# Least count of cesium clock and maximum possible significant figures for time

We know that a second is defined as being equal to the time duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the fundamental unperturbed ground-state of the caesium-133 atom(form wikipedia).Hence least count of this clock will be $$\frac{1}{9192 631770}$$ seconds

From my understanding of least count and significant figures I conclude that it is not possible to measure time duration less than $$\frac{1}{9192 631770}$$ seconds accurately. Is my conclusion correct? Is there any workaround for this?

Your conclusion is not correct. Current atomic clocks based on optical transitions are much more accurate and precise than that. So time durations less than 1/9192631770 s can indeed be accurately measured.

The kernel of truth to your conclusion is that such time durations cannot be accurately known in SI units. However, SI units have no particular existential prominence. Just because we cannot accurately measure such durations in SI seconds does not mean we cannot measure them at all.

As a side note, we can detect phase differences less than $$2\pi$$, so the limit would not be 1/9192631770 s anyway. What is important is not the frequency, but how well that frequency stays in phase so that you can detect differences. Right now that is on the order of $$10^{-16}$$ for Cesium clocks.

• I don’t understand your statement about SI units. Meter used to be based on a metal bar. Did not mean that sub meter distances could not be accurately described with SI units. Feb 7, 2021 at 15:47
• @Ben51 agreed, and similarly we can measure times much more accurately than 1 s.
– Dale
Feb 7, 2021 at 17:01
• But I thought you were suggesting that we couldn’t measure times, using SI seconds, smaller than 1/9192631770 s, which is analogous to 1 meter if you use a stick a meter long as the definition. Feb 7, 2021 at 17:03
• No, I have a whole paragraph talking about that. But I consider that a secondary issue (hence I placed it last). The primary issue in my opinion is that the precision of the definition of the SI second in no way limits the precision of measurements of time. An example is the conventional volt, $V_{90}$ which was much more accurate than the pre-2019 SI volt, $V$. Voltage could be measured much more accurately, but had to be expressed in terms of the precise $V_{90}$ instead of the imprecise $V$.
– Dale
Feb 7, 2021 at 18:40
• I still don’t feel you. Are you saying that the definition is imprecise enough that when you measure a sufficiently long time, say many seconds, you can’t be certain of the absolute number of SI seconds to within closer than a certain small amount? Because if you’re suggesting that an imprecisely defined unit means you can’t describe arbitrarily small amounts with it, that don’t make no sense. Impressive definition makes a relative error, not an absolute one. Feb 7, 2021 at 18:52

The number $$N=9\, 192\, 631\, 770$$ is used to define a second. Do not mistake this as an accuracy or precision. These are completely different concepts from the definition. Thus it is of course possible to measure things with an accuracy lower than $$1/N$$.