The rotation problem

On a large scale, inertial frames seem not to rotate relative to the average matter distribution in the universe. Without absolute space or finely tuned initial conditions, it is difficult to explain the lack of relative rotation. Two classical (non-quantum) arguments have been proposed to explain why: (1) that gravitational fields (including inertial fields) be completely determined by the matter distribution, with no independent degrees of freedom for the gravitational field (AKA Mach's principle). (2) inflation. Although either of these is a possible explanation, a more likely explanation comes from considering reasonable forms of quantum gravity. A semi-classical approximation to quantum gravity shows that phase interference would cancel out cosmologies with significant relative rotation. A generic general estimate for a perfect fluid cosmology with a realistic variation of average vorticity with cosmological scale factor shows that only cosmologies with an average present relative rotation smaller than about $L^*H^2\approx 10^{-71}$ radians per year could contribute significantly to a measurement of relative rotation rate, where $L^*$ is the Planck length and $H$ is the present value of the Hubble parameter.