  Using the HPO approach to consistent histories we re-derive Unruh's result
that an observer constantly accelerating through the Minkowski vacuum appears
to be immersed in a thermal bath. We show that propositions about any symmetry
of the system always form a consistent set and that the probabilities
associated with such propositions are decided by their value in the initial
state. We use this fact to postulate a condition on the decoherence functional
in the HPO set-up. Finally we show that the Unruh effect arises from the fact
that the initial density matrix corresponding to the inertial vacuum can be
written as a thermal density matrix in the Fock basis associated with the
accelerating observer.
