A Photon Model from the Hamiltonian Energy Vector revision 1 (original) (raw)
The science of optics has observed the phenomenon of refraction and recognised that the wave phase speed reduces in a dispersive medium and developed a number of formulae, including Snell's law. However, optics has not provided a mathematical model explaining why the wave phase speed slows in a dispersive medium. The Hamiltonian energy of a photon in free space is given in complex notation as: H = |mc 2 |.e jwt= jh.υ0 Where υ0 is the natural photon frequency, |mc^2 | is the total or mass-energy and h is Planck's constant A proof of the Hamiltonian energy relation formula for a photon has been provided assuming that the photon has a virtual mass, but retains a zero real mass. The virtual and variable photon mass, m, has also been given as: m = jhυ0/c^2 This formula describes how a photon can exhibit wave-particle duality in the form of a quantised virtual mass and an electromagnetic wave with energy dependent upon frequency. An hypothesis describing the phenomenon of refraction for light is given as: 'As a photon traverses a transparent dispersive medium, some portion of the total mass-energy will be dissipated in the medium as kinetic energy thus reducing the wave energy and wave phase speed, producing the bending of light, due to the least action principle.' The Hamiltonian energy vector provides a quantum mechanical mathematical model that can explain the phenomenon of refraction, and furthermore leads to the development of new optical formula.
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