Related papers: The Many Dimensions of Dimension
This paper is the first of a 3-part series that classifies the 5-dimensional Thurston geometries. The present paper (part 1 of 3) summarizes the general classification, giving the full list, an outline of the method, and some illustrative…
The multi-scale expansions and contractions of the Earth's magnetosphere explain fundamental issues of magnetic storm-substorm relationship. This magnetospheric behavior is in agreement with a model of 3D-spirally-faster-inward-oscillating…
We discuss two scenarios of emergent gravity. In one of them the quantum vacuum is considered as superplastic crystal, and the effective gravity describes the dynamical elastic deformations of this crystal. In the other one the…
We consider variations of coupling strengths and mass ratios in and beyond the Standard Model, in the light of various mechanisms of mass generation. In four-dimensional unified models, heavy quark and superparticle thresholds and the…
A physical theory of the world is presented under the unifying principle that all of nature is laid out before us and experienced through the passage of time. The one-dimensional progression in time is opened out into a multi-dimensional…
Several attempts to construct theories of gravity with variable mass are considered. The theoretical impacts of allowing the rest mass to vary with respect to time or an appropriate curve parameter are examined in the framework of Newtonian…
We informally review the construction of spacetime geometries with multifractal and, more generally, multiscale properties. Based on fractional calculus, these continuous spacetimes have their dimension changing with the scale; they display…
Symmetries concerning the ordinary coordinate spacetime and internal spacetime are discussed. A possible unification model of electroweak, strong and gravitational interactions is briefly described.
The discovery of cosmic acceleration has raised the intriguing possibility that we are witnessing the first breakdown of General Relativity on cosmological scales. In this article I will briefly review current attempts to construct a…
The effective dimension-5 operators can be induced by quantum gravity or inspired by string and M theories. They have important impacts on grand unified theories. We investigate the group theoretic nature of them for the well known E(6)…
Although it is well known that any consideration of the variations of fundamental constants should be restricted to their dimensionless combinations, the literature on variations of the gravitational constant $G$ is entirely dimensionful.…
The simple examples of spontaneous breaking of various symmetries for the scalar theory with fundamental mass have been considered (this research was supported by the Belgian National Fund for Scientific Research). Higgs' generalizations on…
Gravity with incorporation of additional dimensions and noncommutative geometry.
Our first experience of dimension typically comes in the intuitive Euclidean sense: a line is one dimensional, a plane is two-dimensional, and a volume is three-dimensional. However, following the work of Mandelbrot \cite{mandelbrot},…
Here we discuss direct links of the number of fundamental dimensions to the fundamental natural constants using simple arguments of dimensional analysis \corr{based on Maxwell's dimensions length (L), time (T) and mass (M) as well as the…
A unified and fully relativistic treatment of the interaction of the electric and magnetic dipole moments of a particle with the electromagnetic field is given. New forces on the particle due to the combined effect of electric and magnetic…
The geometry of rotations in dimensions 3, 4, and 5 is discussed using the matrix exponential map. Explicit closed formulas for the exponential of an antisymmetric matrix, as well as the logarithm of a rotation, are given for these…
Faced with the persisting problem of the unification of gravity with other fundamental interactions we investigate the possibility of a new paradigm, according to which the basic space of physics is a multidimensional space ${\cal C}$…
These lectures provide an elementary introduction to Chern Simons Gravity and Supergravity in $d=2n+1$ dimensions.
We examine the five-dimensional super-de Rham complex with $N = 1$ supersymmetry. The elements of this complex are presented explicitly and related to those of the six-dimensional complex in $N = (1, 0)$ superspace through a specific notion…