Particle decay in six-dimensional relativity

Abstract

Special relativity is developed using a real six-dimensional space-time. It is shown that the imposition of parallel time displacements in each frame necessarily implies subluminal transformations. Conservation of six-momentum yields the usual three-momentum equation together with a vector equation, which replaces the scalar energy equation of the corresponding four-dimensional theory. On energetic grounds alone it is shown that a particle may decay into a set of particles whose total rest mass is greater than that of the original particle, and that particles may be produced from the vacuum state. When virtual particle production is considered, this suggests a tentative link between the uncertainty principle and a six-dimensional theory with a restriction to small deviations from a constant time direction.