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A set of diverse but mutually consistent results obtained in different settings has spawned a new view of loop quantum gravity and its physical implications, based on the interplay of operator calculations and effective theory: Quantum…

The idea that the Universe is a program in a giant quantum computer is both fascinating and suffers from various problems. Nonetheless, it can provide a unified picture of physics and this can be very useful for the problem of Quantum…

Contemporary research programs in fundamental physics appear to suggest that there could be two (physical) times---or none at all. This essay articulates these possibilities in the context of quantum gravity, and in particular of…

I would like to consider the Beginning of space-time in this paper. First of all, we do consideration historical thought. A lot of philosophers have considered the relation between this real phenomenal world and the basic world in which the…

The issues related to bringing together the principles of general relativity and quantum theory are discussed. After briefly summarising the points of conflict between the two formalisms I focus on four specific themes in which some contact…

This is an introductory set of lecture notes on quantum cosmology, given in 1995 to an audience with interests ranging from astronomy to particle physics. Topics covered: 1. Introduction: 1.1 Quantum cosmology and quantum gravity; 1.2 A…

We highlight the general notion of a relative quantum field theory, which occurs in several contexts. One is in gauge theory based on a compact Lie algebra, rather than a compact Lie group. This is relevant to the maximal superconformal…

We present a bird's-eye survey on the development of fundamental ideas of quantum gravity, placing emphasis on perturbative approaches, string theory, loop quantum gravity, and black hole thermodynamics. The early ideas at the dawn of…

The scope of this review is to give a pedagogical introduction to some new calculations and methods developed by the author in the context of quantum groups and their applications. The review is self- contained and serves as a "first aid…

Quantizing the gravitational field described by General relativity being a notorious difficult, unsolved and maybe meaningless problem I use in this essay a different strategy: I consider a linear theory in the framework of Special…

In a purely relational theory there exists a tension between the relational character of the theory and the existence of quantities like distance and duration. We review this issue in the context of the Leibniz-Clarke correspondence. We…

We provide a minimal, self-contained introduction to the covariant DFR flat quantum spacetime, and to some partial results for the corresponding quantum field theory. Explicit equations are given in the Dirac notation.

A fascinating and deep question about nature is what one would see if one could probe space and time at smaller and smaller distances. Already the 19th-century founders of modern geometry contemplated the possibility that a piece of empty…

In quantum gravity space and time lose their status as fundamental parts of the physical reality. However, according to Kant, space and time are the a priori conditions of our experience. Does Kantian characterization of these notions give…

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…

The it Global Time Theory (GTT) is the further development of the General Relativity (GR). GTT significantly differs from GR in the general physical concepts, but retains 90% of the mathematical structure and main results. The dynamics…

I review the present theoretical attempts to understand the quantum properties of spacetime. In particular, I illustrate the main achievements and the main difficulties in: string theory, loop quantum gravity, discrete quantum gravity…

This paper constitutes a background to the paper 'Quantum mechanics as "space-time statistical mechanics"?', arXiv:quant-ph/0501133, presented previously by the author. But it is also a free-standing and self-contained paper. The purpose of…

Usual quantum mechanics requires a fixed, background, spacetime geometry and its associated causal structure. A generalization of the usual theory may therefore be needed at the Planck scale for quantum theories of gravity in which…

Following a line of research that I have developed for several years, I argue that the best strategy for understanding quantum gravity is to build a picture of the physical world where the notion of time plays no role. I summarize here this…