Near-Horizon Quantum Dynamics of 4-d Einstein Gravity from 2-d JT Gravity

Abstract

We study quantum fluctuations in the lightcone metric of the 4-d Einstein-Hilbert action via dimensional reduction to Jackiw-Teitelboim (JT) gravity. In particular, we show that, in Einstein gravity, the causal development of a region in flat Minkowski spacetime, near a horizon defined by light sheets, can be described by an effective two-dimensional dilaton theory. This enables us to make use of known solutions of the JT action, where the spacetime position of a horizon has quantum uncertainty due to metric fluctuations. This quantum uncertainty can be then directly related to the original 4-d light cone coordinates, allowing us to compute the uncertainty in the time of a photon to travel from tip-to-tip of a causal diamond in flat 4-d Minkowski space. We find that both Planck and infrared scales (with the latter set by the size of the causal diamond) enter the uncertainty in photon travel time, such that the quantum fluctuation in the arrival time may be observably large.

Modular Fluctuations from Shockwave Geometries

“…The justification of this heuristic derivation comes from the effective shockwave action (14). This action makes manifest that as operators X u and X v are non-commuting, since they both appear in the first term involving the time-derivative.…”

“…This result can be derived from the gravitational replica trick, following the same steps as in [8]. These same methods can be used to compute the fluctuations in K. It has by now been firmly established, both in AdS [9][10][11][12] and in flat space [13,14], that these modular energy fluctuations ∆K are also determined by the area of the horizon via the relation…”

Interferometer Response to Geontropic Fluctuations

“…It has, however, been recently argued in multiple different contexts that the length scale L of the physical system itself may enter into the observable [1][2][3][4][5][6] (see Ref. [7] for a summary)…”

“…[4], utilizing a scalar field coupled to the metric to model the behavior of the spacetime fluctuations proposed in Refs. [1][2][3][4][5]. In particular, we propose a model in four dimensions, where the metric appears as a breathing mode of a sphere controlled by a scalar field φ:…”

“…Since φ effectively controls the area of a spherical surface, it is thus proportional to the entropy of a causal diamond, and may be identified with the dilaton mode studied in Refs. [3,5]. In the model we consider, φ is a scalar field whose quantum fluctuations will be charac-terized by its occupation number, which we label as σ pix .…”