arXiv subjects

Michel Bounias

Publications and source records attributed to Michel Bounias.

5 recordsLinked to original sources

arXiv2005

The Universe from Nothing: A Mathematical Lattice of Empty Sets

In this work, major principles of the mathematical constitution of space and the principles of construction of the physical space are presented. Generalized conceptions of distances and dimensionality evaluation are proposed, together with their conditions of validity and range of application to topological spaces. The existence of a Boolean lattice with fractal properties originating from non-well-founded properties of the empty set is demonstrated. Space-time emerges as an ordered sequence of mappings of closed 3-D Poincare sections of a topological 4-space-time provided by the lattice of primary empty cells. The fractal kernel stands for a particle and the reduction of its volume is compensated by morphic changes of a finite number of surrounding cells. Quanta of distances and quanta of fractality are demonstrated. It is shown that the families of fractal deformations give rise to families of particle-like structures. Deformation attributes associated to mass determine the inert mass and the gravitational effects, as has previously been shown, but fractal deformations of cells are responsible for the other fundamental characteristics, namely: spin, charges, and electric and magnetic properties.

physics.gen-ph↗

arXiv2003

Scanning the structure of ill-known spaces: Part 3. Distribution of topological structures at elementary and cosmic scales

The distribution of the deformations of elementary cells is studied in an abstract lattice constructed from the existence of the empty set. One combination rule determining oriented sequences with continuity of set-distance function in such spaces provides a particular kind of spacetime-like structure that favors the aggregation of such deformations into fractal forms standing for massive objects. A correlative dilatation of space appears outside the aggregates. At the large scale, this dilatation results in an apparent expansion, while at the submicroscopic scale the families of fractal deformations give raise to families of particle-like structure. The theory predicts the existence of classes of spin, charges, and magnetic properties, while quantum properties associated to mass have previously been shown to determine the inert mass and the gravitational effects. When applied to our observable spacetime, the model would provide the justifications for the existence of the creation of mass in a specified kind of "void", and the fractal properties of the embedding lattice extend the phenomenon to formal justifications of Big-Bang-like events without need for any supply of an extemporaneous energy.

physics.gen-ph↗

arXiv2003

Scanning the structure of ill-known spaces: Part 2. Principles of construction of physical space

Spacetime is represented by ordered sequences of topologically closed Poincare sections of the primary space constructed of primary empty cells. These mappings are constrained to provide homeomorphic structures serving as frames of reference in order to account for the successive positions of any objects present in the system. Mappings from one to the next section involve morphisms of the general structures. Discrete properties of the lattice allow the prediction of scales at which microscopic to cosmic structures should occur. Deformations of primary cells by exchange of empty set cells allow a cell to be mapped into an image cell in the next section as far as mapped cells remain homeomorphic. If a deformation involves a fractal transformation to objects, there occurs a change in the dimension of the cell and the homeomorphism is not conserved. The fractal kernel stands for a "particle" and the reduction of its volume is compensated by morphic changes of a finite number of surrounding cells. Quanta of distances and quanta of fractality are demonstrated. The interaction of a moving particle-like deformation with the surrounding lattice involves a fractal decomposition process that supports the existence and properties of previously postulated inerton clouds as associated to particles. Experimental evidence and further possibilities of the existence of inertons are proposed.

physics.gen-ph↗

arXiv2003

Scanning the structure of ill-known spaces: Part 1. Founding principles about mathematical constitution of space

Necessary and sufficient conditions allowing a previously unknown space to be explored through scanning operators are reexamined with respect to measure theory. Generalized conceptions of distances and dimensionality evaluation are proposed, together with their conditions of validity and range of application to topological spaces. The existence of a Boolean lattice with fractal properties originating from nonwellfounded properties of the empty set is demonstrated. This lattice provides a substrate with both discrete and continuous properties, from which existence of physical universes can be proved, up to the function of conscious perception. Spacetime emerges as an ordered sequence of mappings of closed 3-D Ponicare sections of a topological 4-space provided by the lattice. The possibility of existence of spaces with fuzzy dimension or with adjoined parts with decreasing dimensions is raised, together with possible tools for their study. The work provides the introductory foundations supporting a new theory of space whose physical predictions (suppressing the opposition of quantum and relativistic approaches) and experimental proofs are presented in details in Parts 2 and 3 of the study.

physics.gen-ph↗

arXiv2002

Spacetime differential elements and the distribution of bio-Hamiltonian components

Various Hamiltonian models have been derived for chemical structures belonging to living organisms while the Hamiltonian concept was not applied to life as a whole. However, Hamiltonian components were recently defined for living organisms on the condition to take in consideration their evolutionary implications (Bounias, 2001: CASYS'0l). This paper identifies differential elements of Spacetime, from which it delimits a probabilistic fuzzy-like invariance standing for conservativity of biological Hamiltonians. The distributions of potential and kinetic components in a individual bio-Hamiltonian, and the distribution of such individual Hamiltonians of living organisms interacting in more complex systems are shown to behave as a non-linear generalized convolution of functions.

physics.gen-ph↗