Approaches to Quantum Gravity

New directions in background independent Quantum Gravity 143that this mathematics contains no reference to any background spacetime that thequantum systems may live in and hence it is an example of BI-I.In the past two years, a number of BI-I systems have been put forward: Dreyer’sinternal relativity ([8] and Dreyer, this volume), Lloyd’s computational universe[19], emergent particles from a QCH [16] and Quantum Graphity [14]. All of thesecan be easily written as a QCH (with a single Ɣ and no geometric informationon the state spaces, hence BI-I), so we shall continue the discussion in the moregeneral terms of a pre-geometric QCH, just as it was defined in section 9.2.9.6.1 The geometrogenesis pictureLet us consider a simple scenario of what we may expect to happen in a BI theorywith a good low energy limit. It is a factor of about 20 orders of magnitude fromthe physics of the Planck scale described by the microscopic theory to the standardsubatomic physics. By analogy with all other physical systems we know, it is reasonableto expect that physics at the two scales decouples to a good approximation.We can expect at least one phase transition interpolating between the microscopicBI phase and the familiar one in which we see dynamical geometry. We shall usethe word geometrogenesis for this phase transition.This picture implements the idea that spacetime geometry is a derivative conceptand only applies in an approximate emergent level. More specifically, this isconsistent with the relational principle that spatial and temporal distances are tobe defined internally, by observers inside the system. This is the physical principlethat led Einstein to special and General Relativity. The geometrogenesis pictureimplies that the observers (subsystems), as well as any excitations that they mayuse to define such spatiotemporal measures, are only applicable at the emergentgeometric phase.The breakthrough realization ([8] and Dreyer, this volume, [19]) is that theinferred geometry will necessarily be dynamical, since the dynamics of the underlyingsystem will be reflected in the geometric description. This is most clearlystated by Dreyer who observes that since the same excitations of the underlyingsystem (characterizing the geometrogenesis phase transition) and their interactionswill be used to define both the geometry and the energy-momentum tensor T μν .This leads to the following Conjecture on the role of General Relativity.If the assignment of geometry and T μν from the same excitations and interactions is doneconsistently, the geometry and T μν will not be independent but will satisfy Einstein’sequations as identities.What is being questioned here is the separation of physical degrees of freedominto matter and gravitational ones. In theories with a fixed background, such as