(*Free Digital Article) Relativistic Electromagnetic Law From 4D Relativistic Quantum Mechanics

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Abstract

It is the pinnacular objective of a quantum theory that for any classical physical law, be it relativistic or otherwise, that it flows from a single quantum framework. For example, the non-relativistic mechanical Newtonian laws are readily obtained from quantum mechanics by using the simplest form of the Ehrenfest theorem with a non-relativistic energy operator i.e. the Schrodinger equation. However, in such a classical law, there is the concept of mass, which is central to the theory of relativity. Unfortunately, it’s presence in the Dirac equation has been one of the obstacles in deriving dynamical field laws such as the full electromagnetic laws beyond a static form. Here, it is demonstrated by using the fourth spatial dimension, which has now been incorporated into relativistic quantum mechanics, that this generalization of the Dirac equation to include the fourth does yield the full dynamical electromagnetic law, with the mass concept conserved. The fourth dimension effectively extends the mass-Hamiltonian to a mass-photon energy operator, where change in mass energy creates photon energy described by such relativistic electromagnetic laws.