Quantum Measurement, Gravitation, and Locality

Abstract

This essay argues that when measurement processes involve energies of the order of the Planck scale, the fundamental assumption of locality may no longer be a good approximation. Idealized position measurements of two distinguishable spin-$0$ particles are considered. The measurements alter the space-time metric in a fundamental manner governed by the commutation relations $[x_i\,\,p_j]= i\hbar\,δ_{ij}$ and the classical field equations of gravitation. This {\it in-principle} unavoidable change in the space-time metric destroys the commutativity (and hence locality) of position measurement operators.