Quantum Gravitational Uncertainty of Transverse Position

Abstract

It is argued that holographic bounds on the information content of spacetime might be directly measurable. A new uncertainty principle is conjectured to arise from quantum indeterminacy of nearly flat spacetime: Angular orientations of null trajectories of spatial length L are uncertain, with standard deviation in each transverse direction Δθ> \sqrt{l_P/L}, where l_p denotes the Planck length. It is shown that this angular uncertainty corresponds to the information loss and nonlocality that occur if 3+1-D spacetime has a holographic dual description in terms of Planck-scale waves on a 2+1D screen with encoding close to the Planck diffraction limit, and agrees with covariant holographic entropy bounds on total number of degrees of freedom. The spectrum and spatial structure of predicted quantum-gravitational ``holographic noise'' are estimated to be directly measurable over a broad range of frequencies using interferometers with current technology.

4 pages, LaTex, substantial revisions in response to referees' comments