Phenomenological Quantum Gravity

Abstract

Abstract. These notes summarize a set of lectures on phenomenological quantum gravity which one of us delivered and the other attended with great diligence. They cover an assortment of topics on the border between theoretical quantum gravity and observational anomalies. Specifically, we review non-linear relativity in its relation to loop quantum gravity and high energy cosmic rays. Although we follow a pedagogic approach we include an open section on unsolved problems, presented as exercises for the student. We also review varying constant models: the Brans-Dicke theory, the Bekenstein varying α model, and several more radical ideas. We show how they make contact with strange high-redshift data, and perhaps other cosmological puzzles. We conclude with a few remaining observational puzzles which have failed to make contact with quantum gravity, but who knows... We would like to thank Mario Novello for organizing an excellent school in Mangaratiba, in direct competition with a very fine beach indeed. WHY QUANTUM GRAVITY?The subject of quantum gravity emerged as part of the unification program that led to electromagnetism and the electroweak model. We'd like to unify all forces of Nature. Forces other than gravity are certainly of a quantum nature. Thus we cannot hope to have a fully unified theory before quantizing gravity.To come clean about it right from the start, we should stress that there is no compelling experimental reason for quantizing gravity. For all we know, gravity could stand alone with respect to all other forces, and simply be exactly classical in all regimes. There is no evidence at all that the gravitational field ever becomes quantum 1 . Yet this hasn't deterred a large number of physicists from devoting lifetimes to this pursuit.Assaults on the problem currently follow two main trends: string/M theory [1, 2] and loop quantum gravity [3,4]. Both have merits and deficiencies, commented extensively elsewhere. As a poor third we mention Regge-calculus (and lattice techniques), non-commutative geometry, and several other methods none of which has fared better or worse than the two main strands.This course is not about those theories. Rather it's about the question: Where might experiment fit into these theoretical efforts of quantizing gravity? A middle ground has recently emerged -phenomenological quantum gravity. The requirements are simple: a phenomenological formalism must provide a believable approximation limit for more sophisticated approaches; it must also make clear contact with experimental anomalies that don't fit into our current understanding of the world. The following argument illustrates what we mean by this.When physicists find themselves at a loss they often turn to dimensional analysis. Following this simplistic philosophy we estimate the scales where quantum gravity effects may become relevant by building quantities with dimensions of energy, length and time fromh (the quantum), c (relativity) and G (gravity). These are called the Planck energy E P , the Planck length l P and t...