From amplitude-limited vectors to Maxwell's equations

Abstract

— Physical experiments show c, the speed of light in vacuo to be a universal constant. Relativistic arguments show it to be also an upper bound on physically measurable velocity. Vector addition of velocities, large or incrementally small, is no longer acceptable as the law of composition of measured velocities. Amplitude-limitation is imposed by using velocity vectors as the defining parameters of sophisticated operators such as four-vectors of unit norm and boost matrices whose interactions never allow it to exceed c. In a previous paper the unit energymomentum matrix was added and for a given parametrizing velocity was shown to have the structure of the square of the corresponding boost matrix. As a matrix its Lorentz transformation needs preand post-multiplication by the appropriate boost. Using the same operator, but mapped into SL(2C), to cover electric and magnetic vectors, the preand post multipliers must now be mutually inverse since mere transformation cannot generate an electromagnetic field. The resulting formulae generate Maxwell’s equations.