I How Does Temperature Affect Time Dilation in Clocks?

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Temperature affects time dilation through microscopic movement, but the impact varies depending on the type of clock. For pendulum clocks, heating does not alter their timekeeping, while atomic clocks can be influenced by temperature due to increased atomic motion. The discussion highlights that time dilation typically requires relative motion of the clock's center of mass, which is not affected by random thermal motion. In the case of muons, higher temperatures can lead to slower decay rates, but this does not generalize to all clock types. Ultimately, the relationship between temperature and time dilation is complex and depends on the specific mechanisms of the clocks being considered.
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The solution for cesium is the fountain clock - ultracold atoms in free fall with a known velocity. The alternative is trapping the atoms in an optical lattice, something done for optical clocks: a fountain limits the "readout" time of the atoms and therefore the precision. A lattice allows to use more narrow transitions.
 
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