[tlb]

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.

[AstralStorm]

Technically with billions of events you can. This is how LHC and other particle accelerator data is analysed.

The interesting part is detecting systematic errors. (Human equivalent is "are my senses lying right now".)