Quantifying Clock Imprecision due to Stochastic Gravitational Wave Background*

Current clock models do not account for the imprecision introduced by the stochastic gravitational wave background. We aim to quantify clock imprecision due to stochastic gravitational wave background induced spacetime perturbations. To this end, we use Einstein's geometrodynamic clock and investigate this problem in the context of a clock on a rocking boat on stochastic ocean. We constructed a model for stochastic ocean, established stochastic ocean as a super-diffusive process, and numerically simulated evolution of the clock perturbed by stochastic ocean. We determine the Cramér-Rao lower bound on imprecision of estimating frequency of the clock perturbed by stochastic ocean. Eventually, our goal is to use our results for clock on stochastic ocean to determine the Cramér-Rao lower bound on imprecision of estimating frequency of the clock perturbed by stochastic gravitational wave background. Our approach to quantify clock imprecision due to a stochastic background is an important step forward, conceptually, in extending the precision of current clocks to redefine the SI second, search for variations of fundamental constants, increase GPS capabilities, and detect gravitational waves as part of clock network(s).