# Who first noticed that the radiation pressure formula $p=U/c$ agreed with $E=pc$ from special relativity?

Does anyone know behind stories? As it seems that $p=U/c$ was known before the advent of special theory of relativity, (Halliday, Resnick, Walker says that Maxwell derived this.) when $E=pc$ was first derived by plugging in $m=0$ for $E^2=m^2c^4+p^2c^2$, were physicists happy that the two formulas agreed? Who first noticed this agreement? What was the reaction? And, who derived $E=pc$ from the special theory of relativity point of view? I know that $p=γmv$ was first derived by Planck in 1906, but I do not know much anything else such as who derived $E^2=m^2c^4+p^2c^2$ and who first plugged in $m=0$.

• Considering that in special relativity Einstein explicitly extended Maxwellian formulas from electromagnetic to all objects it would have been odd if they did not match. The radiation pressure formula applied to electromagnetic radiation only, Einstein's formula was postulated to apply kinematically, i.e. to everything, the radiation in particular. The energy formula was derived by Einstein in 1905, and that the rest mass of the radiation is zero was widely accepted at the time. – Conifold May 26 '18 at 23:19
• Could you tell me which paper of Einstein in 1905? Is it possible that E=pc was derived in 1905, considering hat p=gamma mv was derived in 1906? – Youngsub Yoon May 27 '18 at 6:21
• Does the inertia of a body depend upon its energy-content? – Conifold May 29 '18 at 15:09