Related papers: Scale relativistic formulation of non-differentiab…
This article motivates and presents the scale relativistic approach to non-differentiability in mechanics and its relation to quantum mechanics. It stems from the scale relativity proposal to extend the principle of relativity to…
The development of a mechanics of non-differentiable paths suggested by Scale Relativity results in a foundation of Quantum Mechanics including Schr\"odinger's equation and all the other axioms under the assumption the path…
The theory of scale relativity provides a new insight into the origin of fundamental laws in physics. Its application to microphysics allows us to recover quantum mechanics as mechanics on a non-differentiable (fractal) spacetime. The…
Considered is the Schr\"odinger equation in a finite-dimensional space as an equation of mathematical physics derivable from the variational principle and treatable in terms of the Lagrange-Hamilton formalism. It provides an interesting…
The Schrodinger equation for non-relativistic quantum systems is derived from some classical physics axioms within an ensemble hamiltonian framework. Such an approach enables one to understand the structure of the equation, in particular…
We introduce the scale calculus, which generalizes the classical differential calculus to non differentiable functions. The new derivative is called the scale difference operator. We also introduce the notions of fractal functions, minimal…
Geometric (Schrodinger) quantization of nonrelativistic mechanics with respect to different reference frames is considered. In classical nonrelativistic mechanics, a reference frame is represented by a connection on a configuration space…
A non-local hidden variables theory for non-relativisitic quantum theory is presented, which gives a realist completion of quantum mechanics, in the sense of a complete description of individual events. The proposed fundamental theory is an…
If there exists a formulation of quantum mechanics which does not refer to a background classical spacetime manifold, it then follows as a consequence, (upon making one plausible assumption), that a quantum description of gravity should be…
The application of the theory of scale relativity to microphysics aims at recovering quantum mechanics as a new non-classical mechanics on a non-derivable space-time. This program was already achieved as regards the Schr\"odinger and Klein…
One of the main results of Scale Relativity as regards the foundation of quantum mechanics is its explanation of the origin of the complex nature of the wave function. The Scale Relativity theory introduces an explicit dependence of…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
The true dynamical randomness is obtained as a natural fundamental property of deterministic quantum systems. It provides quantum chaos passing to the classical dynamical chaos under the ordinary semiclassical transition, which extends the…
The objective of this series of three papers is to axiomatically derive quantum mechanics from classical mechanics and two other basic axioms. In this first paper, Schreodinger's equation for the density matrix is fist obtained and from it…
The scale transformation laws produce, on the motion equations of gravitating bodies and under some peculiar assumptions, effects which are anologous to those of a "macroscopic quantum mechanics". When we consider time and space scales such…
The qualitatively new concept of dynamic complexity in quantum mechanics is based on a new paradigm appearing within a nonperturbational analysis of the Schroedinger equation for a generic Hamiltonian system. The unreduced analysis…
The widely known but also somewhat esoteric Mach principle envisages a fully relational formulation of physical theories without any reference to a concept of `absolute space'. When applied to classical mechanics, under the guise of an…
This paper posits the existence of, and finds a candidate for, a variable change that allows quantum mechanics to be interpreted as quantum geometry. The Bohr model of the Hydrogen atom is thought of in terms of an indeterministic electron…
In this paper, we propose a new approach to the relativistic quantum mechanics for many-body, which is a self-consistent system constructed by juxtaposed but mutually coupled nonlinear Dirac's equations. The classical approximation of this…
A new kind of gauge theory is introduced, where the minimal coupling and corresponding covariant derivatives are defined in the space of functions pertaining to the functional Schroedinger picture of a given field theory. While, for…