A Newtonian message for quantization

Abstract

The dynamical equations related to Kepler motion are scale-invariant. This means that the dynamical model itself, described by these equations is space scale-invariant: it should work at the microscopic level just as well as it works at the macroscopic level. Why then the first quantization? Is it telling something we could not read by the classical physics? The Bohr's case of quantization, which initiated the first quantization, is presented here as a Newtonian instance of natural philosophy: the force characterizing the model has to account for some experimental observations related to motion. It turns out that the only thing worth considering from the side of quantum revolution is the inspiration it could bring, for instance in problems of astrophysics, the branch of physics which actually helped start the quantum theory. That inspiration existed historically, but was lost due to the attitude of our spirit, which tends to see things "quantal" different from, and more fundamental than, things "classical." This work aims to present all things in a single classical order, and thus explain some of the present-day quantum theoretical findings. V C 2014 Physics Essays Publication. [http://dx. Résumé:Les équations dynamiques liées au mouvement de Kepler sont échelle-invariantes. Cela signifie que le modèle dynamique lui-même, décrit par ces équations est invariant à l'échelle de l'espace: il devrait travailler au niveau microscopique aussi bien qu'au niveau macroscopique. Pourquoi alors cette première quantification? Veut-elle dire quelque chose que nous ne pouvions pas lire par la physique classique? Le cas de quantification de Bohr, qui a lancé la première quantification, est présentée ici comme une instance newtonienne de la philosophie naturelle: la force caractérisant le modèle doit expliquer les observations expérimentales liées au mouvement. Il s'avère que la seule chose qui mérite d'être considérée de côté du révolution quantique, est l'inspiration qu'elle pourrait apporter, par exemple dans les problèmes de l'astrophysique, la branche de la physique qui a effectivement contribué à démarrer la théorie quantique. Cette inspiration existait historiquement, mais elle a été perdue en raison de l'attitude de notre esprit, qui a une tendance à voir les choses "quantiques" fondamentalement différentes des choses "classiques". Ce travail vise à présenter toutes les choses dans un seul ordre classique, et donc à expliquer ainsi certaines des conclusions théoriques d'aujourd'hui.

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“…If (13) has real roots (Agop & Merches, 2019 ; Mazilu & Agop, 2014 ): with , the roots of Hessian and the cubic root of unity , the values of variables , and can be “scanned” by a simple transitive group with real parameters (Agop & Merches, 2019 ; Mazilu & Agop, 2014 ). This group can be revealed through Riemann-type spaces associated with the previous cubic.…”

“…This group can be revealed through Riemann-type spaces associated with the previous cubic. The basis of this approach is the fact that the simply transitive group with real parameters (Agop & Merches, 2019 ; Mazilu & Agop, 2014 ): where are the roots of the cubic (13), induces the simply transitive group in the variables , and , whose actions are: …”

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