Physical Interpretation of General Covariance

Abstract

In his paper of 1916 on general relativity, Einstein sought to interpret the meaning of general covariance. An important postulate of all physical laws is their causal structure, and a causal ‘law has significance for the empirical world only if observable facts alone appear as causes and effects’.²⁰⁰ The postulate of general covariance takes away from space and time

the last vestige of physical objectivity…. All of our assertions concerning space-time always amount to the measurements of space-time coincidences. If, for instance, the physical process is only the motion of a material point, then in effect nothing more could be observed than the encounters of two or three such points. The results of our measurements are in fact nothing but the statement of such encounters of material points of our apparatus with other material points, or coincidences respectively between the pointers of clocks, dials, and other point-events under observation, occurring at the same place and time.²⁰¹