# Does "correcting a clock for gravitational perturbations" mean calculating the sender rate and attributing the sender rate to the sender?

Experiments which are interpreted in terms of "gravitational red- or blueshift" generally involve a sender $$S$$ (or a sample $$S$$ of individual senders), and a receiver (sample) $$R$$, which perceives the signal indications $$S_{(j)}$$ of the sender, such that from the corresponding receiver indications $$R_{\circledR S (j)}$$ the corresponding (averages of) receiver rate can be evaluated as

$$\overline{f}_R^{(jk)} := \frac{k - j}{\tau R[ \, \circledR S (j), \circledR S (k) \, ]}$$

where $$S_{(j)}$$ and $$S_{(k)}$$ denote distinct sender indications, correspondingly labelled with different real numbers $$j \ne k$$,
$$R_{\circledR S (j)}$$ and $$R_{\circledR S (k)}$$ are the corresponding perception indications of receiver $$R$$, which are (generally) required to be distinct as well,
and $$\tau R[ \, \circledR S (j), \circledR S (k) \, ]$$ denotes the duration of receiver $$R$$ from having received sender indication $$S_{(j)}$$, until having received sender indication $$S_{(k)}$$.

Somewhat confusingly, these measured receiver rates $$\overline{f}_R^{(jk)}$$ are often referred to as "shifted rates of the sender"; and, eventually, readers can be left with the incorrect impression that these rates $$\overline{f}_R^{(jk)}$$ indeed are the rates of the sender, stating its signal indications. Even though those latter rates are of course instead defined and measured as

$$\frac{k - j}{\tau S[ \, (j), (k) \, ]}$$

where $$\tau S[ \, (j), (k) \, ]$$ denotes the duration of sender $$S$$ from having stated its signal indication $$S_{(j)}$$ until having stated its signal indication $$S_{(k)}$$; and therefore those latter rates should be confused with the receiver rates $$\overline{f}_R^{(jk)}$$, foremost by being denoted differently, e.g. as

$$\overline{f}_S^{(jk)} := \frac{k - j}{\tau S[ \, (j), (k) \, ]}.$$

Such apparently incorrect attributions of receiver rates $$\overline{f}_R^{(jk)}$$ to the sender have been noted and critizised occasionally, such as here, but the pratice has also been deemed "unobjectionable", or at least "correct enough to be understood".

Very recently, however, a report by T. Bothwell et al. (physics.atom-ph:2109.12238)

"[...] heralds a new regime of clock operation necessitating intra-sample corrections for gravitational perturbations."

Therefore my question:
Does this "new regime of clock operation" supposed by Bothwell et al. involve measuring the rates $$\overline{f}_S^{(jk)}$$, attributing those rates to the sender (regarding its statements of signal indications), and, against previous practice, avoiding any attribution of the corresponding receiver rates $$\overline{f}_R^{(jk)}$$ to the sender ?

(If so, I, for one, welcome this supposed new regime.)