Dimensional reduction in causal set gravity

Counting entropy in causal set quantum gravity

The finiteness of black hole entropy suggest that spacetime is fundamentally discrete, and hints at an underlying relationship between geometry and ”information”. The foundation of this relationship is yet to be uncovered, but should manifest itself in a theory of quantum gravity. We review recent attempts to define a microscopic measure for black hole entropy and for the maximum entropy of sph...

Gravity and matter in causal set theory

The goal of this paper is to propose an approach to the formulation of dynamics for causal sets and coupled matter fields. We start from the continuum version of the action for a Klein-Gordon field coupled to gravity, and rewrite it first using quantities that have a direct correspondent in the case of a causal set, namely volumes, causal relations, and timelike lengths, as variables to describ...

The Causal Set Approach to Quantum Gravity

The causal set approach to quantum gravity

The ideas of spacetime discreteness and causality are important in several of the popular approaches to quantum gravity. But if discreteness is accepted as an initial assumption, conflict with Lorentz invariance can be a consequence. The causal set is a discrete structure which avoids this problem and provides a possible history space on which to build a “path integral” type quantum gravity the...

Dimensional Reduction in Quantum Gravity

The requirement that physical phenomena associated with gravitational collapse should be duly reconciled with the postulates of quantum mechanics implies that at a Planckian scale our world is not 3+1 dimensional. Rather, the observable degrees of freedom can best be described as if they were Boolean variables defined on a two-dimensional lattice, evolving with time. This observation, deduced f...