Since the electron is the photon-generator and the electron is rotating around itself and around the nucleus, the emitted photon from the electron should have the effect of these rotating motions. So, the photon has a three-dimensional motion, including a transition movement and a rotary motion. And it traverses in a helical trajectory. By using this definition, we have proved wave-particle duality at the same time and introduce a new equation for the photon motion and its energy.
Since the electron is the photon-generator and the electron is rotating around itself and around the nucleus, the emitted photon from the electron should have the effect of these rotating motions. So, the photon has a three-dimensional motion, including a transition movement and a rotary motion. And it traverses in a helical trajectory. By using this definition, we have proved wave-particle duality at the same time and introduce a new equation for the photon motion and its energy.
This new explanation is based onWave-Particle DualityandNewtonian Lawsand represents a unique definition of a three-dimensional motion for the photon, whose dual behavior is partly explained by thedouble-slit experimentof Thomas Young, who represents the photon's motion as a wave, and by thePhotoelectric effect, in which the photon is considered as a particle. However, for scientists, the photon's true motion is unclear. In this article, we define a new type of motion for photons to solve both this ambiguity and the difficulty of presenting a three-dimensional trajectory for the photon's motion, and present a new formula to calculate its energy. In addition, because we believe in the helical motion of photons, where r is the gyroradius, we believe that their color is an effect of the order of magnitude ofr. We present real examples that prove our energy formula.
A detailed kinematic analysis was conducted based on the hypothesis of the photon as an electric dipole in combined motions, a rotation and a linear uniform motion perpendicular to its rotational axis. A particle wave coefficient(j) of a rotational object in combined motions is defined based on the analysis of the motion quantities, translational momentum and rotational angular momentum. The motion analysis explains the intrinsic nature of particle-wave duality, the relation among momentum, angular momentum and its wavelength when the rotational particle in combined motions. For the photon, j equals Planck constant (h), is the sum of its translational kinetic energy and rotational energy. The derivation processes of the wave equation of the photon, both the first order derivative method and the second order derivative method, demonstrate that the Dirac Equation is applicable to describe the motions of the photon as the dipole. The four wave components of the photon interpret why the negative energy solutions exist to the Dirac equation, which reveals the disk structure of dimetric spinvectors of the electron.
Relativistic quantum mechanics and many experimental results and observations show that electron-positron annihilation can produce photons; photon-matter and photon-photon interaction can also create electrons and positrons. The photons have no rest mass, e.g. relative to Lab frame, and always travel at the speed of light in the vacuum. In this paper, a rotational moving electric dipole model with negative and positive charges was proposed for photons. In a vacuum, the electric dipoles are moving in a twisted helical motion around their propagation axis (their center of mass). Photon particles are traveling at the speed of light along the propagation axis. This pair of negative and positive charged particles exerts both electrostatic and magnetic force on each other. Both forces are attractive and act as a centripetal force to keep the electric dipole in a continuous helical motion around the axis of rotation. With this model, the wave-particle duality of photons can be described simultaneously. The space is filled by matter (having rest mass relative to Lab frame) and photons (without rest mass); it is a multicomponent mixture fluid. In "vacuum", though there is no rest matter particle, but there are still photon gas particles, the total energy-momentum tensor should include rest matter particles and photon gas particles.
This paper re-examines the mechanism of electron motion inside atoms and the causes of photon radiation and photon absorption, abandoning the inherent cognition of fixed electron orbits and quantum transitions in traditional atomic physics. It clarifies that electrons have no physical fixed orbits; orbits are only imaginary concepts constructed for convenience of description, not objective physical realities. With mass, electrons possess inertia and kinetic energy. Under the three-force equilibrium of Coulomb force, electromagnetic force and inertial effect, electrons naturally move in elliptical trajectories rather than regular circles. When an electron moves along an elliptical trajectory, it naturally passes through low-energy regions near the atomic nucleus and high-energy regions far from the nucleus. This change in position arises entirely from its own inertia, involving only the conversion between kinetic energy and potential energy. The electron neither gains nor loses total energy, so it emits no photons and undergoes no energy-level change. An electron loses total energy when emitting a photon outward, and transitions smoothly and continuously to a lower overall motion range under mechanical equilibrium and inertia. Meanwhile, an electron can also absorb external photons and gain energy; its total energy increases, and it similarly expands smoothly to a higher motion range. Photon energy is indivisible and can only be emitted or absorbed as a complete unit. This is the fundamental reason why atoms show discrete emission and absorption spectra. Electron motion is entirely smooth and continuous; instantaneous quantum transitions assumed in traditional physics do not exist. Based on classical mechanics and energy conservation, this paper unifies the laws of macroscopic celestial bodies and microscopic particles, and reconstructs an atomic motion model closer to the essential nature of physics.
Abstract This paper proposes a geometric theory of wave-particle duality based on the algebra of three-dimensional numbers (3D Numbers). In the 3D number space T = σ + δe + ti (with e²=1, i²=-1, ei=0), the motion of a photon naturally takes the form of a helical trajectory T(t) = e^{δe}·e^{iωt}. The projection of this helix onto the (σ,i) plane yields the standard quantum mechanical wave function ψ(t) = cosh(δ)·e^{±iωt}, while the hyperbolic stretch along the e-direction corresponds to particle nature. Through five numerical experiments, we verify: (1) the helical structure is exact (radius deviation < 2×10⁻¹⁶); (2) projection to the complex plane gives the standard wave function; (3) all quantum mechanical quantities (E=ℏω, p=ℏk, λ=2π/k) are derived directly; (4) δ-parameter scan reveals a continuous wave-particle spectrum; (5) 3D numbers are the unique number system supporting both wave and particle nature. The central thesis: wave-particle duality is not a superposition of two attributes, but the projection decomposition of a single helical motion onto two orthogonal directions. Keywords: 3D numbers, helical motion, wave-particle duality, mid integration, foundations of quantum mechanics, non-associative algebra 摘要 本文提出一种基于三维数(3D Number)代数结构的光子波粒二象性几何理论。在三维数空间 T = σ + δe + ti(其中 e²=1, i²=-1, ei=0)中,光子的运动自然地表现为螺旋运动 T(t) = e^{δe}·e^{iωt}。该螺旋运动在 (σ,i) 平面上的投影给出标准量子力学波函数 ψ(t) = cosh(δ)·e^{±iωt},在 e 方向上的双曲伸缩对应粒子性。通过五组数值实验,我们验证了:(1) 螺旋结构严格成立(半径偏差 < 2×10⁻¹⁶);(2) 投影到复平面给出标准波函数;(3) 从螺旋运动可直接推导能量 E=ℏω、动量 p=ℏk、de Broglie 波长 λ=2π/k 等全部量子力学量;(4) δ 参数扫描揭示了波动-粒子连续谱;(5) 三维数是唯一同时支持波动性和粒子性的数系。本工作表明:波粒二象性的本质不是两种属性的叠加,而是同一螺旋运动在两个正交方向上的投影分解。 关键词:三维数、螺旋运动、波粒二象性、中道积分、量子力学基础、非结合代数
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.