arXiv subjects

Helene Porchon

Publications and source records attributed to Helene Porchon.

5 recordsLinked to original sources

arXiv2016

Infinity of Geodesics in an Homogeneous and Isotropic Expanding Space-Time

In this paper we construct a discrete simulation of an expanding homogeneous and isotropic space-time that expands via expansion of its basic elements to figure out properties and characteristics of such a space-time and derive conclusions. We prove that in such an expanding space-time, the geodesics are curved and more precisely, they fluctuate on the boundaries of the expanding basic elements. The non existence of privileged expansion direction leads to the existence of an infinity of fluctuating geodesics between any two locations in this space-time, that provides a prediction of polarization in geometric optics, and a prediction of an earlier acceleration of the expansion as for the cosmic inflation model. This simulation is a case study and an example of space-time with variable topology using the principle of variation of topology via a transformation that creates holes.

physics.gen-ph↗

arXiv2013

Deterministic Elaboration of Heisenberg's Uncertainty Relation and the Nowhere Differentiability

In this paper the uncertainty principle is found via characteristics of continuous and nowhere differentiable functions. We prove that any physical system that has a continuous and nowhere differentiable position function is subject to an uncertainty in the simultaneous determination of values of its physical properties. The uncertainty in the simultaneous knowledge of the position deviation and the average rate of change of this deviation is found to be governed by a relation equivalent to the one discovered by Heisenberg in 1925. Conversely, we prove that any physical system with a continuous position function that is subject to an uncertainty relation must have a nowhere differentiable position function, which makes the set of continuous and nowhere differentiable functions a candidate for the quantum world.

physics.gen-ph↗

arXiv2012

Variable Topology on Fractal Manifold

In this paper, we study the topology associated to the fractal manifold model. It turns out that this topology is actually a family of topologies that gives to the fractal manifold a structure of variable topological space. Additionally, we prove that using the fractal manifold as model for the universe dynamic, the universe expansion is intimately correlated to the variation of the topology.

math.GM↗

arXiv2012

Topological Expansion, Study and Applications

In this paper, we introduce the notion of expanding topological space. We define the topological expansion of a topological space via local multi-homeomorphism over coproduct topology, and we prove that the coproduct family associated to any fractal family of topological spaces is expanding. In particular, we prove that the more a topological space expands, the finer the topology of its indexed states is. Using multi-homeomorphisms over associated coproduct topological spaces, we define a locally expandable topological space and we prove that a locally expandable topological space has a topological expansion. Specifically, we prove that the expanding fractal manifold is locally expandable and has a natural topological expansion.

math.GM↗

arXiv2012

Fractal Topology Foundations

In this paper, we introduce the foundation of a fractal topological space constructed via a family of nested topological spaces endowed with subspace topologies, where the number of topological spaces involved in this family is related to the appearance of new structures on it. The greater the number of topological spaces we use, the stronger the subspace topologies we obtain. The fractal manifold model is brought up as an illustration of space that is locally homeomorphic to the fractal topological space.

math.GM↗