# Questions about MTW's "thousand" tests of the Einstein principle

In Misner, Thorne, Wheeler (henceforth written as "MTW"), "Gravitation", Box 16.4, there's an experimental setup construction (or method) presented by which

"Each geodesic clock is constructed and calibrated as follows: [...]", where "Those that pass through [event] $\mathcal A$ are calibrated [...] against the [specific timelike] standard interval $\mathcal A B$" and "Any interval $\mathcal P Q$ along the world line of a geodesic clock can be measured by the same method as was used in calibration".

Regarding importance and motivation of this method it is stated that

"The Einstein principle that spacetime is described by Riemannian geometry exposes itself to destruction by a "thousand" tests. Thus, from the fiducial interval, $\mathcal A B$, to the interval under measurement, $\mathcal P Q$, there are a "score" of routes of intercomparison, all of which must give the same value for the ratio $\mathcal P Q / A B$.".

Box 16.4 contains two separate sketches of the setup construction; one concerned with interval $\mathcal A B$, the other equivalently with interval $\mathcal P Q$. Explicitly evident in either sketch are two separate participants ("particles", "timelike world lines") who

• observe pings between each other, and

• both observe one ping to one particular event (event $\mathcal{B}$ in the first setup sketch; or event $\mathcal{Q}$ in the second setup sketch), where

• each participant finds some (integer) number of successive pings to the other as same as the one ping to the "external" event ($\mathcal{B}$, or $\mathcal{Q}$). (The "intercomparison" to be achieved then involves counting those successive pings by the two participants.)

There are additional "demands" stated (which the two sketches alone don't make explicit); among them that the participants who took part in event $\mathcal A$ (referring to the first sketch), or in event $\mathcal Q$ (referring to the second sketch) are required to have been "freely falling"; and their world lines correspondingly "paths of freely falling particles" and "geodesics".

Question 1:
Has there at least one such test been carried out already, presumably by "intercomparison" along at least two distinct "routes", by explicitly using the method indicated by MTW ? (i.e. not involving any further "model dependent assumptions" such as in the arguments presented at the end of box 16.4)

Question 2:
Instead of demanding of the setup(s) that certain participants were "freely falling" and obtaining "a "thousand" tests of the Einstein principle that spacetime is described by Riemannian geometry",
could the described method be explicitly adapted in turn, by assuming "the Einstein principle" as outright valid and by suitably combining sufficiently many (if not "a thousand") of the described setups, to obtain a test of whether (or to which accuracy) a given particle had been "freely falling" (or correspondingly, whether, or to which accuracy, a given timelike world line was "geodesic") ?