Related papers: Local and Global Properties of the World
A model unifying general relativity with quantum mechanics is further developed. It is based on a noncommutative geometry which supposedly modelled the universe in its pre-Planckian epoch. The geometry is totally nonlocal with no time and…
The experimental results that test Bell's inequality have found strong evidence suggesting that there are nonlocal aspects in nature. Evidently, these nonlocal effects, which concern spacelike separated regions, create an enormous tension…
A comprehensive physical theory explains all aspects of the physical universe, including quantum aspects, classical aspects, relativistic aspects, their relationships, and unification. The central nonlocality principle leads to a nonlocal…
Non commutative geometry is creating new possibilities for physics. Quantum spacetime geometry and post inflationary models of the universe with matter creation have an enormous range of scales of time, distance and energy in between. There…
Close to the Planck energy scale, the quantum nature of space-time reveals itself and all forces, including gravity, should be unified so that all interactions correspond to just one underlying symmetry. In the absence of a full quantum…
A framework which combines ideas from Connes' noncommutative geometry, or spectral geometry, with recent ideas on generally covariant quantum field theory, is proposed in the present work. A certain type of spectral geometries modelling…
A century after the advent of Quantum Mechanics and General Relativity, both theories enjoy incredible empirical success, constituting the cornerstones of modern physics. Yet, paradoxically, they suffer from deep-rooted, so-far intractable,…
Noncommutative geometry, in its many incarnations, appears at the crossroad of various researches in theoretical and mathematical physics: from models of quantum space-time (with or without breaking of Lorentz symmetry) to loop gravity and…
The Special Theory of Relativity and Quantum Mechanics merge in the key principle of Quantum Field Theory, the Principle of Locality. We review some examples of its ``unreasonable effectiveness'' (which shows up best in the formulation of…
With the two most profound conceptual revolutions of XXth century physics, quantum mechanics and relativity, which have culminated into relativistic spacetime geometry and quantum gauge field theory as the principles for gravity and the…
We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…
All existing experimental results are currently interpreted using classical geometry. However, there are theoretical reasons to suspect that at a deeper level, geometry emerges as an approximate macroscopic behavior of a quantum system at…
The conflict between the locality of general relativity, reflected in its space-time description, and the non-locality of quantum mechanics, contained in its Hilbert space description, is discussed. Gauge covariant non-local observables…
We give an overview of the applications of noncommutative geometry to physics. Our focus is entirely on the conceptual ideas, rather than on the underlying technicalities. Starting historically from the Heisenberg relations, we will explain…
In recent years, many new developments in theoretical physics, and in practical applications rely on different techniques of noncommutative algebras. In this review, we introduce the basic concepts and techniques of noncommutative physics…
Together with collaborators, we introduced a noncommutative Riemannian geometry over Moyal algebras and systematically developed it for noncommutative spaces embedded in higher dimensions in the last few years. The theory was applied to…
This is a research announcement on what is best termed `nonlocal' methods in mathematics. (This is not to be confused with global analysis.) The nonlocal formulation of physics in \cite{principia} points to a fresh viewpoint in mathematics:…
The Standard Model of the elementary particles is controlled by more than 20 parameters, of which it is not known today how they can be linked to deeper principles. Any attempt to clean up this theory, in general results in producing more…
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…
This is a brief review where some basic elements of non-commutative geometry are given. The rules and ingredients that enter in the construction of the standard model and grand unification models in non-commutative geometry are summarized.…