Related papers: Scale relativity and fractal space-time: theory an…
An attempt is made here to extend to the microscopic domain the scale invariant character of gravitation - which amounts to consider expansion as applying to any physical scale. Surprisingly, this hypothesis does not prevent the redshift…
The Principle of Relativity has so far been understood as the {\it covariance} of laws of Physics with respect to a general class of reference frame transformations. That relativity, however, has only been expressed with the help of {\it…
The relevance of the Planck scale to a theory of quantum gravity has become a worryingly little examined assumption that goes unchallenged in the majority of research in this area. However, in all scientific honesty, the significance of…
Scaling properties inherent in quantum dynamics have been studied for various systems in terms of acceleration, deceleration and time reversing. We show a scaling property of quantum dynamics on curved space-time where gravity plays an…
We highlight the fact that the lack of scale invariance in the gravitational field equations of General Relativity results from the underlying assumption that the appropriate scale for the gravitational force should be linked to the atomic…
We introduce fractional flat space, described by a continuous geometry with constant non-integer Hausdorff and spectral dimensions. This is the analogue of Euclidean space, but with anomalous scaling and diffusion properties. The basic tool…
General relativity promotes space-time to a physical, dynamical object subject to equations of motion. Quantum gravity, accordingly, must provide a quantum framework for space-time, applicable on the smallest distance scales. Just like…
Quantum mechanical effects related to the recently developed projective theory of relativity are considered. It is shown that at cosmological time intervals the light velocity increases and the atomic units of length and time are shrinking.…
While the universe becomes more and more homogeneous at large scales, statistical analysis of galaxy catalogs have revealed a fractal structure at small-scales (\lambda < 100 h^{-1} Mpc), with a fractal dimension D=1.5-2 (Sylos Labini et al…
The traditional concept of space in geography is based on the notion of distance. Where there is a spatial analysis, there is a distance measurement. However, the precondition for effective distance-based space is that the geographical…
In a recent paper (arXiv:1412.6000) a general mechanism for emergence of cosmological space-time geometry from a quantum gravity setting was devised and departure from standard dispersion relations for elementary particle were predicted. We…
We present evidences of the diffusive motion of the ground and tunnels and show that if systematic movements are excluded then the remaining uncorrelated component of the motion obeys a characteristic fractal law with the displacement…
Scale invariance is considered in the context of a gravitational theory where the action, in the first order formalism, is of the form S = \int L_{1} \Phi d^4x + \int L_{2}\sqrt{-g}d^4x where \Phi is a density built out of degrees of…
I briefly review some scenarios for the role of the Planck length in quantum gravity. In particular, I examine the differences between the schemes in which quantum gravity is expected to introduce a maximum acceleration and the schemes in…
We apply the property of selfsimilarity that corresponds to the concept of a fractal universe, to the dimension of time. It follows that any interval of time, given by any tick of any clock, is proportional to the age of the universe. The…
We present a scale-invariant theory, conformal gravity, which closely resembles the geometrodynamical formulation of general relativity (GR). While previous attempts to create scale-invariant theories of gravity have been based on Weyl's…
A class of simplified measures is constructed to capture the key features of generic spatio-temporally chaotic systems. A combined analytical and numerical investigation allows us to extablish the scaling beahviour of the fractal dimension…
`How do our ideas about quantum mechanics affect our understanding of spacetime?' This familiar question leads to quantum gravity. The complementary question is also important: `How do our ideas about spacetime affect our understanding of…
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…
A physical interpretation of axioms of the differential structure of space-time is presented. Consequences of such interpretation for cosmic string's space-time with a scalar field are studied. It is shown that the assumption of smoothness…