Sur l'Interprétation d'Eddington de l'équation de Dirac

Boris Podolsky

Eddington, in his book Relativity Theory of Protons and Electrons, makes statements to the effect that the invariance of Dirac's equation is an elementary consequence of the tensor form which it acquires in the new wave tensor calculus, in which it is merely an identity derivable on epistemological principles and not on physical hypothesis. It is shown in this article that the invariance of Dirac's equation referred to by Eddington is a purely formal one, while the invariance which is of particular interest in quantum mechanics depends upon the physical interpretation of the wave function. The generalization of physical interpretation suggested by Eddington's work, however, has the desirable quality of leaving Dirac's equation invariant in the physical sense. It is further shown that in the derivation of Dirac's equation Eddington makes use of the usual physical assumptions, but in somewhat disguised form.

Denis Guthleben

Г. А. Зайцев

Clive W. Kilmister

I conclude the first part of this book by carrying the story up to 1928, to the lightning flash in Eddington's mind produced by Dirac's paper on the wave equation of the electron. Setting out the context and Eddington's thinking about it is a very different matter for quantum mechanics and relativity. Both theories are commonly expressed in austere mathematical language. In the case of relativity the basic ideas behind the mathematics are now well understood and can be set out with little complication. These ideas were mostly already clear to Eddington. But for quantum mechanics the mathematics, yoked to the wealth of experimental results, drove the development of the theory at a breakneck speed, mostly without anyone pausing for deeper understanding. It is indeed only in the last decade that it has become generally accepted that quantum mechanics still lacks any coherent interpretation. To explain Eddington's context it is therefore necessary to say something about the mathematical formalism. It is true, as will become clear, that Eddington was a little more sceptical than most, but by and large the mathematics drove him as it did those directly working in the theory. I begin, then, with a description of that part of the early (pre-1925) history of quantum mechanics that was in Eddington's mind in 1923. Then I explain what happened in 1925–6 and Eddington's reaction to it. The chapter concludes with Dirac's relativistic wave equation of 1928 and Eddington's further reaction to that. The old quantum theory What is now called the old quantum theory arose at the turn of the century. Two related experimental contradictions with classical physics played important roles in this.

J. Charon

L'équation relativiste de Dirac pour l'électron peut être considérée comme la description d'une « singularité » d'un champ relativiste d'Univers. On montre dans cette note que l'on peut retrouver cette équation à l'aide d'un modèle d'Univers particulièrement simple en assimilant l'électron à un seul point de cet Univers. On tire des résultats obtenus une interprétation de la fonction d'onde ψ de la mécanique ondulatoire.