Scientific Series

The causal set -- mathematically a finitary partial order -- is a candidate discrete substratum for spacetime. I will introduce this idea and describe some aspects of causal set kinematics, dynamics, and phenomenology, including, as time permits, a notion of fractal dimension, a (classical) dynamics of stochastic growth, and an idea for explaining some of the puzzling large numbers of cosmology. I will also mention some general insights that have emerged from the study of causal sets, the most recent one concerning the role of intermediate length-scales in discrete spacetime theories.

We point out that there exit operators, having a clear meaning in cosmology -- they select a given realization of the distribution of primordial density fluctuations --, which can violate Bell inequalities when evaluated in the ''standard'' inflationary quantum distribution. We then consider density matrices which describe partially decohered distributions and show how the importance of the violation decreases with the decoherence level. We determine the critical level beyond which no violation can be obtained. We argue that the corresponding density matrix is the quantum version of the stochastic ensemble used in numerical codes, and consisting of growing modes with random amplitudes.