Quantum Gravity and the Past Hypothesis

In canonical quantum gravity, the quantum state of matter and geometry does not depend on an external notion of time. In fact, there is no classical causal structure in the theory. In contrast, our observations patently discern a classical, directed time - many phenomena occur in an effectively irreversible order. We review how a boundary condition for the timeless quantum state in configuration space could reconcile the quantum theory with the classical arrow of time, leading to a state of low entanglement entropy in the regime where a classical notion of time emerges and probabilities are conserved.