Epilogue
The mathematical structure of general relativity makes its equations quite remote
from a direct understanding of their content. Indeed, the combination of a covari-
ant four-dimensional description of the physical laws and the need to cope with
the relativity of the observations makes a physical measurement an elaborate
procedure. The latter consists of a few basic steps:
(i) Identify the covariant equations which describe the phenomenon under
investigation.
(ii) Identify the observer who makes the measurements.
(iii) Choose a frame adapted to that observer, allowing the space-time to be split
into the observer’s space and time.
(iv) Decide whether the intended measurement is local or non-local with respect
to the background curvature.
(v) Identify the frame components of those quantities that are the observational
targets.
(vi) Find a physical interpretation of the above components, following a suitable
criterion such as a comparison with what is known from special relativity
or from non-relativistic theories.
(vii) Verify the degree of residual ambiguity in the interpretation of the measure-
ments and decide on a strategy to eliminate it.
Clearly, each step of the above procedure relies on the previous one, and the
very first step provides the seed of a measurement despite the mathematical
complexity.
• Fixing the observer is independent of the coordinate representation; we can
have many observers with a given choice of the coordinate grid, but we can
also deal with a given observer within many coordinate systems.
• Whatever the choice of the coordinate system, one may adapt to a given
observer many spatial frames, each providing a different perspective.
• A measurement requires a mathematical modeling of the target, but also of the
measuring conditions which account for the dynamical state of the observer
and the level of accuracy of his measuring devices.
• The physical interpretation of a measurement requires some previous knowledge
of the object of investigation, so that it can be identified as a generalization from