A solitary electron in free space is not a fixed particle at rest in a given inertial frame of reference. It is always oscillating in a simple harmonic motion (SHM) in its own electromagnetic inertia field, even at zero kelvin temperature. A Newtonian particle exhibits uniform motion in a straight line. A quantum particle like the electron exhibits uniform motion along a sine wave path. This explains the physical concept of the wave-particle nature of the electron. As the mass of a quantum particle increases, the wavelength of the particle decreases as per French physicist Louis de Broglie. In the limiting case the sine wave becomes a straight line. Also, a hypothetical electron without an electric charge is like the bob of a simple pendulum without a string. In an electron-spin qubit, the electron can oscillate either clockwise or anti-clockwise and cannot oscillate both clockwise and anti-clockwise at the same time. It cannot be both spin-up and spin-down at the same time.
A solitary electron in free space is not a fixed particle at rest in a given inertial frame of reference. It is always oscillating in a simple harmonic motion (SHM) in its own electromagnetic inertia field, even at zero kelvin temperature. A Newtonian particle exhibits uniform motion in a straight line. A quantum particle like the electron exhibits uniform motion along a sine wave path. This explains the physical concept of the wave-particle nature of the electron. As the mass of a quantum particle increases, the wavelength of the particle decreases as per French physicist Louis de Broglie. In the limiting case the sine wave becomes a straight line. Also, a hypothetical electron without an electric charge is like the bob of a simple pendulum without a string. In an electron-spin qubit, the electron can oscillate either clockwise or anti-clockwise and cannot oscillate both clockwise and anti-clockwise at the same time. It cannot be both spin-up and spin-down at the same time.
distributed for no-profit educational & research purposes. Not for commercial use. An isolated static electron in free space is not a fixed particle at rest. It is always oscillating in a SHM in its own electromagnetic inertia field, rest frame even at zero kelvin temperature. This is non-thermal, standing wave, resonance Compton frequency, oscillation along a linear path or, along an elliptical or a circular (clockwise or anti-clockwise) path, corresponding to the electron’s intrinsic magnetic moment (spin up or spin down). An electron with spin behaves like a tiny magnet. Intrinsic spin does not imply that a subatomic particle is spinning like a toytop about its axis. A hypothetical electron without a charge is like the bob of a simple pendulum without a string. INTRINSIC SPIN & ORBITAL ANGULAR MOMENTUM
Physical objects from quarks to planets have wavelike attributes. Q uantum theory offers an excellent mathematical structure for the wave -particle duality nature of photons, electrons, protons, neutrons, atoms and molecules. This article explains the electromagnetic inertia harmonic oscillation nature of quantum particles and gives a simple physical interpretation of the string theory, wave mechanics, two-slit interference and the Faraday effect. 1.0 The ELECTRON. An electron is an elementary particle with the smallest non -zero rest mass. It has a negative electric charge, w hich generates a field in free space, extending to infinity, and is conversely acted on by forces due to the field.
In this article, it is shown that if a particle is at rest and has some harmonic oscillation, then a traveling particle with a constant speed corresponds to a De Broglie Wave.In 1924, De Broglie proposed that particles of matter exhibit wave like behavior, the expression for which became fundamental in the creation of wave mechanics (quantum mechanics).The main equation for this is the Schrödinger equation, which in the case of free motion of a particle becomes the expression for the De Broglie wave.This hypothesis is supported by many early experiments on the diffraction of electrons, and later the development of modern physics.However until now, the origin of this hypothesis remains unclear.We show that the expression for the De Broglie wavelength can be obtained from a more general well-known concept, that any particle at rest has a corresponding harmonic oscillation that transforms into a wave of a moving particle with the help of relativistic change of coordinates (the Lorentz transformations).In this way, a De Broglie wave can be explained as a spacetime wave.
The Simple Harmonic motion is ubiquitous in nature at every scale from macroscopic bodies to the very microscopic elementary particles like electrons and photons. In the usual macroscopic scales motion of particles obey Newtonian and Relativistic dynamics which is modeled very accurately by linear Mathematics developed over the last few centuries. But at the quantum scales we inherently have to deal with probabilities and the wave particle dual nature becomes apparent at microscopic scales. To describe the energy of photons in Quantum Field Theory we have to use the notion of frequency which is a Simple Harmonic Motion Notion which in turn requires Sines and Cosines. In this Paper I would like to formulate a Mathematical Model by generalizing some symmetry principles from Simple Harmonic motion and show how this Model reduces to linear Mathematics at high frequencies or longer time scales and how this model maybe useful in general for quantum physicists in particular for dealing with infinities.
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.
One of the fundamental questions resolved in the early development of quantum mechanics was whether the electron motion was wavelike or particle-like. The answer was provided by De Broglie who showed that the particle linearmomentum, p, was related to an electromagnetic wavelength, l, as follows: l ¼ h p= , where h¼Planck’s constant ¼ 6:65 1034 J sec. This relationship was important, because it says that the motion of a particle can be described in terms of wave propagation. Thus, for example, a particle enclosed in a microwave cavity can be described in terms of an electromagnetic standing mode or as a particle in a box. De Broglie’s equation proved to be a great triumph in the early development of quantum physics, especially when applied to atomic physics. Let’s apply the De Broglie relationship to a ring resonator. The ring resonator consists of a simple wire loop and is coupled to a microwave source. Further, let’s imagine a hypothetical situation in which the loop is so small that very few, perhaps one single electron, is flowing around the wire loop. Thus, the motion is constrained to be circular. Remarkably, it radiates maximum energy at resonance, as determined by nl ¼ 2pr, where n ¼ 1, 2, 3, . . . , l is the electrical wavelength of the radiated energy or the wavelength of the particle within the wire loop, and r is the radius of the loop. If we assume that De Broglie’s equation is applicable, l is related to the linear momentum, p, of the few particles ‘‘entrapped’’ in the resonator. Since the motion is circular, the angular momentum, G, is simply G ¼ pr. This implies that (applying the De Broglie relationship) 2pr ¼ h G rn or G ¼ nh: G is in units of h and discrete. This implies that the magnetic moment of the ring resonator must also be quantized, since G is discrete.