Quantum

The effects of relativity are large when the speed of a particle approaches that of light or, equivalently, when its energy is an appreciable fraction of its rest energy mc². This occurs in atomic physics only in the inner shells of heavier elements and plays a relatively minor role even in the physics of atomic nuclei. However, in treating such problems as the scattering of X-rays and gamma rays (the Compton effect), relativity and quantum theory are both important. In 1928 Dirac used his transformation theory to deduce for the electron a relativistic analog of the Schrödinger equation with remarkable properties. He found that it required four associated wave functions, where Schrödinger used only one. Dirac's equation automatically endowed the electron with its observed spin of ½ (h/2π), and gave it its observed magnetic moment and the relativistic fine structure of spectral lines. That accounted for one doubling of the number of wave functions. The second doubling resulted from the formalism of relativity and was very troubling, as it allowed electrons to have negative energy, which in relativity implies meaningless negative mass. After several years of pondering the problem, Dirac suggested an interpretation of the theory that predicted the existence of a positive electron, capable of annihilating with a negative electron, the result being gamma rays, an example of the transmutation of mass into energy. A year later, in 1932, the positive electron (anti-electron or positron) was found in the cosmic rays and then was produced in the laboratory. All particles have been found to have antiparticles (some are their own antiparticles) and so there exists a world of antimatter.