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Why Is a Second Defined by 9,192,631,770 Cesium Radiation Cycles? How the Second Moved From the Day to the Atom

Category: Technology

Today, one second is officially the duration of 9,192,631,770 periods of the radiation corresponding to a transition between two hyperfine levels of the ground state of a cesium-133 atom. [1] That is not a round number, and nobody would pick it for fun. The short answer is that it was chosen to match the old second, which was a fraction of the day, so that clocks and records would not suddenly change. [4] The rest of this page follows how the second got from the spinning Earth to an atom, and what problem showed up at each step.

What Was a Second Before 1960?

Until 1960, a second was a fraction of a day. A day has 24 hours, an hour has 60 minutes, and a minute has 60 seconds, and 24 × 60 × 60 = 86,400. So the second was defined as 1/86,400 of the mean solar day, which is the average length of a solar day over a year. The exact meaning of "mean solar day" was left to astronomers. [2]

That made sense for ordinary life, since people organize their days by the Sun. But a definition is only useful if the thing it is based on stays the same length. That is where the trouble started.

Why Was the Spinning Earth Not Steady Enough?

Measurements showed that the Earth does not spin at a perfectly even rate, which made "a fraction of the day" an unsatisfactory definition. [2] The US National Institute of Standards and Technology (NIST) describes the pattern this way: the spin sometimes speeds up and sometimes slows down, but over long periods it is gradually slowing, so the average solar second slowly gets longer compared with an atomic second. [5]

Think of using a rubber band as a ruler. If the band stretches a little from year to year, every measurement made with it quietly changes too. Scientists wanted a second whose length did not change.

Why Did the Second Switch From the Day to the Year in 1960?

In 1960, the 11th General Conference on Weights and Measures (CGPM), the international meeting where countries agree on units, adopted a new definition. It came from the International Astronomical Union: the second became 1/31,556,925.9747 of the tropical year (the time it takes for the seasons to complete one cycle) at the beginning of 1900. [3] [2] Dividing 31,556,925.9747 by 86,400 gives about 365.2422, the number of days in that year, which matches the familiar length of a year.

Fixing the year to 1900 gave the second a single, named target rather than a moving one. This "ephemeris second" avoided the wobbles of the day. But it had a practical weakness, which we will see next: to use it, you had to watch the sky for a long time.

Why Did Scientists Turn to Atoms Instead of the Sky?

Even before 1960, experiments had shown that an atomic standard, based on a transition between two energy levels of an atom, could be produced and reproduced much more accurately. [2] The first practical cesium-beam atomic clock was built at the National Physical Laboratory (NPL) in the United Kingdom in 1955. It would gain or lose only about one second in 300 years. [6]

An atom's vibration has a useful property: cesium-133 atoms provide a reproducible frequency reference, so a lab does not have to depend on the sky. Nobody needs to wait a year to check it.

How Did Scientists Make the Atomic Second Match the Old Second?

There was a catch. If scientists had simply picked a nice round number of atom vibrations, the new second would have been a little longer or shorter than the old one, and old records would no longer line up. So they measured first. In 1958, William Markowitz of the US Naval Observatory worked with the NPL's Louis Essen to find the cesium frequency in terms of the ephemeris second, the astronomical unit of time then in use. [4] The result was 9,192,631,770 hertz, with an uncertainty of 2 or 3 parts in a billion. [4]

The opening text of the same article attributes the main uncertainty to the astronomical observations. [4] In that comparison, the sky was the less steady partner.

In 1967, the 13th CGPM adopted the new definition: the second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom. [1] From then on, the number was not a measurement but an exact definition. [4] That is why it looks so odd: the strange digits are a fossil of the old second, kept so that the new one would be the same length.

The wording was updated again in 2018 (in force from 2019), now stated as fixing the cesium frequency at that exact number. The BIPM, the international organization responsible for the SI units, describes it as a more precise wording of the same definition. [2]

What Does the Spinning Earth Have to Do With Leap Seconds Today?

Once the second was tied to atoms, the Earth's spin no longer set its length. Yet people still want clocks to match the Sun. To keep both, Coordinated Universal Time (UTC), the time used for everyday timekeeping, is nudged by a "leap second" when needed, so that it stays within 0.9 seconds of the time based on Earth's rotation. The first leap second was added on June 30, 1972, and NIST's page currently (October 2026) gives the difference between UTC and International Atomic Time as 37 seconds. [7]

NIST adds a surprising twist: because the atomic second was set by comparing cesium clocks with the ephemeris second, which was slightly shorter than the mean solar second, that small difference was passed on. Had the atomic second been matched to the mean solar second, leap seconds would probably have been needed much less often. [5] A choice made in 1958 is still visible in our clocks.

Will the Second Be Redefined Again?

Possibly. Scientists are working on clocks that use light instead of microwaves, and an international group has kept 2030 as the key milestone for deciding on a new definition. But a decision needs agreement and certain tests to be passed, and it has not been made. [8] Every earlier change followed the same rule: measure the new standard against the old second first, so that nobody's second suddenly gets longer.

You can try the arithmetic yourself. Multiply 24 × 60 × 60 to get the seconds in a day. Then divide 31,556,925.9747 by 86,400 and see if you land near 365.24. The next time someone says "just a second," you will know how much work went into keeping it the same length.

Sources

  1. BIPM, "Resolution 1 of the 13th CGPM (1967)." https://www.bipm.org/en/committees/cg/cgpm/13-1967/resolution-1 (Read in full. The wording of the 1967 definition, and the note that it was replaced in 2018 with effect from 2019.)
  2. BIPM, "History of the SI: the second." https://www.bipm.org/en/history-si/second (Read in full. The pre-1960 definition, the problem with Earth's rotation, the 1960 and 1967 changes, and the 2018 rewording.)
  3. BIPM, "Resolution 9 of the 11th CGPM (1960)." https://www.bipm.org/en/committees/cg/cgpm/11-1960/resolution-9 (Read in full. The wording of the 1960 definition.)
  4. Physics Today, "Of time and the atom…" https://physicstoday.aip.org/features/of-time-and-the-atom (Only the abstract-length opening text was readable; the full article is a PDF. It supports the 1958 Markowitz/Essen measurement, the 2 or 3 parts in a billion uncertainty, and the point that the limit was in the astronomy. The statement that the number was chosen to match the old second is also supported by the BIPM 1967 resolution text.)
  5. NIST, "Leap Seconds FAQs." https://www.nist.gov/pml/time-and-frequency-division/leap-seconds-faqs (Opening explanation read; the page was truncated in the tool. Covers the slowing of Earth's rotation and why the ephemeris second was slightly short.)
  6. NPL Training, "Fundamentals of metrology: the second and time and frequency metrology." https://training.npl.co.uk/product/fundamentals-of-metrology-the-second-and-time-and-frequency-metrology/ (Course description page, read in full. The 1955 cesium-beam clock and its accuracy of one second in 300 years.)
  7. NIST, "Leap second and UT1-UTC information." https://www.nist.gov/pml/time-and-frequency-division/time-realization/leap-seconds (Opening text read, including the statements that the first leap second was inserted on June 30, 1972 and that the current UTC-TAI difference is 37 seconds; the table itself was not read. The 0.9 s limit.)
  8. BIPM, "FAQ on the redefinition of the second." https://www.bipm.org/en/faq-redefinition-second (Timeline section read. 2030 as the decisive milestone, conditional on consensus and criteria being met.)