Speed of light has been experimentally determined long before the 40s. The discovery of the speed of light being constant lead to the special relativity (aka before GR which is the E=mcc). http://www.speed-light.info/measure/speed_of_light_history.h...
The speed of light is easy to measure. What's hard is measuring the change in mass when something gains or loses energy. A large nuclear reactor running for a year only loses a few grams of mass-energy -- you can't measure it accurately enough or be sure that the mass didn't go somewhere else like into the cooling water.