Statistical Model of Exotic Rotational Correlations in Emergent Space-Time

A Lorentz invariant statistical model is presented for rotational fluctuations in the local inertial frame that arise from new quantum degrees of freedom of space-time. The model assumes invariant classical causal structure, and a Planck information density in invariant proper time determined by the world line of an observer. It describes macroscopic spacelike correlations that appear as observable timelike correlations in phase differences of light propagating on paths that begin and end on the same world line. The model allows an exact prediction for the autocorrelation of any interferometer time signal from the shape of the light paths. Specific examples computed for configurations that approximate realistic experiments show that the model can be rigorously tested, allowing a direct experimental probe of Planck scale degrees of freedom.