相关论文: Emergence of complex and spinor wave functions in …

Owing to the non-differentiable nature of the theory of Scale Relativity, the emergence of complex wave functions, then of spinors and bi-spinors occurs naturally in its framework. The wave function is here a manifestation of the velocity…

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…

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…

The theory of scale relativity provides a new insight into the origin of fundamental laws in physics. Its application to microphysics allows to recover quantum mechanics as mechanics on a non-differentiable (fractal) space-time. The…

A central notion of physics is the rate of change. While mathematically the concept of derivative represents an idealization of the linear growth, power law types of non-linearities even in noiseless physical signals cause derivative…

The internal interactions of fluids occur at all scales therefore the resulting force fields have no reason to be smooth and differentiable. The release of the differentiability hypothesis has important mathematical consequences, like scale…

In the first part of this contribution, we review the development of the theory of scale relativity and its geometric framework constructed in terms of a fractal and nondifferentiable continuous space-time. This theory leads (i) to a…

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…

This article is the second in a series of two presenting the Scale Relativistic approach to non-differentiability in mechanics and its relation to quantum mechanics. Here, we show Schroedinger's equation to be a reformulation of Newton's…

We develop a calculus of variations for functionals which are defined on a set of non differentiable curves. We first extend the classical differential calculus in a quantum calculus, which allows us to define a complex operator, called the…

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…

First steps in incorporating Nottale's scale-relativity principle to string theory and extended objects are taken. Scale Relativity is to scales what motion Relativity is to velocities. The universal, absolute, impassible, invariant scale…

We present a new interpretation of quantum mechanics, called the double-scale theory, which expends on the de Broglie-Bohm (dBB) theory. It is based, for any quantum system, on the simultaneous existence of two wave functions in the…

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…

Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a non-differentiable continuum, which implies it is fractal, i.e., explicitly dependent on internal scale variables. Owing to…

We explore the problem of time in quantum gravity in a point-particle analogue model of scale-invariant gravity. If quantized after reduction to true degrees of freedom, it leads to a time-independent Schr\"odinger equation. As with the…

In this paper we first show that the usual three dimensionality of space, which is taken for granted, results from the spinorial behaviour of Fermions, which constitute the material content of the universe. It is shown that the resulting…

In the framework of the theory of scale relativity, we suggest a solution to the cosmological problem of the formation and evolution of gravitational structures on many scales. This approach is based on the giving up of the hypothesis of…

A principle is proposed according to which the dynamics of a quantum particle in a one-dimensional configuration space (OCS) is determined by a variational problem for two functionals: one is based on the mean value of the Hamilton…

Nottale's special scale-relativity principle was proposed earlier by the author as a plausible geometrical origin to string theory and extended objects. Scale Relativity is to scales what motion Relativity is to velocities. The universal,…