Weber-like interactions and energy conservation

Abstract

Velocity dependent forces varying as $k(\hat{r}/r)(1-\mu {\dot{r}}^2+\gamma r\ddot{r})$ (such as Weber force), here called Weber-like forces, are examined from the point of view of energy conservation and it is proved that they are conservative if and only if $\gamma =2\mu$. 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.

latex, 11 pages, no figures

Cited by in corpus (2)

• Photon and Graviton Mass Limits
• On the origin of the deflection of light