# Does the definition of the SI unit “second” require that possible perturbation of primary frequency standards should be measured?

The definition of the SI unit "second" is stated as

with the explicitly added note that

In referring to a caesium atom in its "ground state", does this definition pertain to caesium atoms that are plainly and exactly unperturbed, whether by black body (ambient) radiation or due to any known or unknown perturbation?

If so, is there any requirement to determine (and possibly correct for) the perturbation, or "shift", of any and all primary frequency standards, besides the described "shift due to ambient radiation"?

In particular, is there any requirement to measure whether the durations of 9 192 631 770 periods of different primary frequency standards and/or of the same primary frequency standard in different trials, had been and remained equal to each other, by (presumably) unambiguous means (such as the "ideal clocks" described in MTW §16.4) ?

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This seems like two different questions to me. Most of the question is about the perturbing effect of blackbody radiation, but the final paragraph seems to be about anomalous shifts in clock rates over time. –  Ben Crowell Aug 26 at 18:49
@Ben Crowell: "This seems like two different questions to me." -- Well: the present OP question text contains (even) three separate question marks. "Most of the question is about the perturbing effect of blackbody radiation" -- Not at all. I'll accept for the purpose of my question that "the perturbing effect of blackbody radiation" is settled, e.g. with results as seen in arxiv.org/abs/1107.2412 (Tab. 2). Instead, I am (only) trying to ask about "the perturbing effect of anything else" not listed e.g. in that table. Is that called "(due to) anomalous (reasons)"? –  user12262 Aug 26 at 20:44

I don't know if I'm right, but here is an attempt to estimate one effect that might be relevant. If a 133Cs atom of mass $m$ is in thermal equilibrium with blackbody radiation at temperature $T$, then it has an average kinetic energy $(1/2)mv^2=(3/2)kT$. This will cause Doppler shifts. The longitudinal Doppler shift cancels out on the average, but the transverse Doppler shift, which is by a factor of $\gamma$, doesn't. The average effect is $\gamma-1=3kT/2mc^2$. I suppose the cesium has to be a gas, so the minimum actual temperature would be 944 K. Putting this in, I get $\gamma-1\sim 10^{-12}$. This seems below the $\sim10^{-10}$ precision implied by the number of sig figs in the standard, but maybe it's anticipated that future improvements in technology would make it relevant.
Ben Crowell: "I don't know if I'm right, but here is an attempt to estimate one effect that might be relevant." -- Well, you've completely missed the intended point of my question ... Perhaps it's helpful to contrast rather symbolically: Your answer seems to be concerned with "reasoning out" $$\frac{\partial}{\partial~T}[~f~]~|_{~T =0~ \text K,~f = f_S} \times (T - 0~\text K)$$ while I like to know about (how to determine experimentally) $$f - f_S,$$ where $f_S$ denotes the "standard transition frequency of a plainly and exactly unperturbed Cs133 atom", and $f$ is "of the given sample". –  user12262 Aug 26 at 23:00