The law of conservation of energy states that the total amount of energy in an isolated system remains constant over time. In an isolated system, this law states that energy is localized and can change its location within the system, it can change form within the system. However, two initially isolated systems with no external interactions can be composed into a single isolated system. The total amount of energy of the composite system is equal to the sum of the respective total amounts of energy of the two component systems.
The conservation of mass, previously called vis viva, or living force was first attempted to be explained in 1676-1689 by Gottfried Wilhelm Leibniz. The equation was changed multiple times until 1807 when Thomas Young recalibrated it to:
1/2 ∑_i =〖m_i v_i^2 〗
Where δQ is the amount of energy added to the system by a heating process, δW is the amount of energy lost by the system due to work done by the system on its surroundings and dU is the change in the internal energy of the system.
Conservation of energy over time in special relativity was described by Albert Einstein. It states the relativistic energy of a single massive particle contains a term related to its rest mass in addition to its kinetic energy of motion. The equation is: