Schrödinger’s equation works well for slow particles but does not respect special relativity. Paul Dirac searched for a relativistic quantum equation for the electron.
His 1928 equation naturally described electron spin and magnetic behavior. It also produced negative-energy solutions: an entire set of answers nobody had ordered.
Dirac eventually interpreted the mathematics as requiring a particle with the electron’s mass and opposite charge. In 1932 Carl Anderson found a cosmic-ray track curving like an electron in the opposite direction. The positron was real.
Particles and antiparticles can annihilate into radiation, while sufficient energy can create pairs.
Beautiful mathematics is not automatically true. But this episode established a more careful lesson: when a theory repeatedly gives an unwelcome answer, removing it may be less sensible than asking what in nature it describes.
