The standard model of accelerating expansion is successful in matching parameters to observation, but substantial observational problems with both CDM and MOND are now well reported in the literature. While there is no true reconciliation between general relativity and quantum mechanics, science should remain open to the prospect that these phenomena may have some deep underlying reason in new physics. This paper investigates the empirical implications of an extension to general relativity which applies to evolution in quantum theory. Standard general relativity and quantum mechanics are assumed, but light from distant astronomical objects treated quantum mechanically, as photons. A class of coordinate systems is found for Friedmann Cosmologies with local gravity such that it is possible to formulate quantum theory over astronomical and cosmological distances. When light from distant objects is treated as a quantum motion, new predictions are found for cosmological redshift and lensing. Good agreement is found between predictions and supernova redshifts for a closed Friedmann Cosmology with no cosmological constant and expanding at half the rate of the standard model. A previously unmodelled component of cosmological redshift accounts for the anomalous Pioneer blueshift, and for the flattening of galaxy rotation curves simulating a MONDian law and finding a value for the critical MOND acceleration in agreement with observation. Distant lenses have a quarter of the mass required by standard general relativity. Missing mass can be accounted by a massive neutrino. CDM is not required. The paper is http://arxiv.org/abs/0904.3973 I have carried out a statistical test on a population of 20 574 Hipparcos stars inside 300 pc with known radial velocities and with accurate parallaxes in the New Hipparcos Reduction. The test rejects the null hypothesis, "there is no systematic error in spectrographic determinations of heliocentric radial velocity", with 99.9993% confidence. This is reported in http://arxiv.org/abs/0903.5193 I am expecting that shortly there will be a still more convincing result. Herschel will give us images of the early universe predicted to show many galaxies at redshifts so high that they could not have formed at the age of the universe according to standard general relativity.