Interferometers as Holographic Clocks

It is proposed that the spatial positions of bodies, relative to a classical metric and measured by interactions with classical radiation, are represented by directional quantum operators with Planck scale quantum conditions. With an antisymmetric commutator, the measured speed of light is the same at all frequencies, null fields are nondispersive, and phase is invariant on null sheets, but spacetime position measurements in different directions do not commute. This hypothesis leads to a new source of spatially coherent, Planckian “holographic noise” in relative measured phases of null fields propagating in different directions. Predicted phase correlations are estimated and compared with the sensitivities of current and planned interferometer experiments. Nearly co-located Michelson interferometers correlated at high frequency should be able to achieve the Planckian noise limit.