Principle of general covariance and quantum theory

Abstract

We emphasise the distinction between formal and operational notions of general covariance. Classically, formal covariance implies operational covariance. This is not true in quantum theory. Two observers may not agree on the results of measurement of a tensorial object like T_ik (stress tensor) in quantum theory. In particular, one observer might conclude that the measured value is zero while another might attribute non-zero value to it.