Five-dimensional Relativity with Energy as Extra Dimension

Abstract

A Kaluza-Klein-like framework is developed infive-dimensional spaces in which the extra dimension isassumed to be the energy of physical processes and thefour-dimensional spacetime is endowed with anenergy-dependent metric. The detailed analysisof some classes of solutions of the (vacuum) Einsteinequations shows that the E = const. slices possessenergy-dependent four-dimensional metrics whichintriguingly reproduce the phenomenological“deformed” metrics derived from theexperimental data on some physical phenomena ruled bythe four fundamental interactions (electromagnetic,weak, strong and gravitational). This extends previous results concerning theslowing down of clock rates in a gravitational field.Incidentally it is also shown that a special solution ofthe five-dimensional geodesics equation allowsto derive a sort of quantum-mechanicaltime-energy uncertainty relation.