The Effect of Cosmic Gravity on the Time Measured by Clocks Moving through the Universe
Unnikrishnan, C.S.
Tata Institute of Fundamental Research

I show that the gravitational potential from the matter in the universe, known to be at about the critical density, modify significantly the time measured by clocks moving through the universe with a Lorentz factor corresponding to the speed of the clock relative to the isotropic cosmic microwave background radiation. A rigorous derivation in terms of the Robertson-Walker metric corresponding to the matter-filled universe at near-critical density will be presented. An interpretation in terms of the 4-vector gravitational potentials, as an approximation to the metric, will be discussed. The derivation using the correct metric automatically includes the effect of dark matter and dark energy since all gravitationally active matter is included in the derivation. Usual time dilation factors, including the Sagnac term will be derived as special cases of this cosmic gravitational effect. A significant prediction is that a transported clock can run faster relative to a clock that stationary in the earth laboratory frame, as already seen in some clock comparison experiments. It also directly and correctly predicts timing asymmetries between clocks moving in different directions. The approach based on cosmic gravity provides a complete characterisation of time measured by clocks in motion along arbitrary inertial or noninertial trajectories and allows calculation of relative time dilations without any ambiguity and thus provides a rigorous and error free method for accurate time keeping of moving clocks. These results on clocks have a direct counterpart in the calculation of phase accumulated in optical and atomic interferometers. The main thrust of my presentation will be that the cosmic gravitational effects on time measured by moving clocks and phase accumulated in quantum systems are indeed the most significant gravitational contributions to be taken into account in real experimental situations. I will also discuss how the cosmic gravitational effects remain relatively insensitive to local matter density fluctuations and inhomogeneity of matter distribution in the solar system and in its vicinity. Possible implication to other timing experiments, including the timing acceleration that can be attributed to the Pioneer Doppler data will be commented on.