  The idea that asymptotic de Sitter space can be described by a finite Hilbert
Space implies that any quantum measurement has an irreducible innacuracy. We
argue that this prevents any measurement from verifying the existence of the
Poincare recurrences that occur in the mathematical formulation of quantum de
Sitter (dS) space. It also implies that the mathematical quantum theory of dS
space is not unique. There will be many different Hamiltonians, which give the
same results, within the uncertainty in all possible measurements.
