Question

How are the classical laws of conservation of energy and conservation of mass modified by modern relativity?

Answer 1

In classical mechanics, the law of energy conservation was a fundamental law. The mass was a constant that doesn't change. In relativity, the mass is not constant anymore, with the connection $E=mc^2$ mass can be converted into other kinds of energy.

$E^2 =(pc)^2 +(mc^2)^2$