On Motions of The Photon To Demystify Quantum Mechanics And To Harmonize It With General Relativity-Spinvector Motion IV

Harry Ian Epstein

Jason D. Tran, Leanne Doughty, James K. Freericks

The introduction of complex numbers to solve the damped harmonic oscillator in classical mechanics can seem mysterious to students. We show how an approach based on Born and Jordan's 1930 quantum mechanics textbook both demystifies the use of complex numbers in classical mechanics and makes a strong connection to quantum mechanics. In that work, they converted the harmonic oscillator equations of motion into two uncoupled first-order equations. In classical mechanics, this mapping explicitly introduces complex numbers into the motion of the oscillator and directly shows how to solve for the position and momentum observables. Here, we explain how this mapping works and show how to demystify the use of complex numbers in damped-driven harmonic oscillators. As an added bonus, this approach also shows how to determine the energy as a function of time and makes a strong connection to quantum mechanics.

Ya.I. Frenkel

Zhonglin BO

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.

M. Bertolotti

Zhonglin BO

A new planetary motion theory, spin-vector motion is developed, based on Kepler's second laws of planetary motion that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. The planetary motion follows the same Schrodinger wave equation as quantum particles. The planets have same particle-wave duality, wave length and momentum relation, energy and wave frequency relation as quantum particles too. Based on our deduction we conclude that the Schrodinger equation can be applied successfully to photons, quantum particles, and celestial bodies, but with different energy constant for celestial bodies. Even though these objects are with different masses, sizes and with different wave speeds. And we predict that the wave speed exceeding light speed will not have any impacts on the wave equation form. This spin-vector in motion theory or Spin-vector Mechanics will be a candidate theory leading to the theory of everything.