Weber-like interactions and energy conservation

Abstract

Velocity dependent forces varying as $k(\hat{r}/r)(1-\hat{I}¼{\dot{r}}^2+{\hat{I}}^{3}r\ddot{r})$ (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 ${\hat{I}}^3=2\hat{I}¼$. 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