Related papers: Scale relativity and fractal space-time: theory an…
The two-fractal overlap model of earthquake shows that the contact area distribution of two fractal surfaces follows power law decay in many cases and this agrees with the Guttenberg-Richter power law. Here, we attempt to predict the large…
The relativity of cosmic time is developed within the framework of Cosmological Relativity in five dimensions of space, time and velocity. A general linearized metric element is defined to have the form $ds^2 = (1+\phi) c^2 dt^2 - dr^2 +…
A gravity theory is developed with the metric ${\hat g}_{\mu\nu}= {g}_{\mu\nu}+B\partial_\mu\phi\partial_\nu\phi$. In the present universe the additional contribution from the scalar field in the metric ${\hat g}_{\mu\nu}$ can generate an…
In contrast to the symmetries of translation in space, rotation in space, and translation in time, the known laws of physics are not universally invariant under transformation of scale. However, the action can be invariant under change of…
The curves of scaling behavior is a significant concept in fractal dimension analysis of complex systems. However, the underlying rationale of this kind of curves for fractal cities is not yet clear. The aim of this paper is at researching…
It is proposed that spacetime should be regarded as an evolving block universe, bounded to the future by the present time, which continually extends to the future. This future boundary is defined at each time by measuring proper time along…
We develop the spectral point of view on geometry based on the formalism of quantum physics. We start from the simple physical question of specifying our position in space and explain how the spectral geometric point of view provides a new…
The structure of the large scale distribution of the galaxies have been widely studied since the publication of the first catalogs. Since large redshift samples are available, their analyses seem to show fractal correlations up to the…
General relativity as one the pillar of modern cosmology has to be thoroughly tested if we want to achieve an accurate cosmology. We present the results from such a test on cosmological scales using cosmic shear and galaxy clustering…
General relativity is applied to the strong interaction; the nexus between the two being arrived at by constructing a line element having the Yukawa form, which is used to describe geometrically the classical dynamics of a particle moving…
We consider multiple scalar fields coupled to gravity, with special attention given to two-field theories. First, the conditions necessary for these theories to meet solar system tests are given. Next, we investigate the cosmological…
Scaling laws in astrophysical systems that involve the energy, the geometry, and the spatio-temporal evolution, provide the theoretical framework for physical models of energy dissipation processes. A leading model is the standard…
The divergences coming from a particular sector of gravitational fluctuations around a generic background in general theories of quadratic gravity are analyzed. They can be summarized in a particular type of scalar model, whose properties…
The ordinary quantum theory points out that general relativity is negligible for spatial distances up to the Planck scale. Consistency in the foundations of the quantum theory requires a``soft'' spacetime structure of the general relativity…
A set of scaling laws, based on the stochastic motions of the granular components of astronomical systems, is applied to a cosmological model with a positive cosmological constant. It follows that the mass of the dominant particle in the…
Spatio-temporal models are widely used for inference in statistics and many applied areas. In such contexts interests are often in the fractal nature of the sample surfaces and in the rate of change of the spatial surface at a given…
Besides two fundamental postulates, (i) the principle of relativity and (ii) the constancy of the one-way speed of light in all inertial frames of reference, the special theory of relativity uses the assumption about the Euclidean structure…
It is widely hoped that quantum gravity will shed light on the question of the origin of time in physics. The currently dominant approaches to a candidate quantum theory of gravity have naturally evolved from general relativity, on the one…
Standard quantum mechanics and gravity are used to estimate the mass and size of idealized gravitating systems where position states of matter and geometry become indeterminate. It is proposed that well-known inconsistencies of standard…
Suppose the usual description of spacetime as a 4-dimensional manifold with a Lorentzian metric breaks down at Planck energies. Can we still construct sensible theoretical models of the universe? Are they testable? Do they lead to a…