Weber-like interactions and energy conservation

Abstract

Velocity-dependent forces varying as k(rˆ/r)(1−μr˙2+γrr¨) (such as Weber force), here calledWeber-like forces, are examined from the point of view of energy conservation and it is proved that they are conservative if and only ifγ=2µ. As a consequence, it is shown that gravitational theories employing Weber-like forces cannot be conservative and also yield both the precession of the perihelion of Mercury as well as the gravitational deflection of light.