Related papers: Classical Spacetime Structure
This paper explores the status of some notions which are usually associated to time, like datations, chronology, durations, causality, cosmic time and time functions in the Einsteinian relativistic theories. It shows how, even if some of…
A method has been recently proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example a version of quantized space-time is considered here. It is found that there is a…
In this review, we present some fundamental classical and quantum phenomena in view of time fractional formalism. Time fractional formalism is a very useful tool in describing systems with memory and delay. We hope that this study can…
Under normal circumstances most members of the general relativity community focus almost exclusively on the local properties of spacetime, such as the locally Euclidean structure of the manifold and the Lorentzian signature of the metric…
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…
The full causal ladder of spacetimes is constructed, and their updated main properties are developed. Old concepts and alternative definitions of each level of the ladder are revisited, with emphasis in minimum hypotheses. The implications…
The concept of the space-time as emerging in the world phase transition, vs. a priori existing, is put forward. The theory of gravity with two basic symmetries, the global affine one and the general covariance, is developed. Implications…
Collapse models possibly suggest the need for a better understanding of the structure of space-time. We argue that physical space, and space-time, are emergent features of the Universe, which arise as a result of dynamical collapse of the…
These lecture notes provide an overview of different aspects of de Sitter space and their plausible holographic interpretations. We start with a general description of the classical spacetime. We note the existence of a cosmological horizon…
When compared to quantum mechanics, classical mechanics is often depicted in a specific metaphysical flavour: spatio-temporal realism or a Newtonian "background" is presented as an intrinsic fundamental classical presumption. However, the…
A brief review about the Newman-Penrose formalism and the asymptotic structure of the spacetime is given. The goal of this review is to describe the latest developments in these topics and make a summary of the most important articles…
I present the theoretical evidence which suggests that gravity is an emergent phenomenon like gas dynamics or elasticity with the gravitational field equations having the same status as, say, the equations of fluid dynamics/elasticity. This…
This book is dedicated to Grassmannians associated with buildings of classical types: usual, polar, and half-spin Grassmannians. Grassmannians of vector spaces and Grassmannians consisting of totally isotropic subspaces of non-degenerate…
I propose that Physics should be formulated using minimal mathematical structure, beginning with its foundational arena: spacetime. This paper opens with a concise overview of several research directions explored in previous work. Among…
The formulation of General Relativity in which the 4-dimensional space-time is embedded in a flat host space of higher dimension is reconsidered. New classes of embeddings (modeled after Nash's classical free embeddings) are introduced.…
This essay presents an accessible introduction to the basic motivations to seek a quantum theory of gravity. It focuses on one approach- loop quantum gravity - as an example of the rich philosophical issues that arise when we try to combine…
This work presents instructive, yet comprehensive derivation of quantized gravity theories in relativistic, classical, and semi-classical spacetime structure based on the Poincar\'e, Galilean, and Bargmann algebra, respectively. The…
The concept of the space-time as emerging in the world phase transition, vs. a priori exiting, is put forward. The theory of gravity with two basic symmetries, the global affine one and the general covariance, is developed. Implications for…
An introduction is given to discussions on the possiblity of fabricating spacetime geometries allowing time-travel scenarios with the help of matter possessing typically quantum features. Those scenarios are considered in the framework of…
Which geometries on a smooth manifold (apart from Lorentzian metrics) can serve as a spacetime structure? This question is comprehensively addressed from first principles in eight lectures, exploring the kinematics and gravitational…