The universal meaning of the quantum of action

Abstract

Napolitano (IFSC/USP) for reading and criticizing the preliminary versions of this paper, Nícolas Morazotti (IFSC/USP) for his precious help in LaTeX, Miled Y. H. Moussa (IFSC/USP) for his hospitality along 2016 and to Programa Nacional de Pós-Doutorado (PNPD) from Coordenação de Aperfeiçoamento de Pessoal de Ensino Superior (CAPES). K. Pelogia would like to thank to Carlos Brasil, for this oportunity, to Dr. Klaus Hentschel (Universität Stuttgart) for his time to help us and to Christian Wilde, Cristal da Rocha (USP) , James Payne, Sheila Clark: thank you for read and re read this paper always looking for mistakes and helping us to improve our paper. Conventions: The a, b, c letters between brackets indicate the original author's notes. The numbers indicate the translators analysis. Both the bibliographic citations by the author and by the translators obey the EPJH format. The numbers in the margins indicate the starts of original pages translated. † deceased (1881-1947)1 Ishiwara uses "state space" instead "phase space" -we will discuss this detail in section III of [Pelogia 2017]. 2 Sommerfeld's, "The Planck's constant and its overall importance for the molecular physics", was presented on 25 September 1911 at the "83rd Scientific meeting in Karlsruhe", published in Physikalische Zeitschrift [Sommerfeld 1911], a German magazine published from 1899 to 1945. In the book of Planck, "Lectures on the theory of heat radiation" [Planck 1913], Ishiwara specifies chapter 3 "Entropy and probability".3 Ishiwara refers not only to the classic set of papers [Bohr 1913a, Bohr 1913b, Bohr 1913c where Bohr presents his atomic model, but also to a paper [Bohr 1914] where he tries to explain the Stark and Zeeman effects and the spectral lines of other elements -it is worth noting that Bohr, in this work, had proposed the possibility of elliptical orbits for the electron, but did not consider it explicitly in his calculations. See section III of [Pelogia 2017] for more details about it.