Consider the following hypothetical:
An atom is traveling with a velocity of v to the left, directly towards an incoming photon, as crudely depicted below.
Question (1): What is the resonance absorption frequency of the atom?
Question (2): What is the threshold frequency of the atom?
Question (1) requires that we assume that time-dilation is occurring within the atom, in order to be consistent with experimental evidence that shows that the resonance absorption frequency of an atom does in fact decrease due to time-dilation.
Note that the Kundig experiment shows that the threshold frequency of the atom itself is reduced due to time-dilation. This is distinct from any Doppler shifting that occurs with respect to light incident upon the atom.
Question (2) requires that we assume that time-dilation is NOT occurring within the atom, in order to be consistent with the equations for the work function of an electron, which, as far as I can tell, assume that time-dilation is not occurring within the atom.
Electron Work Function
This seems to imply that there is no single answer to "how much time has elapsed" as measured within the atom, since (1) and (2), by definition, require different measurements of time.
What is the correct measure of time in this set of facts?
Here is my question, presented as an experiment:
If I rotate a metallic plate with a threshold frequency of $f_0$ around a light source with a frequency of $f_0$, in the same manner that was done in the Kundig experiment, would the threshold frequency of the plate be reduced below $f_0$ due to time-dilation?
For those that are interested, I came across this in connection with my research applying information theory to time-dilation (the working paper is here: https://www.researchgate.net/publication/323684258_A_Computational_Model_of_Time-Dilation)