Antimatter: Theoretical Abstraction to Practical Application

A Puzzling Symmetry: The Negative Energy Solutions The Dirac equation was a triumph, but it presented a deep puzzle. Much like the simple algebraic equation x2=4 has two valid solutions (x=2 and x=−2), Dirac's equation yielded two sets of solutions. One set corresponded to the familiar electron with positive energy. The other, equally valid from a mathematical standpoint, described an electron with negative energy.3 In classical physics, such negative energy solutions could often be dismissed as unphysical artifacts of the mathematics. However, in quantum mechanics, they could not be so easily ignored. The theory implied that an electron in a positive energy state could spontaneously jump to an empty negative energy state, a transition that had never been observed.3 To resolve this paradox, Dirac initially proposed his "hole theory" in a 1929 paper. He imagined that the vacuum was not empty but was, in fact, a "sea" of fully occupied negative energy states (the "Dirac sea"). According to the Pauli exclusion principle, an electron from the positive energy world could not jump into this sea because all the states were already filled. However, if enough energy (e.g., from a photon) were supplied to one of these negative-energy electrons, it could be kicked out into the positive-energy world, becoming a normal electron. This would leave behind a "hole" in the sea. Dirac argued that this hole—the absence of a negative-energy, negatively charged particle—would behave as if it were a particle with positive energy and a positive electric charge.3