Physicist Amok

I found myself in need of a rough form for the -decay spectrum, so I went and fetched Fermi’s Nuclear Physics from the library. I thought I would share a passage which suddenly made a lot of things go click for me:

According to the relativistic theory of the electron, an electron has energy . This equation permits negative energy values.

In Dirac’s theory, practically all negative states are filled at all points in space. A vacuum is then a sea of electrons in negative energy states. The presence of this charge is not observed because it is uniformly distributed.

A photon of sufficiently high energy may lift an electron from a negative energy state. The energy threshold for the photon is , since for a free electron there are no states between and . Physically, this means that the photon must supply enough energy to create two particles of mass . Momentum must be conserved and this requires either that the negative energy electron be near a nuclear or an electron, i.e., not free, or that two photons coming from different directions coalesce and lift an electron from a negative energy state. If the electron is near a nucleus it may occupy discrete states just below . These are within a few eV of 510,000eV. Strictly, then, the threshold for pair formation near a nucleus is . This is of no importance because binding energy and because transitions from negative energy states to the discrete part of the spectrum are improbable and not yet observed.