212 The Poetry of Physics and The Physics of Poetry
model of the electron, which attributed its magnetic moment to the
rotation of the electron’s charge always involved velocities greater than
the velocity of light and hence, contradicted relativity. Dirac’s equation,
however, successfully related the magnitude of the magnetic moment of
a charged particle to its spin, its charge and its mass. In addition to
providing explanations for the spin and magnetic momentum of the
electron, Dirac’s equation was also able to explain the minute splitting of
certain spectral lines, which the non-relativistic quantum mechanics had
not been able to explain.
Dirac’s equation was a great success. It contained one difficulty,
however, the resolution of which would prove to be interesting. Dirac’s
equation contained two types of solutions. One set of solutions
corresponded to normal electrons with positive energies greater than or
equal to mec^2 , the rest mass energy of the electron. Another set of
solutions corresponded to electrons with negative energies less than or
equal to –mec^2. The existence of the negative energy states seems quite
unfeasible experimentally. If such states existed, electrons would
spontaneously make quantum jumps from the positive energy states to
the negative energy states emitting photons as they made this transition.
Dirac excluded this possibility by a very imaginative and speculative
application of the Pauli exclusion principle. He postulated that all of the
negative energy electron states were occupied and that there existed an
infinite sea of negative energy electrons. Transitions from positive
energy states to negative energy states could not take place because the
Pauli exclusion principle does not allow an electron to make a transition
into a state, which is already occupied. This resolved the problem of the
transition to negative energy states but then we are left with the problem
of an infinite sea of negative energy electrons.
Dirac concluded that the sea of negative energy states is unobservable
and corresponds to the vacuum state. The vacuum state is the state of no
observable electrons. Although Dirac believed that the negative energy
sea was not observable he assumed that one could observe the absence of
an electron in one of the negative energy states. A hole in the negative
energy sea should behave like a positively charged particle since
negatively charged particles would be attracted towards the hole to fill it
and hence, would seem to be attracted by a positive charge. An
analogous situation is observed in the behaviour of the Chlorine atom,
which is missing one electron to fill its outer shell. The missing electron