Interaction between an Accelerated Mass in Straight Motion and a Hidden Energy Reservoir as a Strict Mathematical Consequence of Special Relativity

Abstract

A. Einstein and H.A. Lorentz had found that the mass of an accelerated body traveling at relativistic velocity appears to depend on whether the acceleration is performed in the direction of motion or in a transverse direction. E.P. Epstein rejected this result in the “Annalen der Physik”; he rather postulated an additional force that turns up when the body is accelerated in the longitudinal direction. It can be shown that the concept of an increased longitudinal mass is based on a simple mathematical error. When correcting this error, it turns out that Epstein’s additional, hidden force is indispensable in order to avoid an inner inconsistency of Special Relativity. It does most of the total work absorbed by the moving object, and is thus responsible for most of the increase in its energy (=mass), given the speed attained is relativistic. In other words: While the total force on the body needed to maintain a constant acceleration a 0 is “ (1- v 2 / c 2 ) -1 m a 0 = m 0 (1- v 2 / c 2 ) -3/2 a 0 ”, the technical force needed to maintain that acceleration amounts only to “ m a 0 = m 0 (1 - v 2 / c 2 ) -1/2 a 0 ”. The total energy of two objects that undergo a symmetrical, elastic head-on collision is therefore not conserved during the collision, thus requiring the involvement of a hidden reservoir of energy. This result is confirmed by calculations that use the concept of momenergy. The phenomenon of an apparent disappearance of energy has been noticed in particle physics already (target-experiment), but its consequences have been ignored. Instead, an explanation has been given (reduced “energy of the center of mass”) which is inconsistent and violates the relativity principle.