Related papers: How to Recover Spacetime Structure from Privileged…
Besides two fundamental postulates, (i) the principle of relativity and (ii) the constancy of the speed of light in all inertial frames of reference, special relativity uses the assumption about the Euclidean structures of gravity-free…
We introduce a framework of structural approximation to represent Lorentz-invariant Minkowski space-time as the limit of finite cyclic lattices, each equipped with the action of a finite quasi-Lorentz group. This construction provides a…
Every spacetime is defined by its metric, the mathematical object which further defines the spacetime curvature. From the relativity principle, we have the freedom to choose which coordinate system to write our metric in. Some coordinate…
We discuss the problem of determining the spacetime structure. We show that when we are using only topological methods the spacetime can be modelled as an R- or Q-compact space although the R-compact spaces seem to be more appropriate.…
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…
We investigate structure that describes physical data in gravitational systems that is, to one degree or another, independent of the metric and affine structure. We dub such structure surplus structure and seek to incorporate it into our…
The structure of the coincidence symmetry group of an arbitrary $n$-dimensional lattice in the $n$-dimensional Euclidean space is considered by describing a set of generators. Particular attention is given to the coincidence isometry…
In this note we discuss the possibility to define a space-time with a DSR based approach. We show that the strategy of defining a non linear realization of the Lorentz symmetry with a consistent vector composition law cannot be reconciled…
The advantages to consider the ordinary space-time as the symplectic rather than pseudo-orthogonal one are indicated, and the consequences of extending this view to extra space/time dimensions are discussed.
We classify simply-connected homogeneous ($D+1$)-dimensional spacetimes for kinematical and aristotelian Lie groups with $D$-dimensional space isotropy for all $D\geq 0$. Besides well-known spacetimes like Minkowski and (anti) de Sitter we…
In this paper we examine various properties/constructions which are known for reductive groups and we do some experiments to see to what extent they generalize to symmetric spaces.
The idea that possible configurations of a physical system can be represented as points in a multidimensional configuration space ${\cal C}$ is explored. The notion of spacetime, without ${\cal C}$, does not exist in this theory. Spacetime…
Lexicographic or first choice constructions of geometric objects sometimes lead to amazingly good results. Usually it is difficult to determine the precise identity of these geometries. Here we find infinitely many cases where the…
It is shown that if a space-time has non-compact Cauchy surface, then its topological, differentiable, and causal structure are completely determined by a class of compact subsets of its Cauchy surface. Since causal structure determines its…
We model quantum space-time on the Planck scale as dynamical networks of elementary relations or time dependent random graphs, the time dependence being an effect of the underlying dynamical network laws. We formulate a kind of geometric…
Authors derive the Lorentz-Einstein transformation for the space-time coordinates starting with a one-space dimension approach. They add to the results the invariance of the space coordinates measured perpendicular to the direction of…
The dimensional structure of space-time is investigated according to physical and mathematical methods. We show that ther are various empirical and theoretical restrictions on the number of independent dimensions of space-time, consequently…
It is argued that a noncommutative geometry of spacetime leads to a reconciliation of electromagnetism and gravitation while providing an underpinning to Weyl's geometry. It also leads to a cosmology consistent with observation. A few other…
A priori, the set of birational transformations of an algebraic variety is just a group. We survey the possible algebraic structures that we may add to it, using in particular parametrised family of birational transformations.
We describe a class of modified gravity theories that deform general relativity in a way that breaks time reversal invariance and, very mildly, locality. The algebra of constraints, local physical degrees of freedom, and their linearized…