On Vacuum Fluctuations in Quantum Gravity and Interferometer Arm Fluctuations

Understand

We propose a simple model of spacetime vacuum fluctuations motivated by AdS/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 the Bekenstein-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 theoretical results are intriguing, but it is not known how to precisely extend such ideas about holographic quantum gravity to ordinary flat space.