The standing and traveling waves of the electron are longitudinal in form. Even at rest, when the electron has no motion, these longitudinal waves exist. When an electron vibrates, a secondary wave form appears. The transverse wave is perpendicular to the vibration of a particle like the electron. It’s what we know as the electromagnetic (EM) wave that is responsible for light, radio, microwaves and more. These are all from the same EM wave, but are properties based on different frequencies of the transverse wave. A chart showing the properties of the EM wave is below. The electromagnetic wave gets its name because it is made of two components: the electric field and the magnetic field. These fields are at right angles of each other. The electric field is the transverse wave component. The magnetic field is the longitudinal wave component.
Temperature is the measurement of a particle’s kinetic energy. The faster a particle is vibrating, the higher the temperature that we measure. The faster the vibration, the higher the frequency of the transverse wave that is created.
Evidence
When an electron is at rest, its energy is calculated with the Longitudinal Energy equation. This is shown in the Electron Particle section. When vibrating, it has a maximum amplitude that it can be displaced and is confined within this space. The transverse wave amplitude is fixed, but its frequency is dependent upon the speed at which the particle vibrates. This can be illustrated as:
The volume of wave energy for a particle with spherical, longitudinal waves is spherical (Vl) in which amplitude decreases with distance. But a transverse wave is a focused packet of energy, called a photon in the Standard Model. The transverse wave has a cylindrical shape as follows:
The complete derivation can be found in the Wave Equation for Particle Energy and Interaction paper. The derivation of this energy transfer yields the transverse energy equations:
Transverse Energy Equation – Transverse energy absorbed or emitted when two or more particles interact.
The density, wavelength and amplitude constants are the same as the longitudinal wave. These equations also contain δ, which is the amplitude factor as a result of constructive or destructive wave interference between particles. For the Transverse Energy Equation, there is one particle and thus no constructive interference. The amplitude factor is one (δ = 1).
Evidence of the transverse equations are shown in the Atom section for orbital energies of hydrogen and other atoms, calculating both the transverse energies and wavelengths of photons.