Dirac se encuentra con el problema de la energía negativa en su teoría del electrón relativista. Veamos hoy cómo encuentra una solución, y un nuevo problema:
I found that it was not really very hard to see a way out of this difficulty. The idea was suggested by the chemical theory of valency in which one is used to the idea of electrons in an atom forming closed shells which do not contribute at all to the valency. One gets a contribution from an electron outside closed shells and also a possible contribution coming from an incomplete shell or a hole in a closed shell.
En química, esto sucede porque los electrones son fermiones y obedecen el principio de exclusión de Pauli. Dirac tuvo suerte en encontrar esta solución trabajando sobre un fermión como el electrón. No hubiera encontrado la misma solución en caso de trabajar con un bosón, inicialmente, que no forman "closed shells".
One could apply the same idea to the negative energy states and assume that normally all the negative energy states are filled up with electrons, in the same way in which the closed shells in the chemical atom are filled up. In that way an ordinary positive energy electron would not be able to jump into a state of negative energy. However, one would expect that under certain conditions there might be a hole in the negative energy states and one had to get an interpretation for these holes.
Es muy original la idea de los agujeros, digna de la imaginación de Dirac. Y veamos también cómo él se inclina por considerar que electrones y agujeros son "lo mismo", son simétricos en cualidades. Estuvo a punto de predecir la existencia de una partícula nueva, que hoy llamamos positrón. Pero no fue ese el paso que dió. Se vió influido por lo que se conocía entonces: sólo había protones como partículas de carga positiva.
One can see at once that such a hole will appear as a particle. It will be a particle with a positive charge and a positive mass. From the beginning when I had this idea, it seemed to me that there would be symmetry between the holes and the electrons and therefore the holes must have the same mass as the electrons. How could one interpret the holes? They would be particles of positive charge. The only particles of positive charge known at that time were protons. For decades physicists had been building up their theory of matter entirely in terms of electrons and protons. They were quite satisfied to have just these two basic particles. The electrons carry the negative charge, the protons carry the positive charge. That was all that was needed. Rutherford had put forward some tentatives ideas that there might be a third particle - a neutron. That was a speculation which people talked about occasionally, but nobody took it very seriously.
Vemos que tampoco los neutrones había pasado de ser un modelo teórico hasta entonces.
On this basis, that the only particles in nature are electrons and protons, it seemed to me that the holes would have to be protons. And that was a great worry because the protons have a very different mass from the electrons. They are very much heavier. How could one explain this difference in mass?
El explicar la diferencia de masa es, digamos, el problema equivocado, vamos a verlo en el próximo post.
Angel "Java" Lopez