This is a nontechnical introduction to recent work on quantum gravity using ideas from higher-dimensional algebra. We argue that reconciling general relativity with the Standard Model requires a ‘background-free quantum theory with local degrees of freedom propagating causally’. We describe the insights provided by work on topological quantum field theories such as quantum gravity in 3-dimensio...

We measure the spectral dimension of universes emerging from nonperturbative quantum gravity, defined through state sums of causal triangulated geometries. While four-dimensional on large scales, the quantum universe appears two-dimensional at short distances. We conclude that quantum gravity may be “selfrenormalizing” at the Planck scale, by virtue of a mechanism of dynamical dimensional reduc...

For a 1+1 dimensional theory of gravity with torsion different approaches to the formulation of a quantum theory are presented. They are shown to lead to the same finite dimensional quantum system. Conceptual questions of quantum gravity like e.g. the problem of time are discussed in this framework. Vienna, November 1992 e-mail: [email protected] e-mail: [email protected]

The two dimensional substructure of general relativity and gravity, and the two dimensional geometry of quantum effect by black hole are disclosed. Then the canonical quantization of the two dimensional theory of gravity is performed. It is shown that the resulting uncertainty relations can explain black hole quantum effects. A quantum gravitational length is also derived which can clarify the ...

1. Introduction Certain difficulties associated with any theory of quantum gravity stem from the different mathematical framing of our gravity and quantum theories. While general relativity is based on a real, deterministic, differentiable manifold structure, the elements of quantum theory are complex-valued and probabilistic. Consider two ways to reconcile these differences by placing one of t...

The theory of gravity without free gravitational fields is considered. It is assumed that gravitational radiation is some hypothetical matter fields. Gravitational emission is a process of the decay of proton into hypothetical matter fields at the Planck scale. In the Einstein theory of gravity [1] with the Lagrangian L = − 1 16πG √ gR, (1) gravitational field is defined by the components of th...

This is a nontechnical introduction to recent work on quantum gravity using ideas from higher-dimensional algebra. We argue that reconciling general relativity with the Standard Model requires a ‘background-free quantum theory with local degrees of freedom propagating causally’. We describe the insights provided by work on topological quantum field theories such as quantum gravity in 3-dimensio...

We investigate the critical behaviour of both matter and geometry of the threestate Potts model coupled to two-dimensional Lorentzian quantum gravity in the framework of causal dynamical triangulations. Contrary to what general arguments on the effects of disorder suggest, we find strong numerical evidence that the critical exponents of the matter are not changed under the influence of quantum ...

While observational cosmology has recently progressed fast, it revealed a serious dilemma called dark energy: an unknown source of exotic energy with negative pressure driving a current accelerating phase of the universe. All attempts so far to find a convincing theoretical explanation have failed, so that one of the last hopes is the yet to be developed quantum theory of gravity. In this artic...