a perpetual motion, which for a free electron has a circular path in the spin-center 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 corresponding electric dipole energy is consistent with the spin-orbit coupling term in the corrected Pauli non-relativistic Hamiltonian but the magnetic dipole energy is one half of that in Dirac's theory. 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. These equations of motion can then be expressed using operators applied to a state function of proper time satisfying a Dirac-Schrödinger spinor equation. The operators produce dynamic variables without any probability implications. For the free electron, the state function satisfies Dirac's relativistic wave equation when the Lorentz transformation is applied to express proper time in terms of an observer's space-time coordinates.
The spin of an electron is an intrinsic quantum property that cannot be explained using classical mechanics. Nevertheless, it is possible to conceive semiclassical systems with internal degrees of freedom that exhibit spin-like properties. Building on the analysis of phase modulation by elliptical gears and kinematically equivalent antiparallelogram linkages, we present a novel semiclassical model of Zitterbewegung, a rapid oscillatory motion closely connected with spin. The kinematical analog is based on including the internal rotation of the linkage represented in spacetime. The system’s dynamics is related to two-center electron models, which describe the constant momentum of the center of mass and the lightlike oscillation of the center of charge at twice the Compton frequency for a particle at rest. A two-dimensional extension provides an intuitive illustration of topological spin properties and can be used to calculate the spin and magnetic moment of an electron.