Arrows of Time in the Bouncing Universes of the No-boundary Quantum
  State
  We derive the arrows of time of our universe that follow from the no-boundary
theory of its quantum state (NBWF) in a minisuperspace model. Arrows of time
are viewed four-dimensionally as properties of the four-dimensional Lorentzian
histories of the universe. Probabilities for these histories are predicted by
the NBWF. For histories with a regular `bounce' at a minimum radius we find
that fluctuations are small at the bounce and grow in the direction of
expansion on either side. For recollapsing classical histories with big bang
and big crunch singularities we find that the fluctuations are small near one
singularity and grow through the expansion and recontraction to the other
singularity. The arrow of time defined by the growth in fluctuations thus
points in one direction over the whole of a recollapsing spacetime but is
bidirectional in a bouncing spacetime. We argue that the electromagnetic,
thermodynamic, and psychological arrows of time are aligned with the
fluctuation arrow. The implications of a bidirectional arrow of time for
causality are discussed.
