"Dirac's equation consists of... four separate s to describe electrons. Two components have an... immediately successful interpretation... describing the two possible directions of an electron's spin. ...The extra ...equations contain solutions with negative energy... Assuming Dirac's equation, if you start with an electron in one of the positive-energy solutions, you can calculate the rate for it to emit a photon and move into one of the negative-energy solutions. Energy must be conserved, but that... means... the emitted photon has higher energy than the electron that emitted it! ...Dirac was well aware of this problem. ...He proposed ...empty' space ...contains electrons obeying all the negative-energy solutions. ... A positive-energy electron can't go to a negative energy solution, because there's always another electron already there, and the won't allow a second... [T]he idea... the ordinary state of 'empty' space is far from empty... a different word for it... is 'vacuum'... a medium, with dynamical properties... [S]hine light [photons with enough energy] on the vacuum... then a negative-energy electron can absorb... [a] photon... and go into a positive-energy solution... an ordinary electron... But in the final state there is... a hole... originally occupied by the negative-energy electron... [I]f there is a pre-existing hole... a positive-energy electron can emit a photon and occupy the vacant negative-energy solution. ...Dirac's first hole-theory paper was... 'A theory of electrons and protons'."