Angel "Java" Lopez en Blog

Publicado el 16 de Julio, 2016, 16:13

Tengo tanto pendiente para escribir sobre Heisenberg (ver Entendiendo a Heisenberg, Heisenberg desarrollando la mecánica cuántica)

Hoy encontré en el excelente libro de Zeidler, Quantum Field Theory, I, esta cita del discurso de Heisenberg cuando fue invitado, junto con Dirac, por Abdus Salam a una conferencia en Trieste, Italia, 1968. Es interesante ver cómo dejó por un tiempo el modelo de átomo de hidrógeno y se concentró en un problema más simple:

I had the impression from my conversation with Bohr (1885-1962) that one should go away from all these classical concepts, one should not speak of the orbit of an electron. ..

When I came back from Copenhagen to Gottingen I decided that I should again try to do some kind of guess work there, namely, to guess the  intensities in the hydrogen spectrum... That was early in the summer 1925 and I failed completely. The formulae got too complicated... At the same time I also felt, if the mechanical system would be simpler, then it might be possible just to do the same thing as Kramers (1894-1952) and I had done in Copenhagen and to guess the amplitudes. Therefore I turned from the hydrogen atom to the anharmonic oscillator, which was a very  simple model. Just then I became ill and went to the island of Heligoland to recover. There I had plenty of time to do my calculations. It turned out that it really was quite simple to translate classical mechanics into quantum mechanics. But I should mention one important point. It was not sufficient simply to say "let us take some frequencies and amplitudes to replace orbit quantities" and use a kind of multiplication which we had already used in Copenhagen and which later turned out to be equivalent to matrix multiplication...

Heisenberg quería algo más, y Born, Jordan, independientemente Dirac,llegaron a completar el modelo matemático:

It turned out that one could replace the quantum conditions of Bohr's theory by a formula which was essentially equivalent to the sum-rule by Thomas and Kuhn... I was however not able to get a neat mathematical scheme out of it. Very soon afterwards both Born and Jordan in Gottingen and Dirac in Cambridge were able to invent a perfectly closed mathematical scheme; Dirac with very ingenious new methods on q-numbers and Born and Jordan with more conventional methods of matrices33...

Pero Heisenberg se preocupaba más por el aspecto físico, más allá del modelo matemático:

When you try too much for rigorous mathematical methods you fix your attention on those points which are not important from the physics point and thereby you get away from the experimental situation. If you try to solve a problem by rather dirty mathematics, as I have mostly done, then you are forced always to think of the experimental situation; and whatever formulae you write down, you try to compare the formulae with reality and thereby, somehow, you get closer to reality than by looking for the rigorous methods. But this may, of course, be different for different people...

In 1926 Niels Bohr and I discussed the question on the physical  interpretation of quantum mechanics many, many nights and we were frequently in a state of despair. Bohr tried more in the direction of duality between waves and particles; I preferred to start from the mathematical formalism and to look for a consistent interpretation. Finally Bohr went to Norway to think alone about the problem and I remained in Copenhagen. Then I remembered Einstein's remark in our discussion. I remembered that Einstein had said that "It is the theory which decides what can be observed." From there it was easy to turn around our question and not to ask "How can I represent in quantum mechanics this orbit of an electron in a cloud chamber?", but rather to ask "Is it not true that always only such situations occur in nature, even in a cloud chamber, which can be described by the mathematical formalism of quantum mechanics?" By turning around I had to investigate what can be described in this formalism; and then it was very easily seen, especially when one used the new mathematical discoveries of Dirac and Jordan about transformation theory, that one could not describe at the same time the exact position and the exact velocity of an electron; one had these uncertainty relations. In this way things became clear. When Bohr returned to Copenhagen, he had found an equivalent  interpretation with his concept of complementarity, so finally we all agreed that now we had understood quantum theory...

Y llegamos al tema Einstein, discutiendo con Bohr en el Solvay 1927:

Again we met a difficult situation in 1927 when Einstein and Bohr discussed these matters at the Solvay Conference. Almost every day the  sequence of events was the following. We all lived in the same hotel. In the morning for breakfast Einstein would appear and tell Bohr a new fictitious experiment in which he could disprove the uncertainty relations and thereby our interpretation of quantum theory. Then Bohr, Pauli and I would be very worried, we would follow Bohr and Einstein to the meeting and would discuss this problem all day. But at night for dinner usually Bohr had solved the problem and he gave the answer to Einstein, so then we felt that everything was alright and Einstein was a bit sorry about that and said he would think about it. Next morning he would bring a new fictitious experiment, again we had to discuss,  and so on. This went on for quite a number of days and at the end of the conference the Copenhagen physicists had the feeling that they had won the battle and that actually Einstein could not make any real objection... Einstein never accepted the probabilistic interpretation of quantum mechanics. He said : "God does not play at dice."

Nos leemos!

Angel "Java" Lopez

Por ajlopez, en: Ciencia