A Hundred Years of Larmor Formula

Abstract

Sir Joseph LARMOR showed in 1897 that an oscillating electric charge emits radiation energy proportional to (acceleration)$^2$. At first sight,the result appears to be valid for arbitrary accelerations. But, perpetual uniform acceleration has been a case of nagging doubts, as radiation reaction vanishes and the equivalence principle, as also conformal symmetry of Maxwell equations each require nil energy loss. Special hypotheses are devised by some to justify the assumption of radiation loss for both perpetual and non-perpetual (uniform) accelerations which, as in the case of (uniform) velocities, are really different. The problem is here simply resolved by an explicit computation to show absence of radiation for the perpetual case and by illustrating that Larmor formula makes sense {\it only if} there is {\it change} in acceleration, just as kinetic energy has nontrivial quantitative sense, only when there is change in velocity.