@saila

[How to determine whether an atomic clock had "ticked at the Moon's natural pace"? (Nature 614, 13-14 (2023))](https://physics.stackexchange.com/questions/748237/how-to-detetermine-whether-an-atomic-clock-had-ticked-at-the-moons-natural-pac)

#time #LunarTime #UTC #relativity #clock #clockrate #rate #duration

@abetterjulie #relativity

Rotation does matter:
The ride #duration (a.k.a. #pathlength of a #worldline segment; or "proper time") of a child circling in a carousel 𝒊𝒔 𝒔𝒉𝒐𝒓𝒕𝒆𝒓 𝒕𝒉𝒂𝒏 the corresponding wait #duration of a parent "standing by".

In contrast, #clockrate and whether/which #clock "ran faster/slower" than another is only secondary; calculated from comparisons of durations, and from Δ of readings.

On the Nature article:
"clocks that tick at the Moon's natural pace" is a disaster, IMHO.

(3/3):
How should therefore the relations between these two resulting #clock​s, \(\mathfrak E \equiv (\mathcal E, t_{\mathfrak E}) \) and \(\mathfrak M \equiv (\mathcal M, t_{\mathfrak M}) \), therefore be characterized in terms of comparison of their (average) #clockrate​s:

@heafnerj
Joe Heafner wrote:
> <em> [...] Callahan’s The #Geometry of #Spacetime: An Introd. to [...] #Relativity [...] I really like the first 2 chap.s </em>

Please let us know whether Callahan gives there any hints #HowTo find out whether a clock was "running at a specific #ClockRate"; or even whether any 2 (separated) clocks were "running at equal rates"; or even whether 2 clocks "kept fixed #Distance from" each other.

Looking for "clock" in the Index of Callahan's book leads to chap 4 ...