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.)


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