<P> Matter is composed of such things as atoms, electrons, neutrons, and protons . It has intrinsic or rest mass . In the limited range of recognized experience of the nineteenth century it was found that such rest mass is conserved . Einstein's 1905 theory of special relativity showed that it corresponds to an equivalent amount of rest energy . This means that it can be converted to or from equivalent amounts of other (non-material) forms of energy, for example kinetic energy, potential energy, and electromagnetic radiant energy . When this happens, as recognized in twentieth century experience, rest mass is not conserved, unlike the total mass or total energy . All forms of energy contribute to the total mass and total energy . </P> <P> For example, an electron and a positron each have rest mass . They can perish together, converting their combined rest energy into photons having electromagnetic radiant energy, but no rest mass . If this occurs within an isolated system that does not release the photons or their energy into the external surroundings, then neither the total mass nor the total energy of the system will change . The produced electromagnetic radiant energy contributes just as much to the inertia (and to any weight) of the system as did the rest mass of the electron and positron before their demise . Likewise, non-material forms of energy can perish into matter, which has rest mass . </P> <P> Thus, conservation of energy (total, including material or rest energy), and conservation of mass (total, not just rest), each still holds as an (equivalent) law . In the 18th century these had appeared as two seemingly - distinct laws . </P> <P> The discovery in 1911 that electrons emitted in beta decay have a continuous rather than a discrete spectrum appeared to contradict conservation of energy, under the then - current assumption that beta decay is the simple emission of an electron from a nucleus . This problem was eventually resolved in 1933 by Enrico Fermi who proposed the correct description of beta - decay as the emission of both an electron and an antineutrino, which carries away the apparently missing energy . </P>

State and prove energy conservation theorem for a system of particles