Related papers: The Concept of Time in 2D Quantum Gravity
We show that in general a spacetime having a quantum group symmetry has also a scale dependent fractal dimension which deviates from its classical value at short scales, a phenomenon that resembles what observed in some approaches to…
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…
The space-time length R between a moving source and the observation point is calculated in order to substitute with it the spatial distance D, normally used in the Newton's law of gravitation, as well as in any inverse-square-law.…
The Hamiltonian structure of spacetimes with two commuting Killing vector fields is analyzed for the purpose of addressing the various problems of time that arise in canonical gravity. Two specific models are considered: (i) cylindrically…
We consider spacetime to be a 4-dimensional differentiable manifold that can be split locally into time and space. No metric, no linear connection are assumed. Matter is described by classical fields/fluids. We distinguish electrically…
Among the many disparate approaches towards quantum gravity, the reduction of spacetime dimension in the ultraviolet regime is expected to be a common thread. The dimensionality of spacetime can be defined in various contexts. The spectral…
Early work by the author with Prof. Ishibashi [Scott et al., J. Appl. Phys. 64, 787 (1988)] showed that switching kinetics in ferroelectrics satisfy a constraint on current transients compatible with d = 2.5 dimensionality. At that time…
In scaled relational particle mechanics, only relative times, relative angles and relative separations are meaningful. It arose in the study of the absolute versus relative motion debate. It has then turned out to be a useful toy model of…
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…
We consider a $SO(d)$ gauge theory in an Euclidean $d$-dimensional space-time, which is known to be renormalizable to all orders in perturbation theory for $2\le{d}\le4$. Then, with the help of a space-time representation of the gauge…
This paper puts forward a broad critical analysis of the concept of physical time. Clock effect is conceived as a consequence of the variation of the gravitational or pseudo gravitational potential, and it is remarked that only some real…
The concept of space group has long served as the fundamental framework to describe the physical properties of crystalline materials, from electronic bands to photonic dispersions. The recent progress of spatiotemporal control, such as…
Recently I proposed a simple dynamical network model for discrete space-time which self-organizes as a graph with Hausdorff dimension d_H=4. The model has a geometric quantum phase transition with disorder parameter (d_H-d_s) where d_s is…
Starting from the revelation of the nature of inertial forces, this article discusses the subdivision of the basic physical concept of space-time and raises questions about the metric of standard cosmology. A new form of particle dynamics…
In recent years several approaches to quantum gravity have found evidence for a scale dependent spectral dimension of space-time varying from four at large scales to two at small scales of order of the Planck length. The first evidence came…
General relativity in three spacetime dimensions is used to explore three approaches to the ``problem of time'' in quantum gravity: the internal Schr\"odinger approach with mean extrinsic curvature as a time variable, the Wheeler-DeWitt…
The critical behavior of the Ising model on a fractal lattice, which has the Hausdorff dimension $\log_{4} 12 \approx 1.792$, is investigated using a modified higher-order tensor renormalization group algorithm supplemented with automatic…
It is possible to describe a universal scalar field of time but not a universal coordinate of time and to attribute its non-geodesic alignment to the electromagnetic phenomena. A very surprising outcome is that not only mass generates…
A classical two dimensional theory of gravity which has a number of interesting features (including a Newtonian limit, black holes and gravitational collapse) is quantized using conformal field theoretic techniques. The critical dimension…
The spectral principle of Connes and Chamseddine is used as a starting point to define a discrete model for Euclidean quantum gravity. Instead of summing over ordinary geometries, we consider the sum over generalized geometries where…