The apparent contradiction between Einstein's equation E=mc^2 and the principle of conservation of mass arises from a common misunderstanding. It is important to clarify that Einstein's equation does not violate the conservation of mass; rather, it expands our understanding of mass and energy and their interconversion.
The principle of conservation of mass states that within a closed system, mass cannot be created or destroyed; it remains constant. This principle holds true in classical mechanics, where mass is considered a separate and conserved entity.
However, in Einstein's theory of relativity, mass and energy are not separate quantities but different aspects of the same underlying physical entity. The equation E=mc^2 demonstrates the equivalence between mass (m) and energy (E) and reveals that they are interchangeable.
In situations where mass is converted into energy or vice versa, such as nuclear reactions or particle annihilation, the total mass-energy of the system is conserved. While mass can appear to "disappear," it is actually converted into energy according to E=mc^2. The sum of mass and energy remains constant, adhering to the principle of conservation.
So, there is no contradiction between Einstein's equation and the conservation of mass. Rather, the equation provides a deeper understanding of the relationship between mass and energy, highlighting their interchangeability in certain physical processes.