Related papers: On Space's Topology
"Quantum Topology" deals with the general quantum theory as the theory of the functional quantum space; space time and energy momentum forms form a connected manifold; a functional quantum space on the quantum level. The general quantum…
Spacetime dualities arise whenever two theories -- despite being structurally equivalent in some sense -- seemingly provide us with two radically different spatiotemporal descriptions of the world. This often involves radical differences in…
The gauge symmetry of classical general relativity under space-time diffeomorphisms implies that any path integral quantization which can be interpreted as a sum over space-time geometries, gives rise to a formal invariant of smooth…
It is shown that cosmological spacetime manifold has the structure of a Lie group and a spinor space. This leads naturally to the Minkowski metric on tangent spaces and the Lorentzian metric on the manifold and makes it possible to dispense…
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 holistic view of the cosmological appearance and development of space is obtained by studying space as a spherically closed surface of a 4-sphere in a zero energy balance between motion and gravitation. Such an approach re-establishes…
This article explores the overall geometric manner in which human beings make sense of the world around them by means of their physical theories; in particular, in what are nowadays called pregeometric pictures of Nature. In these, the…
The 4-dimensional space-time is extended to pseudo-complex coordinates. Proposing the standard quantization rules in this extended space, the ones for the 4-dimensional sub-space acquire, as one solution, the commutation relations with…
The tangent hyperplanes of the "manifolds" of this paper equipped a so-called Minkowski product. It is neither symmetric nor bilinear. We give a method to handing such an object as a locally hypersurface of a generalized space-time model…
The purpose of this paper is to survey the possible topologies of branching space-times, and, in particular, to refute the popular notion in the literature that a branching space-time requires a non-Hausdorff topology.
We describe how a physical theory incorporating the properties of fields deriving from extra-dimensional structures over a four-dimensional spacetime manifold can in principle be obtained through the analysis of a simple initial structure…
Piecewise Euclidean structures (identified solid Euclidean polyhedra) on topological 3-dimensional manifolds and pseudo-manifolds are constructed so that they admit pseudo-foliations, a generalized type of foliation. The construction of…
Space-times which allow a slicing into homogeneous spatial hypersurfaces generalize the usual Bianchi models. One knows already that in these models the Bianchi type may change with time. Here we show which of the changes really appear. To…
There are many spacetime geometries in general relativity which contain closed timelike curves. A layperson might say that retrograde time travel is possible in such spacetimes. To date no one has discovered a spacetime geometry which…
It is shown that properties of a discrete space-time geometry distinguish from properties of the Riemannian space-time geometry. The discrete geometry is a physical geometry, which is described completely by the world function. The discrete…
Spacetime, understood as a globally hyperbolic manifold, may be characterized by spectral data using a 3+1 splitting into space and time, a description of space by spectral triples and by employing causal relationships, as proposed earlier.…
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…
Space-time in quantum mechanics is about bridging Hilbert and configuration space. Thereby, an entirely new perspective is obtained by replacing the Newtonian space-time theater with the image of a presumably high-dimensional Hilbert space,…
The aim of this contribution is to provide a short introduction to recently investigated models in which our accessible universe is a four-dimensional submanifold, or brane, embedded in a higher dimensional spacetime and ordinary matter is…
A new theory of fundamental physics is presented; it predicts that the new dimensions that may be observed by the Large Hadron Collider are timelike.