Related papers: Combinatorial Spacetimes
It is proposed that gravity may arise in the low energy limit of a model of matter fields defined on a special kind of a dynamical random lattice. Time is discretized into regular intervals, whereas the discretization of space is random and…
In any dimension $D$, the Euclidean Einstein-Hilbert action, which describes gravity in the absence of matter, can be discretized over random discrete spaces obtained by gluing families of polytopes together in all possible ways. In the…
We present a new scheme of defining invariant observables for general relativistic systems. The scheme is based on the introduction of an observer which endowes the construction with a straightforward physical interpretation. The…
In this letter we briefly investigate the mathematical structure of space-time in the framework of discretization. It is shown that the discreteness of space-time may result in a new mechanical system which differ from the usual quantum…
All differences between the role of space and time in nature are explained by proposing the principles in which none of the spacetime coordinates has an {\it a priori} special role. Spacetime is treated as a non-dynamical manifold, with a…
A covariant algorithm for deriving the conserved quantities for natural Hamiltonian systems is combined with the non-relativistic framework of Eisenhart, and of Duval, in which the classical trajectories arise as geodesics in a higher…
Generic models of cosmological inflation and the recently proposed scenarios of a recycling universe and the string theory landscape predict spacetimes whose global geometry is a stochastic, self-similar fractal. To visualize the…
Visualizations such as bar charts, scatter plots, and objects on geographical maps often convey critical information, including exact and relative numeric values, using shapes. The choice of shape and method of encoding information is often…
We examine the fundamental question whether a random discrete structure with the minimal number of restrictions can converge to continuous metric space. We study the geometrical properties such as the dimensionality and the curvature…
In the event symmetric approach to quantum gravity it is assumed that the fundamental laws of physics must be invariant under exchange of any two space-time events. The fact that this symmetry if obviously not observed is attributed to the…
The automorphism group of a one dimensional shift space over a finite alphabet exhibits different types of behavior: for a large class with positive entropy, it contains a rich collection of subgroups, while for many shifts of zero entropy,…
A generalised equivalence principle is put forward according to which space-time symmetries and internal quantum symmetries are indistinguishable before symmetry breaking. Based on this principle, a higher-dimensional extension of Minkowski…
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…
Finite projective (lattice) geometries defined over rings instead of fields have recently been recognized to be of great importance for quantum information theory. We believe that there is much more potential hidden in these geometries to…
In pregeometry a metric arises as a composite object at large distances. We investigate if its signature, which distinguishes between time and space, could be a result of the dynamics rather than being built in already in the formulation of…
Establishing the existence of periodic orbits is one of the crucial and most intricate topics in the study of dynamical systems, and over the years, many methods have been developed to this end. On the other hand, finding closed orbits in…
General relativity does not allow one to specify the topology of space, leaving the possibility that space is multiply rather than simply connected. We review the main mathematical properties of multiply connected spaces, and the different…
We develop a kind of pregeometry consisting of a web of overlapping fuzzy lumps which interact with each other. The individual lumps are understood as certain closely entangled subgraphs (cliques) in a dynamically evolving network which, in…
Spacetime is modelled by binary relations - by the classes of the automorphisms $\GL(\C^2)$ of a complex 2-dimensional vector space with respect to the definite unitary subgroup $\U(2)$. In extension of Feynman propagators for particle…
Diffeomorphism invariance is a feature that gets sometimes highlighted as something with profound implications in the physics of spacetime. Moreover, it is often wrongly associated exclusively with General Relativity. The fact that…