<Dd> d U = δ Q − δ W + u ′ d M, (\ displaystyle \ mathrm (d) U = \ delta Q - \ delta W + u' \, dM, \,) </Dd> <P> where d M (\ displaystyle dM) is the added mass and u ′ (\ displaystyle u') is the internal energy per unit mass of the added mass, measured in the surroundings before the process . </P> <P> The conservation of energy is a common feature in many physical theories . From a mathematical point of view it is understood as a consequence of Noether's theorem, developed by Emmy Noether in 1915 and first published in 1918 . The theorem states every continuous symmetry of a physical theory has an associated conserved quantity; if the theory's symmetry is time invariance then the conserved quantity is called "energy". The energy conservation law is a consequence of the shift symmetry of time; energy conservation is implied by the empirical fact that the laws of physics do not change with time itself . Philosophically this can be stated as "nothing depends on time per se". In other words, if the physical system is invariant under the continuous symmetry of time translation then its energy (which is canonical conjugate quantity to time) is conserved . Conversely, systems which are not invariant under shifts in time (an example, systems with time dependent potential energy) do not exhibit conservation of energy--unless we consider them to exchange energy with another, external system so that the theory of the enlarged system becomes time invariant again . Conservation of energy for finite systems is valid in such physical theories as special relativity and quantum theory (including QED) in the flat space - time . </P> <P> With the discovery of special relativity by Henri Poincaré and Albert Einstein, energy was proposed to be one component of an energy - momentum 4 - vector . Each of the four components (one of energy and three of momentum) of this vector is separately conserved across time, in any closed system, as seen from any given inertial reference frame . Also conserved is the vector length (Minkowski norm), which is the rest mass for single particles, and the invariant mass for systems of particles (where momenta and energy are separately summed before the length is calculated--see the article on invariant mass). </P>

Energy may change from one form to another but the total amount of energy never changes