1 - Introduction

Summary

A physical measurement requires a collection of devices such as a clock, a theodolite, a counter, a light gun, and so on. The operational control of this instrumentation is exercised by the observer, who decides what to measure, how to perform a measurement, and how to interpret the results. The observer's laboratory covers a finite spatial volume and the measurements last for a finite interval of time so we can define as the measurement's domain the space-time region in which a process of measurement takes place. If the background curvature can be neglected, then the measurements will not suffer from curvature effects and will then be termed local. On the contrary, if the curvature is strong enough that it cannot be neglected over the measurement's domain, the response of the instruments will depend on the position therein and therefore they require a careful calibration to correct for curvature perturbations. In this case the measurements carrying a signature of the curvature will be termed non-local.

Observers and physical measurements

A laboratory is mathematically modeled by a family of non-intersecting time-like curves having u as tangent vector field and denoted by C_u; this family is also termed the congruence. Each curve of the congruence represents the history of a point in the laboratory. We choose the parameter τ on the curves of C_u so as to make the tangent vector field u unitary; this choice is always possible for non-null curves.