Lorentz Invariance, Scattering Amplitudes and the Emergence of Semiclassical Geometry

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.