Of the seven SI base units, the second is by far the most precisely realized. Modern atomic clocks reach accuracies orders of magnitude beyond any direct length, mass, or temperature measurement. This is why the 2019 SI redefinition anchored four other base units on top of the second.
A short history
Before the 20th century. The second was defined as $\dfrac{1}{86400}$ of a mean solar day:
$$
1\ \text{s} \;=\; \dfrac{1\ \text{mean solar day}}{86400}
$$
Intuitive, but it rested on an assumption that turned out to be wrong: Earth’s rotation is not uniform. Tidal friction from the Moon slowly brakes Earth, and the solar day lengthens by about 2 ms per century. Irrelevant for daily life; a real problem for astronomy and navigation.
1956 (ephemeris second). CIPM redefined the second as a fraction of the 1900 tropical year:
$$
1\ \text{s} \;=\; \dfrac{1}{31{,}556{,}925.9747}\ \text{of the tropical year 1900}
$$
This dropped Earth’s rotation and anchored the second to Earth’s orbit around the Sun (more stable). Big drawback: could not be realized in a lab — required years of astronomical observations.
1967 (current). The CGPM redefined the second using a specific atomic transition in Cs-133:
$$
1\ \text{s} \;=\; 9{,}192{,}631{,}770 \times T
$$
where $T$ is the period of the electromagnetic radiation emitted by the transition between the two hyperfine sublevels of the ground state of Cs-133 (F=4 → F=3, $\Delta F = \pm 1$) at 0 K — i.e., a radiation frequency of exactly 9,192,631,770 Hz.
Why this odd number? Not arbitrary: chosen so the new definition would numerically agree with the older ephemeris second, keeping historical astronomical records valid. Nature did not dictate the number — international agreement did.
2019 (SI redefinition). The second’s definition did not change, but its role did: it became the anchor from which the meter (via constant $c$), the kilogram (via Planck’s constant $h$), and the ampere (via electron charge $e$) are all derived.
Why Cs-133?
- Single stable isotope — cesium has only one naturally occurring stable isotope, so samples require no special preparation
- Microwave transition — the
9.2 GHzfrequency is well within reach of RF technology (unlike optical transitions, which demand precision optics) - Narrow linewidth — the natural width of the transition is extremely small, so the frequency can be pinned down to many decimals
Atomic clocks — real precision
Modern atomic clocks reach staggering precision:
| Generation | Example | Relative uncertainty |
|---|---|---|
| First (1950s) | NBS-1 | $\sim 10^{-9}$ |
| Microwave fountain | NIST-F1 | $\sim 10^{-16}$ |
| Optical lattice (Sr, Yb) | current best | $\sim 10^{-18}$ |
$10^{-18}$ means a drift of about 1 second over 30 billion years — longer than the age of the universe.
Consequence: optical clocks are now so far ahead of Cs-based clocks that the SI second may itself be redefined via an optical transition sometime in the 2030s. The same move that happened for the meter in 1983 is now brewing for the second.
🔬 Want to know how these clocks actually work?
The six-stage cycle — from laser cooling to Ramsey interferometry and the feedback loop — is walked through in a supplementary article:
Appendix — How the cesium atomic clock works
The pattern
| Era | Anchor |
|---|---|
| Before 1956 | Earth’s rotation |
| 1956 | Earth’s orbit around the Sun |
| 1967 | Hyperfine transition in Cs-133 |
| Coming (probably 2030s) | Optical transition in Sr or Yb |
The pattern from the meter repeats: move from a variable phenomenon (Earth’s rotation), to a more stable one (an atom), to an even more stable one (optical clocks). Each step is a jump in precision, and other base units can inherit that precision.
What you should be able to do
After this section you should be able to:
- Explain why defining the second from Earth’s rotation is inadequate (day length is drifting)
- Write the current definition (
9,192,631,770 Hz) and explain why the number is so uneven - Explain why, in the 2019 redefinition, the second became the anchor for the meter, kilogram, and ampere
- Estimate how many seconds of drift per year an atomic clock at $10^{-16}$ accuracy accumulates (answer: nanoseconds)
📚 See also: Halliday Vol 1, Ch 1 §1-5 (time standard).
🎓 Watch: Veritasium — “The Insane Precision of Atomic Clocks” (youtube.com/@veritasium).
📖 Free reading: NIST Time and Frequency (nist.gov/pml/time-and-frequency-division).
📖 SI Brochure (9th ed.), BIPM — appendix on unit definitions (bipm.org).
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