Related papers: What `shape' is space-time?
A literature review of related articles, either by affinity or by contrast, to a fundamental theory of time and space - time previously developed. It shows how from a primitive concept of preparticle and membership relation of set theory,…
We consider the geometry of spacetime based on a non-metric, Finslerian, length measure, which, in terms of physics, represents a generalized clock. Our defnition of Finsler spacetimes ensure a well defined notion of causality, a precise…
The conflict between quantum theory and the theory of relativity is exemplified in their treatment of time. We examine the ways in which their conceptions differ, and describe a semiclassical clock model combining elements of both theories.…
What is the shape of the Universe? Is it curved or flat, finite or infinite ? Is space "wrapped around" to create ghost images of faraway cosmic sources? We review how tessellations allow to build multiply-connected 3D Riemannian spaces…
Several examples are used to illustrate how we deal cavalierly with infinities and unphysical systems in physics. Upon examining these examples in the context of infinities from Cantor's theory of transfinite numbers, the only known…
We develop the spectral point of view on geometry based on the formalism of quantum physics. We start from the simple physical question of specifying our position in space and explain how the spectral geometric point of view provides a new…
We present the case for a fundamentally discrete quantum spacetime and for Group Field Theories as a candidate consistent description of it, briefly reviewing the key properties of the GFT formalism. We then argue that the outstanding…
We discuss the distinction between the notion of partial observable and the notion of complete observable. Mixing up the two is frequently a source of confusion. The distinction bears on several issues related to observability, such as (i)…
Inspired by the work of Wheeler among others, we have studied the problem of quantum measurements of space-time distances by applying the general principles of quantum mechanics as well as those of general relativity. Contrary to the…
The difficulties with the measurability of classical space-time distances are considered. We outline the framework of quantum deformations of D=4 space-time symmetries with dimensionfull deformation parameter, and present some recent…
Based on the concept of curved spacetime in Einsteinian General Relativity, the field theories and their quantum theories in the curved octonion spaces etc are discussed. The research results discover the close relationships of the curved…
The notion of "reference frame" is a central theoretical construct for interpreting the physical implications of spacetime diffeomorphism invariance in General Relativity. However, the alternative formulation of classical General Relativity…
I propose a general geometric framework in which to discuss the existence of time observables. This frameworks allows one to describe a local sense in which time observables always exist, and a global sense in which they can sometimes exist…
The space rotation invariance hypothesis is examined. The basic space-time properties and the physical object description from this point of view are considered. An $\omega$-invariance as an approximation of the space rotation invariance…
For many years now it has become conventional for theorists to argue that "space-time is doomed", with the difficulties in finding a quantum theory of gravity implying the necessity of basing a fundamental theory on something quite…
We provide five rearticulations of the thesis that the structure of spacetime is conventional, rather than empirically determined, based upon variation of the structures that are empirically underdetermined and modal contexts in which this…
The classical spacetime is usually described by a differentiable manifold with infinitely many degrees of freedom. Occasionally though, it is useful to consider an approximation whose number of degrees of freedom is finite. There are…
A new kind of duality between the deep structures of spacetime and matter is proposed here, considering two partial orders which incorporate causality, extensity, and discreteness. This may have surprising consequences for the emergence of…
Time is absolute in standard quantum theory and dynamical in general relativity. The combination of both theories into a theory of quantum gravity leads therefore to a "problem of time". In my essay I shall investigate those consequences…
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…