Causal Set Approach to Discrete Quantum Gravity
Causal set approach, Discrete quantum gravity, Quantum sequential growth process
We begin by describing a sequential growth model in which the universe grows one element at a time in discrete time steps. At each step, the process has the form of a causal set and the “completed” universe is given by a path consisting of a discretely growing chain of causal sets. We then introduce a quantum dynamics to obtain a quantum sequential growth process (QSGP) which may lead to a viable model for discrete quantum gravity. A discrete version of Einstein’s field equation is derived and a definition for discrete geodesics is proposed. A type of QSGP called an amplitude process is introduced. An example of an amplitude process called a complex percolation process is studied. This process conforms with general principles of causality and covariance. We end with some detailed quantum measure calculations for a specific percolation constant.
Gudder, S. (2012). Causal set approach to discrete quantum gravity. Mathematics Preprint Series. Retrieved from https://digitalcommons.du.edu/math_preprints/29