  We describe how general covariance for QFT defined on a space-time background
with horizons leads to the need of adding an extra quantum degree of freedom.
The definition of traces and entropies involves the use of a formally thermal
state (weight) on the algebra of observables of the added degree of freedom.
This extra degree of freedom is promoted into a physical clock after defining
an hermitian and positive clock Hamiltonian. The so modified weight can be used
to associate to both dS and the BH a type $II_1$ factor and a finite trace. The
Murray-von Neumann dimension ( coupling constant) for this type $II_1$
description of the black hole naturally produces an algebraic version of Page's
curve.
