The causal set approach to Quantum Gravity

Abstract

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 theory. Motivation, results and open problems are discussed and some comparisons to other approaches are made. Some recent progress on recovering locality in causal sets is recounted. On the occasion of his 60th birthday, this article is dedicated to Rafael Sorkin, without whom the causal set idea would not have survived its infancy.How can we reach a theory of quantum gravity? Many answers to this question have been proposed, motivated by different experiences and views of current theories [1]. A more specific set of questions might be: what demands should we put on our framework, so that it is best able to meet all the challenges involved in creating a theory of quantum gravity? What choices are most likely to give the correct theory, according to the clues we have from known physics? Are there any problems with our initial assumptions that may lead to trouble further down the road? The latter seems to be one of the most important strategic questions when beginning to formulate a candidate theory. For example, can a canonical approach overcome the multifaceted problem of time? And how far can a theory based on a fixed background spacetime be pushed? On the one hand, these questions may only be answered in the very attempt to formulate the theory. On the other, many such attempts have been made, and now that quantum gravity research has built up some history, perhaps it is time to plough some of the experience gained back into a new approach, laying the groundwork for our theory in such a way as to avoid well-known problems. The causal set program [2,3,4,5,6] represents such an attempt.In this review, some answers to the above questions, as embodied by the causal set program, are set out and explained, and some of their consequences are given. As part of this, the results and open problems in the program are discussed. In section 1, reasons for hypothesising spacetime discreteness are reviewed. The definition of a causal set is given, along with the proposed correspondence principle between this structure and the effective continuum description of spacetime. Then some of the unique features of this discretisation scheme are discussed. In section 2, ideas for causal set dynamics are given. Next, a review is made of some phenomenological models based on this quantum gravity program, and successes and challenges in this line of work are summarised. The final section deals with the issue of recovering locality for causal sets, something which touches

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