Quantum Indeterminacy of Emergent Spacetime

TL;DR

This paper demonstrates that emergent 3+1D spacetime from a 2+1D quantum field theory exhibits observable quantum fluctuations and holographic noise, linking quantum indeterminacy to macroscopic geometric uncertainty.

Contribution

It introduces a covariant holographic model showing quantum fluctuations in emergent spacetime, connecting quantum uncertainty with observable holographic noise.

Findings

Quantum fluctuations cause angular uncertainty in null trajectories.

Observable holographic quantum noise is linked to geometric fluctuations.

A statistical estimator quantifies deviations from classical Euclidean geometry.

Abstract

It is shown that nearly-flat 3+1D spacetime emerging from a dual quantum field theory in 2+1D displays quantum fluctuations from classical Euclidean geometry on macroscopic scales. A covariant holographic mapping is assumed, where plane wave states with wavevector k on a 2D surface map onto classical null trajectories in the emergent third dimension at an angle \theta=l_P k relative to the surface element normal, where l_P denotes the Planck length. Null trajectories in the 3+1D world then display quantum uncertainty of angular orientation, with standard deviation \Delta\theta=\sqrt{l_P/z} for longitudinal propagation distance z in a given frame. The quantum complementarity of transverse position at macroscopically separated events along null trajectories corresponds to a geometry that is not completely classical, but displays observable holographic quantum noise. A statistical estimator of the fluctuations from Euclidean behavior is given for a simple thought experiment based on measured sides of triangles. The effect can be viewed as sampling noise due to the limited degrees of freedom of such a theory, consistent with covariant bounds on entropy.