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.

In the Weyl-Dirac non-relativistic hydrodynamics approach, the non-linear interaction between sub-quantum level and particle gives non-differentiable properties to the space. Therefore, the movement trajectories are fractal curves, the dynamics are described by a complex speed field and the equation of motion is identified with the geodesics of a fractal space which corresponds to a Schrödinger non-linear equation. The real part of the complex speed field assures, through a quantification condition, the compatibility between the Weyl-Dirac non-elativistic hydrodynamic model and the wave mechanics. The mean value of the fractal speed potential, identifies with the Shanon informational energy, specifies, by a maximization principle, that the sub-quantum level "stores" and "transfers" the informational energy in the form of force. The wave-particle duality is achieved by means of cnoidal oscillations modes of the state density, the dominance of one of the characters, wave or particle, being put into correspondence with two flow regimes (non-quasi-autonomous and quasi-autonomous) of the Weyl-Dirac fluid. All these show a direct connection between the fractal structure of space and holographic principle.

Abstract. The present paper analyzes the morphogenesis of gravitational structures, assuming that dynamics of a test particle in a gravitational field takes place on continuous but non-differentiable curves. The dynamics of such gravitational system is described by an equation for a complex speed that characterizes its rheological behavior. Moreover, the separation of movements on interaction scales in the dynamics equation implies a non-differentiable hydrodynamical model. Finally, such an approach was applied both to one and two body problems and, via numerical simulation, to the morphogenesis of gravitational structures. Consequently, quantization at intragalactic (Solar System) and extragalactic scales (Tifft's effect) as well as certain modifications of Newton's force occur. At the same time there is a tendency to form gravitational structures at any epoch, without inflationary phase.