Jim Green's "holes"

[James Espinosa <F_ESPINOSA@TWU.EDU>]

Several weeks ago Jim asked about the relationship between "holes" and positrons.  All the replies that I read referred to solid state physics and semiconductors where p-type means positive holes.  At the risk of being totally wrong, there is another possible answer to his question.  It has to do with relativistic quantum mechanics.  In the late 20's Dirac introduced the equation that bears his name, it was a relativistic  equation, something like the "square-root" of the Klein-Gordon equation.  When Dirac found that the solutions to the equation came in both positive and negative energy eigenvalues he had a problem of what to do with the negative ones.  His solution was to use the fact that electrons were fermions and therefore no two could be in the same state.  Therefore he assumed that all the negative energy states were filled so that all of space was an ocean of negative energy electrons, but were also undetectable, except if one could make a transition to the positive energy levels.  When this happened there would be left a "hole" in this ocean and since it would be a missing negative energy, negative charge electron, the "hole" would show as up as a positive energy, positive charge particle.  At first Dirac interpreted these "holes" as protons, but it was soon found that they were positive charge electrons or positrons, as they came to be called after Anderson discovered them in a cloud chamber detector.  After the development of field theory there was no need for "holes", only for antiparticles.  So if Jim's question was along these lines, then indeed "holes" are positrons.

 

James M. Espinosa