Angel "Java" Lopez en Blog

Publicado el 21 de Noviembre, 2016, 17:51

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A Dirac le preocupa que en la explicación con modelo matemático de la interacción entre electrón y campo electromagnético, hay divergencias, integrales cuyas sumas divergen. Las divergencias surgen de tener que lidiar con singularidades en el campo, o en interacciones cada vez más cercanas, alrededor de un punto. El tema de llegar a divergencias (o a sumas infinitas) al disminuir las distancias es una señal que nos hace la naturaleza: para mí, nos está diciendo "el modelo que adoptaron es incorrecto, en la realidad no hay singularidades". Veamos que piensa Dirac:

If one deals classically with point electrons interacting with the electromagnetic field, one finds difficulties connected with the singularities in the field. People have been aware of these difficulties from the time of Lorentz, who first worked out the equations of motion for an electron. In the early days of the quantum mechanics of Heisenberg and Schrodinger, people thought these difficulties would be swept away by the new mechanics. It now became clear that these hopes would not be fulfilled. The difficulties reappear in the divergencies of quantum electrodynamics, the quantum theory of the interaction of electrons and the electromagnetic field. They are modified somewhat by the infinities associated with the sea of negative-energy electrons, but they stand out as the dominant problem.

De nuevo es un tema técnico, pero vemos que para Dirac es importante. Los físicos no siempre se preocupan a tal grado por alguna imperfección en la teoría, pero Dirac ha sido consecuente con sus ideas, y durante décadas pregonó sobre este problema "básico".

The difficulty of the divergencies proved to be a very bad one. No progress was made for twenty years. Then a development came, initiated by Lamb's discovery and explanation of the Lamb shift, which fundamentally changed the character of theoretical physics. It involved setting up rules for discarding the infinities, rules which are precise, so as to leave well-defined residues that can be compared with experiment. But still one is using working rules and not regular mathematics. Most theoretical physicists nowadays appear to be satisfied with this situation, but I am not. I believe that theoretical physics has gone on the wrong track with such developments and one should not be complacent about it. There is some similarity between this situation and the one in 1927, when most physicists were satisfied with the Klein-Gordon equation and did not let themselves be bothered by the negative probabilities that it entailed.

Como había yo mencionado, a Dirac le preocupaba que la Klein-Gordon pudiera producir probabilidades negativas. Notablemente, el efecto Lamb fue explicado exitosamente por la QED aún usando los trucos de eliminar los infinitos, siendo uno de los valores mejor deducidos de la historia de la física.

We must realize that there is something radically wrong when we have to discard infinities from our equations, and we must hang on to the basic ideas of logic at all costs. Worrying over this point may lead to an important advance. Quantum electrodynamics is the domain of physics that we know most about, and presumably it will have to be put in order before we can hope to make any fundamental progress with the other field theories, although these will continue to develop on the experimental basis.

Y no sólo aparecen divergencias en electrodinámica cuántica.

Nos leemos!

Angel "Java" Lopez

Por ajlopez, en: Ciencia