For much of its history, the second was a fraction of a day. The modern SI definition instead fixes the frequency associated with a particular transition in a caesium-133 atom. The familiar interval remained roughly the same; what changed was the physical reference used to reproduce it.12
This is a less obvious achievement than inventing a more accurate clock. Two laboratories can build different machines and still aim to produce the same unit. Their clocks need to be compared against a definition that does not depend on the gears, crystal or electronics of either machine. The history of the second is partly the history of finding such a reference.
Earth was not a steady enough clock
A day divided into twenty-four hours, with sixty minutes in each hour and sixty seconds in each minute, contains 86,400 seconds. But Earth’s rotation is not perfectly uniform. As measurements improved, variations that were unimportant for daily life became a problem for a scientific unit. Astronomers developed an alternative based on Earth’s orbital motion, the ephemeris second, which the General Conference on Weights and Measures approved in 1960.1
That astronomical reference was difficult to realise in practice. Caesium clocks offered a more accessible and reproducible alternative, and an atomic definition was adopted in 1967. The apparently awkward number chosen for it, 9,192,631,770, came from measurements comparing the caesium frequency with the ephemeris second. Changing the reference was meant to preserve continuity with the existing unit, rather than introduce a noticeably longer or shorter second.1
What the number defines
Today the SI fixes the unperturbed ground-state hyperfine transition frequency of caesium-133 at exactly 9,192,631,770 hertz. One hertz means one cycle per second. Equivalently, a second lasts for 9,192,631,770 periods of the radiation corresponding to that specified transition. The current formulation fixes the numerical value of the frequency; the length of the unit follows from that choice.2
The qualifiers identify a particular physical reference. “Caesium-133” specifies the isotope. “Ground state” and “hyperfine transition” identify two closely spaced energy levels within its lowest-energy configuration. “Unperturbed” describes the ideal reference, without the shifts introduced by unwanted external influences. A laboratory must account for departures from those conditions when it evaluates its clock.2
The number in the definition is exact. A measurement made with a real instrument is not automatically exact because it uses that definition. A ruler may be intended to reproduce the metre but still have marks in the wrong places; similarly, a clock can be intended to reproduce the second while retaining a small uncertainty in its output.
The clock needs an oscillator
An atom does not have a dial or a counter attached to it. An atomic clock uses an oscillator producing electromagnetic radiation and tests that radiation against the atoms. When the radiation is close to a suitable resonant frequency, it can change their internal energy state. Measuring their response supplies information about whether the oscillator is correctly tuned.3
Electronics then turn an oscillation into a usable time signal by counting cycles and dividing the frequency. The atoms provide the reference for controlling the oscillator. This explains why a description such as “counting an atom’s ticks” is only shorthand: the useful signal comes from an apparatus whose frequency is checked against an atomic transition. An atomic clock is a carefully maintained experiment as well as a timepiece.3
The distinction also explains how two clocks can disagree. They may use the same type of atom and target the same transition, yet differ in how they prepare the atoms, interrogate them and estimate disturbances. Agreement between independent instruments is an important check on whether their treatment of those effects is working.
Making a measurement last longer
In a caesium fountain clock, laser cooling slows a cloud of atoms, which is then launched upwards. The atoms pass through a microwave interaction region on the way up and again as they fall. Their response after these interactions helps the clock determine how closely its microwave oscillator matches the atomic resonance.4
The time between the two interactions is useful. Fast atoms in a conventional beam pass through an apparatus quickly; the fountain arrangement allows a longer interrogation. That improves the ability to resolve small frequency differences. Detectors measure the populations of the atomic states, and their results feed back into adjustments of the microwave frequency.4
The cooling, vacuum system and detection equipment are therefore not decoration around an ideal atom. They are part of the measurement. The definition specifies the reference to be reproduced; the engineering determines how well a particular laboratory can reproduce it.
Why this precision leaves the laboratory
GPS makes the consequences of a timing error unusually concrete. Satellites broadcast timing and position information, and a receiver combines signals from several satellites to estimate its own position and clock offset. Since radio signals travel at the speed of light, a small error in their travel time can correspond to a substantial distance error. Atomic clocks on the satellites, together with corrections from ground systems, make the measurements useful.5
A phone does not need to contain a laboratory caesium fountain to benefit. It can use a system whose signals are supported by much better clocks elsewhere. NIST describes the relationship between ground clocks and satellite clocks as an ongoing process of correction, not a one-time synchronisation that then remains perfect.5