The problem of measurement in general relativity

Question

I am looking for a good selection of articles and books on the topic of measurements in general relativity. The only one I'm really aware of is Reichenbach's "The Philosophy of Space and Time", which is fairly a fairly old one by now (1928) and does not really go in great details for all issues.

Are there any such resources covering topics such as:

• The set of (local) metrics one can associate with a set of measurements
• Conditions on the metric (smoothness, analyticity, bounded variation, etc) that it is considered reasonable to apply to the metric to narrow down the possible metrics
• The problem of synchronizing observers in general relativity (such as for instance, if we assume a globally hyperbolic spacetime, the existence of a foliation such that for a Cauchy surface $\Sigma_t$ and some observers $\gamma_i$, then $\forall p_i \in \Sigma_t \cap \gamma_i$, $\gamma(t) = p_i$, in the proper time parametrization)
• Boundaries we can establish on the distance between a set of observers exchanging light signals without knowing the geometry

and other such topics. These issues seem seldomly discussed, even in weirder texts like Earman or Malament. Is there a good set of papers on that kind of topics outside of Reichenbach? I'm guessing part of the issue is that those may pop up more in philosophical papers.

Answer 1

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Turns out this is indeed not a commonly discussed topic, and it is usually mostly discussed for static globally hyperbolic spacetimes (in this case there is a very nice decomposition of the spacetime as a principal bundle with a bundle metric and the connection roughly corresponds to the simultaneity convention). A common set of coordinates from light clocks discussed are the Märzke-Wheeler coordinates, discussed in "Gravitation as Geometry-I: The Geometry of Space-Time and the Geometrodynamical Standard Meter" from Gravitation and Relativity (Chiu & Hoffman), which is itself a shorter version of Märzke's thesis, "The theory of measurement in general relativity".

Among the papers discussing the topic are :

• For the case of accelerated observers in Minkowski space, Pauri and Vallisneri [1]
• For general relativity, Minguzzi makes the bulk of the papers, with various papers on the simultaneity bundle formalism [1] [2]

Edit : More sources :

• The first person to try to address the problem for GR without the local approximation was Ruse

• Synge's book (Relativity, the general theory) contains a lot of informations on the topic of measurement by null and timelike geodesics. He also wrote an entire article on the topic here.

• A common construction for getting the metric for measurement is the EPS construction. There's more details and more different constructions in Semantical aspects of spacetime theories, Axiomatization of the Theory of Relativity

• Relativistic Geodesy talks about a variety of methods for measurement.

• Perlick did a variety of papers on the topic of standard clocks.