Angel "Java" Lopez en Blog

13 de Octubre, 2015

Publicado el 13 de Octubre, 2015, 6:50

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Veamos una explicación de Dirac a un aparente error en una fórmula, en su primer trabajo sobre la ecuación relativista que lleva su nombre:

If you look up my first work on that subject (I do not know if anybody does that nowadays except the historians of science), there is one thing which you can hardly fail to notice. There is an equation which I wrote down which contains the following combination of terms:

w2/c2 + p21 + p22 + p23

Now, when you look at that, if you know anything at all you will say that that is wrong. There should be minus signs here before the p's. So, you will conclude that there was a misprint in the paper. But it was a very prominent misprint and you will perhaps wonder how I could have been so careless as to overlook it. I was a careful proof-reader in those days.

Resulta que no era un error de imprenta. sino parte de lo que se habituaba en aquel entonces. Dirac explica:

Well, the explanation of that is that it is not really a misprint but the appearance of that equation is again the expression of a fear. This work was done in the 1920's when the whole idea of relativity was still quite young. It did not make a splash in the scientific world until the end of the first world war and then it made a very big splash. Everyone was talking about relativity, not only the scientists, but the philosophers and the writers of columns in newspapers....

Fue a consecuencia de la confirmación de la teoría general al observar un eclipse, observación hecha por británicos para confirma la teoría de un alemán, luego de la primera guerra. Por alguna causa, esa noticia causó sensación en la prensa, y de alguna manera llegó a conocimiento de un Dirac aún estudiante. Fue su comienzo en el tema relatividad: desde entonces siempre trató de encontrar expresiones compatibles con las simetrías que muestra esa teoría.

... I do not think there has been any other ocassion in the history of science when an idea has so much caught the public interest as relativity did in those early days, starting from the relaxation which ocurred with the ending of a very serious war.

Now the basic idea of relativity was a symmetry between space and time. But this symmetry is not quite perfect symmetry. In order to  make it perfect, one has to change the signs in some of the equations. One can bring about that necessary change in sign by introducing the root of minus 1 into certain physical quantities. (Wherever we have a four-vector we have to introduce the root of minus 1 in certain coordinates.) Referring to quantities which have been doctored in this way, one has complete symmetry between space and time. The early workers in relativistic theory were very much impressed by the symmetry between space and time and wanted to cling to it - to hold onto it at all costs. So they frequently used this notation containing the root of minus 1, just to bring in the complete symmetry. The result was expressions like the one above. This notation was quite common. I see in my early notes that I was using it all the time. It was so common that people did not bother to mention it; whenever they used it in a paper they let it be understood. One could see from the signs in the expression whether the root of minus 1 should be inserted in the basic variables or not and there was no need to waste time explaining it. So, what appears to be a misprint nowadays, when people no longer feel the need to cling to the symmetry of space and time, was not a mistake, but was a historical consequence of the way in which relativity developed.

Minkowsky debe haber sido el primero en proponer el uso de la raíz de menos 1 para mantener una simetría mejor. Recientemente, en el Goldstein de Mecánica Clásica, encuentro que este autor defiende el uso de los signos menos explícitos, antes de llegar al uso de i (la raíz imaginaria de menos 1).

Este es un ejemplo pequeño, pero también habla de lo difícil que puede ser interpretar los "papers" clásicos, donde las notaciones no son las modernas o habituales en estos días.

Nos leemos!

Angel "Java" Lopez

Por ajlopez, en: Ciencia