Lorentz Invariance, Scattering Amplitudes and the Emergence of Semiclassical Geometry

TL;DR

This paper explores how quantum error correction, Lorentz invariance, and scattering amplitudes collectively contribute to the emergence of semiclassical geometry in quantum gravity, linking kinematic data to quantum codes.

Contribution

It introduces a framework connecting scattering data, quantum geometry states, and error correction codes, emphasizing Lorentz invariance as a code-preserving symmetry.

Findings

Scattering data correspond to coherent quantum geometry states.

Quantum error correction codes model the structure of quantum geometry.

Lorentz invariance ensures code subspace invariance under coordinate transformations.

Abstract

It has been known for some time now that error correction plays a fundamental role in the determining the emergence of semiclassical geometry in quantum gravity. In this work I connect several different lines of reasoning to argue that this should indeed be the case. The kinematic data which describes the scattering of $ N $ massless particles in flat spacetime can put in one-to-one correspondence with coherent states of quantum geometry. These states are labeled by points in the Grassmannian $ Gr_{2,n} $, which can be viewed as labeling the code-words of a quantum error correcting code. The condition of Lorentz invariance of the background geometry can then be understood as the requirement that co-ordinate transformations should leave the code subspace unchanged. In this essay I show that the language of subsystem (or operator) quantum error correcting codes provides the proper framework for understanding these aspects of particle scattering and quantum geometry.