Abstract
We consider the uncertainty in the arm length of an interferometer due to metric fluctuations from the quantum nature of gravity, proposing a concrete microscopic model of energy fluctuations in holographic degrees of freedom on the surface bounding a causally connected region of spacetime. In our model, fluctuations longitudinal to the beam direction accumulate in the infrared and feature strong long distance correlation in the transverse direction. This leads to a signal that could be observed in a gravitational wave interferometer. We connect the positional uncertainty principle arising from our calculations to the 't Hooft gravitational S-matrix.
Highlights
The quantum mechanical description of gravity together with the other forces remains one of the most important questions in physics
While general relativity can be quantized as an effective field theory valid at low energies, and there has been significant theoretical progress in understanding other aspects of quantum gravity, signatures of the quantum nature of gravity have so far remained stubbornly immune to observation
The transverse correlations are generated through the Newtonian potential of these energy fluctuations, allowing us to make a concrete prediction for the spectrum of length fluctuations in an interferometer
Summary
The quantum mechanical description of gravity together with the other forces remains one of the most important questions in physics. One of the intriguing aspects of the holographic principle is that, to ensure the validity of the entropy bound, the spacetime degrees of freedom are necessarily correlated in the infrared This raises the question of whether Planck scale physics could appear at much longer, potentially observable, length scales. The transverse correlations are generated through the Newtonian potential of these energy fluctuations, allowing us to make a concrete prediction for the spectrum of length fluctuations in an interferometer These fluctuations imply a spacetime uncertainty relation in the longitudinal direction, which we connect, albeit in a modified form, to the gravitational S-matrix approach of ’t Hooft The first steps we take–employing a Planckian random walk–shares commonalities with these works, our approach differs in the sense that we present a concrete theoretical model leading to length fluctuations along the longitudinal direction with a distinctive signature for strong transverse correlations, which is, as a consequence, macroscopically observable in an interferometer. A phenomenological result is that constraints from the images of distant astrophysical sources derived for uncorrelated fluctuations in Refs. [13, 14] do not apply to our model
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