Before the mechanical stabilization of time by the pendulum clock, social time remained largely indexed on variable durations. The duration of daylight changes with the seasons: in Paris, the summer day exceeds sixteen hours, the winter day barely exceeds eight. Roman liturgical hours divide this variable day into twelve equal parts, thus hours that lengthen and shorten throughout the year. The cooking of a meal, the duration of a prayer, the time it takes for sand to flow, the time it takes for the candle to burn to the mark: each measure of time was indexed on a singular material phenomenon, which varied according to temperature, the quality of sand, the height of the flame.
Christiaan Huygens conceives in 1656 his pendulum clock, built by Salomon Coster and published in Horologium in 1658. The pendulum oscillates with a period regulated by its length and by gravity, independent of day, season, light. The clock imposes a regular beat, one second, one second, one second, detached from the external phenomena that had organized social time until then. Measured time is no longer indexed on a variable external phenomenon. It is punctuated by an oscillator internal to the device.
The quartz clock, developed at Bell Labs by Warren Marrison and J. W. Horton in 1927, exploits the piezoelectricity of a cut crystal whose electrical oscillation provides a stable frequency. Subsequent quartz clocks and watches will notably stabilize the frequency of 32,768 Hz, a power of two easily divisible to produce one second. The cesium 133 atomic clock, developed by Louis Essen at the National Physical Laboratory in 1955, counts the oscillations associated with the hyperfine transition of the cesium atom. The second will then be defined by 9,192,631,770 periods of this radiation. The best atomic standards then make visible an instability that Earth's rotation had masked.
The tuning fork does not give time. It gives a frequency. But when frequency becomes more stable than the celestial body, it ceases to be a simple beat: it becomes the support of time.
With each generation, the measuring instrument becomes more stable than the phenomenon it initially measured.
The inversion operates at a precise moment. In 1967, the 13th General Conference on Weights and Measures redefines the second. Before 1967, the second is related to Earth's rotation, 1/86,400 of the mean solar day. After 1967, Earth's rotation is related to the atomic second. Earth was the standard, clocks approximated it. Cesium is the standard; Earth becomes the deviation to correct.
The consequence is immediately measurable. Atomic clocks have revealed that Earth's rotation is not constant. Tidal friction slows Earth by about 1.8 milliseconds per century. Internal movements of Earth's core, seasonal atmospheric variations, major earthquakes modify the planet's moment of inertia and change its rotation speed on time scales ranging from day to century. According to NASA/JPL estimates, the Sumatra earthquake in 2004 would have shortened the day by about 6.8 microseconds. The Tōhoku earthquake in 2011, by about 1.8 microseconds.
To catch up with the gap between atomic time and Earth's rotation, IERS periodically inserts a leap second, an additional second added at midnight UTC. Twenty-seven positive leap seconds have been added since 1972, the last at the end of December 2016. No negative leap second has yet been applied. Earth, which was the standard, has become the system that is corrected to keep it aligned with the instrument that was supposed to approximate it.
The leap second is the administrative symptom of metrological inversion.
This inversion has extended to all fundamental units of the International System. The meter, defined in 1799 as the ten-millionth part of a quarter of Earth's meridian, then in 1889 by a platinum-iridium standard kept at Sèvres, is redefined in 1983 as the distance traveled by light in vacuum during 1/299,792,458 of a second. The speed of light is no longer a measured constant. It has become a constant established by definition, fixed at exactly 299,792,458 m/s. The meter is what makes this definition coherent.
The kilogram, since its 2019 redefinition, is no longer a platinum-iridium cylinder kept at the International Bureau of Weights and Measures. It is defined by Planck's constant h, fixed at 6.62607015 × 10⁻³⁴ kg·m²/s. The kilogram is the unit that makes this equation operational, given the definition of the meter and that of the second.
All SI units are now defined by fundamental constants whose numerical value is fixed by international convention. No fundamental unit is any longer related to a singular material artifact. The system of units is no longer suspended from an object. It is suspended from a network of constants, definitions and realization devices.
Doctrine
When an instrument becomes more stable than the phenomenon it measures, it ceases to be a measuring tool. It becomes the referential that defines what is measurable. Measurement absorbs the measured into the order of the referential.
The tuning fork manufactures time not because it creates duration, but because it imposes the beat to which phenomena must be related.
This inversion is not a historical accident. It is the normal trajectory of any mature metrological system. Precision increases until it exceeds that of the phenomenon initially taken as standard. The initial phenomenon then becomes an unstable system that the more precise instrument reveals in its variability. Measurement does not merely change precision. It changes direction.
Open vector
The system is no longer founded on a simple material outside. It is interdefined: the meter depends on the second and the speed of light. The kilogram depends on the meter, the second and Planck's constant. The second depends on the cesium transition. The whole holds by the conventional fixing of the numerical value of physical constants.
When a system of units is no longer backed by an external object, what does it still measure?
