Quantum fluctuations of space-time

Abstract

Using a \emph{gedanken} experiment providing presumably a minimal inaccuracy the uncertainty contributions to the space-time measurement are precisely evaluated for clock and mirror respectively. The resulting expression of minimal uncertainty for the space(time) interval indicates the presence of minimal Planck scale observable length(time). The synthesis of quantum mechanics and general relativity predicts the UV and IR scales for Lorentz invariance violation. The influence of background radiation on the space-time measurement is estimated. Based on the minimal length uncertainty relation which takes into account the wavelength of a quantum used for distance measurement we evaluate the cumulative factor responsible for the magnification of the space-time fluctuation induced phase incoherence of a light propagating over a large distance. We notice that in view of the interferometric observations the quantum fluctuations of space-time in the braneworld model are enormously increased if the fundamental scale is taken much below the Planck one. Present approach to the uncertainty in distance measurement leads to new insight about the bounds of computation. The impact of the space-time fluctuations on the black hole physics is briefly emphasized.