Related papers: Dimensionality and Fractals
A Cantorian fractal spacetime, a family member of von Neumann's noncommutative geometry is introduced as a geometry underlying a new relativity theory which is similar to the relation between general relativity and Riemannian geometry.…
The phenomenologically observed flatness - or near flatness - of spacetime cannot be understood as emerging from continuum Planck (or sub-Planck) scales using known physics. Using dimensional arguments it is demonstrated that any…
We argue that dimensionality is not absolute, but that it depends on the scale of resolution, from the Planck to the macro scale.
Fractals are ubiquitous natural emergences that have gained increased attention in engineering applications, thanks to recent technological advancements enabling the fabrication of structures spanning across many spatial scales. We show how…
A stochastic model relating the parameters of astrophysical structures to the parameters of their granular components is applied to the formation of hierarchical, large-scale structures from galaxies assumed as point-like objects. If the…
We give a simple model to explain the origin of fermion families, and chirality through the use of a domain wall placed in a five dimensional space-time.
A theory of time and space with fractional dimensions (FD) of time and space ($d_{\alpha}, \alpha=t,{\bf r})$ defined on multifractal sets is proposed. The FD is determined (using principle of minimum the functionals of FD) by the energy…
The mechanism of production of a large number of universes is considered. It is shown that universes with parameters suitable for creation of life are necessarily produced as a result of quantum fluctuations. Fractal structures are formed…
The origin of rotation or spin of objects, from stars to galaxies, is still an unanswered question. Even though there are models which try to explain this, none of them can account for the initial impulse that gave rise to this spin. In…
We analyze the early stage of evolution of a universe with two scale factors proposed in [1] when matter is present. The scale factors describe two causally disconnected patches of the universe interacting trough a non-trivial Poisson…
The fractal dimension of large-scale galaxy clustering has been demonstrated to be roughly $D_F \sim 2$ from a wide range of redshift surveys. If correct, this statistic is of interest for two main reasons: fractal scaling is an implicit…
In the theory of modern physics, such as in relativity and quantum mechanics, the three-dimensionality of space is introduced as a presupposed fact. The three-dimensionality of particle motion, that is, the three-dimensionality of particle…
An empirically validated, phenomenological model relating the parameters of an astronomical body to the stochastic fluctuations of its granular components is generalized in terms of fractal scaling laws. The mass of the particle…
The fundamental chiral nature of the observed quarks and leptons and the emergence of the gauge group itself are most puzzling aspects of the standard model. Starting from general considerations of topological properties of gauge field…
We throw further light on a recently discussed Kerr-Newman type formulation of Fermions and the related cosmological scheme which predicted an ever expanding universe, as indeed has subsequently been confirmed. In the spirit of the…
We show a relation between fractional calculus and fractals, based only on physical and geometrical considerations. The link has been found in the physical origins of the power-laws, ruling the evolution of many natural phenomena, whose…
This chapter deals with error and uncertainty in data. Treats their measuring methods and meaning. It shows that uncertainty is a natural property of many data sets. Uncertainty is fundamental for the survival os living species, Uncertainty…
It is shown that the observed fractal distribution of galaxies is, in fact, consistent with homogeneity of the Universe and observational limits on $ \Delta T/T$, if the presence of dark matter and dark charge predicted by the Modified…
I review the basis and limitations of plausible inference in cosmology, in particular the limitation that it can only provide fundamentally true inferences when the hypotheses under consideration form a set that is exhaustive. They never…
The degree by which a function can be differentiated need not be restricted to integer values. Usually most of the field equations of physics are taken to be second order, curiosity asks what happens if this is only approximately the case…