The Dirac Equation and the Prediction of Antimatter

Dirac: Negative energy states already have things you can think of as particles occupying. Since they're already full, you can't put a new particle in there. So Dirac then imagined that like something like a photon might come along and it might hit one of those particles in a negative energy state to create an electron with a positive charge. That's how Dirac got from negative energy states in his equation to the prediction of antimatter.