Quantum Electrodynamics 215
and creation occur. The solutions to the Dirac equation, which seem to
correspond to negative energy can now be viewed as positive energy
solutions of the antielectron. The concept of the negative energy sea of
electrons can be retained, however, to aid the mind’s eye in
conceptualizing pair creation and annihilation. If the idea of the negative
energy sea were absolutely necessary to the formulation of Dirac’s ideas,
we would then have to deal with the mystery of how an infinite sea of
negative energy electrons can remain unobservable. The sea of negative
energy electrons does not exist in real space, it is a concept in the minds
of those physicists who use Dirac’s equation. Hopefully, it has also
become a concept in your mind as well.
In our description of the annihilation of an electron-positron pair we
failed to mention the very curious intermediate state that frequency
occurs just prior to the annihilation process. The electron and positron on
first encountering each other interact through their electric charges and
often form a bound state analogous to the hydrogen atom before
annihilating. The positron plays the role of the proton in the formation of
this peculiar atom, which is referred to by the name of positronium. All
of the energy levels of positronium correspond to those of the hydrogen
atom. All of the levels are shifted naturally because of the difference in
mass between the proton and the positron. The entire Balmer series of
frequencies for positronium have been observed and measured.
Once the positronium is formed, it makes radiative transitions from
level to level until it reaches its ground state. It does not remain in this
ground state for very long. Because of the close proximity of the electron
and the positron in the ground state, they eventually make contact and
annihilate each other. The annihilation of the pair can take place from
any of the levels of positronium. The probability is greatest, however, in
the ground state because there is the greatest overlap of the electron and
positron wave functions in this state. The probability for annihilation is
just equal to the overlap of the two wave functions, i.e. the probability of
finding the electron and the positron at the same place.
Dirac’s relativistic equation not only describes the electron but also
all spin 1/2 particles and hence, describes the proton and the neutron.
We shall learn more about these particles when we study nuclear physics.
For the moment, however, we shall introduce them into our discussion
since Dirac’s theory predicted that these particles would also have
antiparticles, namely the antiproton and the antineutron. The creation of
a proton-antiproton pair requires approximately 200 times the energy