Modelling the Decoherence of Spacetime

The question of whether unobserved short-wavelength modes of the gravitational field can induce decoherence in the long-wavelength modes (“the decoherence of spacetime”) is addressed using a simplified model of perturbative general relativity, in which the metric is assumed to be conformally flat and the quantity of interest is the deviation from unity of some power of the conformal factor. For some long-wavelength coarse grainings, the Feynman-Vernon influence phase is found to be effective at suppressing the off-diagonal elements of the decoherence functional. The requirement that the shortwavelength modes be in a sufficiently high-temperature state places limits on the applicability of this perturbative approach.