Second

• 1. Introduction

  ›

  The second is the smallest unit of time most people use in daily life, and yet almost nobody knows where it came from or what it actually measures. Its symbol is a lowercase s. Its definition today involves a caesium atom, quantum physics, and a number that runs to ten digits. But the story of how humanity arrived at that definition spans millennia, several false starts, and one very famous pendulum.

  Sexagesimal divisions of the day, meaning divisions based on the number sixty, have existed since the third millennium BC. Sundials and water clocks were among the first timekeeping devices. For most of that history, no instrument could actually measure a second. The unit existed as a mathematical idea long before it existed as a physical reality.

  The word itself is a clue. "Minute" comes from the Latin pars minuta prima, meaning "first small part" of the hour. "Second" comes from pars minuta secunda, the "second small part", dividing the minute into sixty again. The name is literally a receipt for how it was derived.

  What the documentary ahead will trace is a journey: from scratches on sundials to pendulums to quartz crystals to atoms cooled to one millionth of a degree above absolute zero, each step pushing timekeeping closer to nature itself.

• 2. Before the Clock

  ›

  Taqi al-Din, working during the third quarter of the 16th century, built a clock that marked every minute. That was already a precision achievement for its era. Seconds on a clock face came slightly later, appearing during the last half of the 16th century. The earliest known spring-driven timepiece with a hand that actually swept through seconds is an unsigned clock depicting Orpheus, held in the Fremersdorf collection and dated between 1560 and 1570.

  Before those instruments existed, the hour itself was not even uniform. Early mechanical clocks, which appeared starting in the 14th century, divided the hour into halves, thirds, and quarters, and sometimes into twelve parts. Sixty minutes per hour was not practical because the hour's duration was not fixed. It was not until the first clocks capable of displaying minutes appeared near the end of the 16th century that the hour gained a stable sixtieth subdivision.

  In 1579, Jost Bürgi built a clock for William of Hesse that marked seconds. Two years later, in 1581, Tycho Brahe modified clocks at his observatory to also display seconds, though he acknowledged those seconds were not accurate. By 1587, Brahe was noting in his records that his four observatory clocks disagreed with each other by plus or minus four seconds, a frustration that tells us how hard reliable timekeeping still was.

  The difference between apparent solar time, the time shown by a sundial, and mean time, the uniform time kept by a mechanical clock, had been recognized by astronomers since antiquity. But until accurate mechanical clocks existed in the mid-17th century, the sundial was the only reliable standard available to most people. That meant the length of a "second" literally varied depending on the season.

• 3. The Pendulum Revolution

  ›

  In 1656, Dutch scientist Christiaan Huygens invented the first pendulum clock. Its pendulum was just under a meter long, which gave it a swing of exactly one second per beat. The escapement ticked every second. For the first time, a machine could count seconds accurately.

  The physics behind this was straightforward: a pendulum about one meter long naturally takes one second to swing from side to side. That physical fact, which Huygens built into his design, tied the second to a property of the Earth itself, specifically the planet's gravitational pull at its surface.

  By the 1730s, roughly eighty years after Huygens, John Harrison's maritime chronometers had pushed accuracy to within one second in one hundred days. That was a different order of precision entirely, and it mattered enormously for navigation at sea, where a few seconds of error in timekeeping could translate to miles of error in longitude.

  In 1832, Carl Friedrich Gauss proposed formally adopting the second as the base unit of time in his millimeter-milligram-second system of units. The British Association for the Advancement of Science declared in 1862 that all scientists agreed to use the second of mean solar time as the unit of time. The CGS system, formally proposed by BAAS in 1874, and the MKS system adopted internationally during the 1940s, both kept the same second as their foundation.

• 4. When Earth Proved Unreliable

  ›

  Sometime in the late 1940s, quartz crystal oscillator clocks operating at around 100 kilohertz became accurate to better than one part in 100 million over a single day. A consensus of those clocks kept better time than the rotation of the Earth itself. That observation opened a scientific crisis: the definition of the second was tied to Earth's rotation, but Earth was an imprecise clock.

  Metrologists noted that Earth's orbit around the Sun was far more stable than its rotation. This led, as early as 1950, to proposals to redefine the second as a fraction of the year rather than the day. The Earth's motion had been described in Newcomb's Tables of the Sun, published in 1895, which drew on astronomical observations made between 1750 and 1892.

  In 1952, the International Astronomical Union adopted a timescale based on the sidereal year at the epoch 1900. In 1955, the tropical year was chosen instead, considered more fundamental. By 1956, the second was officially redefined as a specific fraction of the tropical year for 1900 January 0 at twelve hours ephemeris time. That definition was absorbed into the International System of Units in 1960.

  The ephemeris second solved one problem but created another. It was defined relative to a moment already ninety years in the past, calculated from historical observations. It could not be measured directly. Science needed something reproducible in any laboratory at any time, and in the 1950s, atomic clocks were beginning to offer exactly that.

• 5. The Caesium Definition

  ›

  Since 1967, the second has been defined as exactly 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 caesium-133 atom. That specific number was chosen deliberately to match the length of the ephemeris second that preceded it, preserving continuity across the redefinition.

  The 13th General Conference on Weights and Measures adopted this definition in 1967, at the moment when it had become feasible to realize the second from a fundamental property of nature rather than from astronomical observation. Atomic clocks use that specific microwave frequency to count cycles and thereby measure seconds.

  The radiation involved is one of the most stable and reproducible phenomena in nature. The current generation of caesium atomic clocks is accurate to within one second in a few hundred million years. Since 1967, atomic clocks based on atoms other than caesium-133 have been developed with precision a factor of one hundred greater than the original caesium standard.

  By 1997, the CIPM clarified that the definition refers to a caesium atom at rest at a temperature of zero kelvin, meaning the atom is unperturbed by black-body radiation. The most advanced caesium fountain clocks in operation as of 2022, including IT-CsF2, NIST-F2, and PTB-CSF2, cool caesium atoms to one microkelvin in a magneto-optic trap and then launch them vertically through a microwave cavity. Their systematic uncertainty amounts to fifty picoseconds per day.

• 6. The Second's Reach

  ›

  Most of the other SI base units lean on the second for their definitions. The meter is defined by fixing the speed of light in vacuum to exactly 299,792,458 meters per second. The kilogram, the ampere, the kelvin, and the candela also depend on the second in their formal definitions. Among the seven SI base units, only the mole does not. Among the twenty-two named derived SI units, only the radian and the steradian are free of the second.

  Frequency is measured in hertz, which is simply inverse seconds. Speed is meters per second. Radioactive decay is measured in becquerels, also inverse seconds. Acceleration involves seconds squared, and jerk, the rate of change of acceleration, involves seconds cubed. Everyday quantities like kilometers per hour, kilowatt-hours of electricity, and rotations per minute are all ultimately defined in terms of the SI second.

  Light takes 1.3 seconds to travel from the surface of the Moon to Earth, a distance of 384,400 kilometers. Sound travels about 343 meters in one second through air. A stone dropped from rest falls approximately 4.9 meters in one second. A pendulum roughly one meter long swings once per second, which is why pendulum clocks have pendulums about a meter long. The fastest human sprinters cover ten meters in a single second.

  A Gregorian century averages 3,155,695,200 seconds. In astronomy, a Julian year is precisely 31,557,600 seconds. A gigasecond, meaning one billion seconds, is roughly 31.7 years.

• 7. Optical Clocks and What Comes Next

  ›

  A strontium optical lattice clock operating at 430 terahertz, in the red range of visible light, held the accuracy record during the 2010s. It gains or loses less than one second in fifteen billion years, a span longer than the estimated age of the universe. Such a clock is sensitive enough to detect a change in its own elevation of as little as two centimeters, because gravity itself alters the rate at which time passes, a consequence of general relativity.

  Optical clocks use forbidden optical transitions in ions or neutral atoms. Their operating frequencies are far higher than the microwave frequency of caesium, and their natural linewidth is typically around one hertz, giving them extraordinarily high Q-factors and correspondingly better stability than any microwave clock. They use either a single trapped ion or an optical lattice containing many thousands of atoms.

  A future redefinition of the second around an optical frequency would require optical clock reliability to improve to the point where such clocks can contribute to International Atomic Time, which currently runs on caesium-based atomic seconds. A consistent method for comparing signals between distant optical clocks, such as fiber-optic links, would also need to be established before the BIPM could affirm any new definition.

  One candidate for a future definition involves the Rydberg constant, which describes energy levels in a hydrogen atom. Fixing the Rydberg constant to a precise value would yield a new definition, but trapping and cooling hydrogen is technically difficult: hydrogen atoms are very light, move fast, and cause large Doppler shifts. The radiation needed to cool them, at 121.5 nanometers, adds another layer of experimental difficulty. The strontium clock's record of fifteen billion years of accuracy is already the standard to beat.