Why doesn't time-dilation impact the threshold frequency of the photoelectric effect?

Question

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.

p----> <----A

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.

Kundig Experiment

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)

Comments

The relativistic Doppler effect (formula) demonstrates how the rest-frame frequency is modified as a function of the relative velocity direction and the velocity absolute value. The original frequency is implied exactly defined, without any width $\Delta\omega$. Atoms emit lines with some widths $\Delta\omega$, so the resonance absorption may take place for somewhat different frequencies.

Kundig experiment demonstrates the effect and answers your question; the effect, which may be difficult to realize with the usual light source and a metal plate due to important $\Delta\omega$ and necessity of much higher velocities. I am not familiar with metal threshold uncertainties $\Delta\omega$ so I cannot (and do not want to) estimate the feasibility of your experiment.

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"The relativistic Doppler effect (formula) demonstrates how the rest-frame frequency is modified as a function of the relative velocity direction and the velocity absolute value. The original frequency is implied exactly defined, without any width ΔωΔω. Atoms emit lines with some widths ΔωΔω, so the resonance absorption may take place for somewhat different frequencies."

The relativistic Doppler effect formula tells us how the frequency of the incident LIGHT changes, it doesn't tell us anything at all about the threshold frequency of the ATOM.

"Kundig experiment demonstrates the effect and answers your question; the effect, which may be difficult to realize with the usual light source and a metal plate due to important ΔωΔω and necessity of much higher velocities. I am not familiar with metal threshold uncertainties ΔωΔω so I cannot (and do not want to) estimate the feasibility of your experiment."

It most certainly does not. The Kundig experiment demonstrates that resonance absorption (in the nucleus of an atom) is affected by time-dilation. I'm asking about the photoelectric effect, which deals with the excitation of electrons, and is a completely distinct phenomenon.

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Photoelectric effect is due to absorption. I regret that I was engaged in this useless discussion.

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So you're now saying the photoelectric effect is due to light being absorbed in the nucleus of an atom? I'm almost certain that is incorrect. 

I'm admittedly not an expert on this subject, which is why I posted the question. But, with all due respect, I'm getting the sense you have no idea what you're talking about. I asked you a simple, yes / no question, and you responded with a bunch of cryptic nonsense.

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I am not saying the photoelectric effect is due to light being absorbed in the nucleus of an atom! I impied absorption by an atomic electron or by an electron from a metal plate.

I am not in position to give you some lectures on atomic physics here. Learn from other sources, please.

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With all due respect, you are avoiding a very simple question through obfuscation. 

The resonance absorption frequency of an atom decreases due to time-dilation when it is rotated, as is demonstrated by the experiments of Kundig et all.

Here is my question, presented in a yes / no format:

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 plate eject electrons?

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The answer is given with the relativistic Doppler effect.

Note, the Mössbauer experiment deals with a very narrow resonance, thus very sensitive to the frequency shifts.

Atomic or metal "levels" have much wider resonance curves (spectral line widths) and thus require much higher relative velocities to be observed/non-observed.