2 research outputs found
Disordered locality in loop quantum gravity states
We show that loop quantum gravity suffers from a potential problem with
non-locality, coming from a mismatch between micro-locality, as defined by the
combinatorial structures of their microscopic states, and macro-locality,
defined by the metric which emerges from the low energy limit. As a result, the
low energy limit may suffer from a disordered locality characterized by
identifications of far away points. We argue that if such defects in locality
are rare enough they will be difficult to detect.Comment: 11 pages, 4 figures, revision with extended discussion of result
Evolution in Quantum Causal Histories
We provide a precise definition and analysis of quantum causal histories
(QCH). A QCH consists of a discrete, locally finite, causal pre-spacetime with
matrix algebras encoding the quantum structure at each event. The evolution of
quantum states and observables is described by completely positive maps between
the algebras at causally related events. We show that this local description of
evolution is sufficient and that unitary evolution can be recovered wherever it
should actually be expected. This formalism may describe a quantum cosmology
without an assumption of global hyperbolicity; it is thus more general than the
Wheeler-DeWitt approach. The structure of a QCH is also closely related to
quantum information theory and algebraic quantum field theory on a causal set.Comment: 20 pages. 8 figures. (v3: minor corrections, additional references
[2,3]) to appear in CQ