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We propose a simple model of spacetime vacuum fluctuations motivated byAdS/CFT, where the vacuum is described by a thermal density matrix, $\rho =\frac{e^{-K}}{\mbox{Tr}(e^{-K})}$ with $K$ the modular Hamiltonian. In AdS/CFT,both the expectation value of $K$ and its fluctuations $\langle \Delta K^2\rangle$ have been calculated; both obey an area law identical to theBekenstein-Hawking area law of black hole mechanics: $\langle K \rangle =\langle \Delta K^2 \rangle = \frac{A}{4 G_N}$, where $A$ is the area of an(extremal) entangling surface. It has also been shown that $\Delta K$gravitates in AdS, and hence generates metric fluctuations. These theoreticalresults are intriguing, but it is not known how to precisely extend such ideasabout holographic quantum gravity to ordinary flat space. We take the approachof considering whether experimental signatures in metric fluctuations coulddetermine properties of the vacuum of quantum gravity in flat space. Inparticular, we propose a theoretical model motived by the AdS/CFT calculationsthat reproduces the most important features of modular Hamiltonianfluctuations; the model consists of a high occupation number bosonic degree offreedom. We show that if this theory couples through ordinary gravitationalcouplings to the mirrors in an interferometer with strain sensitivity similarto what will be available for gravitational waves, vacuum fluctuations could beobservable.

On Vacuum Fluctuations in Quantum Gravity and Interferometer Arm Fluctuations