Wave equations onq-Minkowski space

We give a systematic account of a component approach to the algebra of forms onq-Minkowski space, introducing the corresponding exterior derivative, Hodge star operator, coderivative, Laplace-Beltrami operator and Lie-derivative. Using this (braided) differential geometry, we then give a detailed exposition of theq-d'Alembert andq-Maxwell equation and discuss some of their non-trivial properties, such as for instance, plane wave solutions. For theq-Maxwell field, we also give aq-spinor analysis of theq-field strength tensor.     

Why do clocks tick?

Drawing on recent developments in the matrix model approach to string theory and the causal set program for quantum gravity we address the question of the origin of time as one aspect of the phase transition from a topological quantum field theory to a quantum theory of gravity. We construct a model with two phases which can be interpreted as containing clocks which either do not tick or tick exactly once. This demonstrates that while a theory based on causal sets may appear to have inherent notions of time and causality, the existence of a phase transition means, that as Saint Augustine wrote in hisConfessions, the time, if such we may call it, when there was no time was not time at all.Received an Honorable Mention in the 1992 Gravity Research Foundation Essay Contest—Ed.