Einstein's equation, E=mc², is not something that he set out to prove experimentally. Instead, it emerged as a consequence of his theoretical work on special relativity. Einstein developed the theory of special relativity based on a set of postulates and logical deductions rather than conducting specific experiments to validate the equation itself.
However, the equation has been indirectly supported and confirmed by subsequent experimental evidence and observations. Here are a few examples:
Particle physics: In particle accelerators, scientists have observed particle collisions where energy is converted into mass and vice versa. These experiments validate the idea that energy and mass are interconvertible as predicted by the equation E=mc².
Nuclear reactions: Nuclear reactions, such as those that occur in the Sun or during nuclear power generation, involve the conversion of small amounts of mass into vast amounts of energy. The equation E=mc² explains the relationship between the released energy and the lost mass.
Nuclear weapons: The enormous amount of energy released by nuclear weapons, such as atomic bombs, is a result of the conversion of a small fraction of the weapon's mass into energy, in accordance with E=mc².
While direct experiments to prove E=mc² are challenging due to the extremely high energy densities required, the equation has been confirmed indirectly through various experimental observations and technological applications. Its implications have been validated and supported by a wide range of experiments in different areas of physics.
It's important to note that scientific theories, including Einstein's theory of relativity, are not proven in the same way as mathematical theorems. Instead, they are supported by empirical evidence and their ability to make accurate predictions.