Related papers: Mathematical Structure of Discrete Space-time
We strengthen the case that the new logical perspective afforded by topos theory is suitable to the task of describing the physical world around us. In exploring some of the aspects of construction of a simple quantum-mechanical system in a…
With the theory of special relativity, time has been linked with space into a four-dimensional space-time from which a basic question must be asked: can space be really transformed into time and vice-versa? The response is affirmative if…
I propose a version of quantum mechanics featuring a discrete and finite number of states that is plausibly a model of the real world. The model is based on standard unitary quantum theory of a closed system with a finite-dimensional…
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…
Alternative approaches to the study of the quantum-gravity problem are handling the role of spacetime very differently. Some are focusing on the analysis of one or another novel formulation of "empty spacetime", postponing to later stages…
Starting from the hypothesis that both physics, in particular space-time and the physical vacuum, and the corresponding mathematics are discrete on the Planck scale we develop a certain framework in form of a '{\it cellular network}'…
We present a brief review of discrete structures in a finite Hilbert space, relevant for the theory of quantum information. Unitary operator bases, mutually unbiased bases, Clifford group and stabilizer states, discrete Wigner function,…
We show that the geometric structure of an arbitrary relativistic spacetime can be determined by the transformation groups associated with a collection of privileged coordinate systems.
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…
This paper is part of a program to combine a staggered time and staggered spatial discretization of continuum wave equations so that important properties of the continuum that are proved using vector calculus can be proven in an analogous…
A class of simplified measures is constructed to capture the key features of generic spatio-temporally chaotic systems. A combined analytical and numerical investigation allows us to extablish the scaling beahviour of the fractal dimension…
We apply the ``consistent discretization'' approach to general relativity leaving the spatial slices continuous. The resulting theory is free of the diffeomorphism and Hamiltonian constraints, but one can impose the diffeomorphism…
In the present paper, a discrete differential calculus is introduced and used to describe dynamical systems over arbitrary graphs. The discretization of space and time allows the derivation of Heisenberg-like uncertainty inequalities and of…
Recent progress in quantum gravity and string theory has raised interest among scientists to whether or not nature behaves discretely at the Planck scale. There are two attitudes twoards this discretenes i.e. top-down and bottom-up…
Over the last decade a growing number of quantum-gravity researchers has been looking for opportunities for the first ever experimental evidence of a Planck-length quantum property of spacetime. These studies are usually based on the…
The rules of quantum mechanics require a time coordinate for their formulation. However, a notion of time is in general possible only when a classical spacetime geometry exists. Such a geometry is itself produced by classical matter…
We review an approach to non-commutative geometry, where models are constructed by quantisation of the coordinates. In particular we focus on the full DFR model and its irreducible components; the (arbitrary) restriction to a particular…
We introduce a revised de Broglie relation in discrete space-time, and analyze some possible inferences of the relation.
The nonadiabatic geometric phase in a time dependent quantum evolution is shown to provide an intrinsic concept of time having dual properties relative to the external time. A nontrivial extension of the ordinary quantum mechanics is thus…
In this paper, we demonstrate how space-time is, rather than a differentiable manifold, a Random Heap, and how this ties up with fractal dimension 2 of a Quantum Mechanical path. In this light, we can see that there is a harmonious…