Just a Second…

A close-up photograph of an analog clock showing the hands just reaching the hour.What Does a Second Look Like?

1/60 minute.  1/3,600 hour.  1/86,400 day.  1/1 hertz.  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 a 133 55Cs caesium isotope corresponds to one second.  But what does it look like?  And where might you find a second?

A diagram showing the transition energy levels of the electron in a caesium atom.
Energy levels transition in a Caesium-133 atom

As a unit of time, the ‘second entered the English language in the late 16th century, about a hundred years before it came to be measured accurately.  Scientists who used Latin, including Danish astronomer Tycho Brahe (1546 – 1601) and German Johannes Kepler (1571 – 1630), used the Latin term secunda – the second division by 60 of an hour – with the same meaning as far back as the 1200s.


An animation showing the pendulum of a clock swinging back and forth.
This clock pendulum sways every half-second. Source: Wikipedia

Astronomical Second

Measuring time with extreme precision is a relatively recent development in human history.  Until the 17th century, minutes and seconds could not be accurately assessed.

Then, the pendulum clock was invented.  It uses a pendulum – a swinging weight – as its timekeeping element.


The Ideal Pendulum


The pendulum is a harmonic oscillator that swings back and forth in a precise fashion dependent on its length.  The pendulum swings at regular time intervals, and it effectively resists swinging at other rates.

When a pendulum is displaced sideways from its resting equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back towards its equilibrium position.  When released, the restoring force combined with the pendulum’s mass causes it to oscillate about the equilibrium position, swinging back and forth.

The graph of a typical sine wave, showing how its amplitude, its period, its phase and vertical shifts are calculated.
Graphic Representation of the Pendulum’s Oscillation  Source: Mathsisfun.com

The time for one complete cycle – a left swing and a right swing – is called the period.  The period depends on the length of the pendulum, and also to a slight degree on its weight distribution (the moment of inertia about its own centre of mass) and the amplitude – the width of the pendulum’s swing.

At standard gravity, its length is 0.994 m (39.1 in).  In 1660, the Royal Society proposed that it be taken as the standard unit of length.  In 1675, Italian polymath Tito Livio Burattini proposed that it be named the metre.  In 1790, one year before the metre was ultimately based on a quadrant of the Earth, Talleyrand proposed that the metre be the length of the seconds pendulum at a latitude of 45°.

A 19th century etching representing Henry Kater and two of his assistants using his invention - a reversible freeswinging pendulum - to measure gravity.
Measuring Gravity using Kater Invariable Pendulum in India, 1821

Pendulums in clocks are usually made of a weight or bob (P) suspended by a rod of wood or metal.  To reduce air resistance (which accounts for most of the energy loss in clocks), the bob is traditionally a smooth disk with a lens-shaped cross section.  For quality clocks, the bob is made as heavy as the suspension can support and the movement can drive it, since this improves the regulation of the clock.

A slightly different apparatus was used by British-German physicist Henry Kater (1777-1835) to determine local gravity.  The pendulum consists of a rigid metal bar with two pivot points, one near each end of the bar.  It can be suspended from either pivot and swung.  It also has either an adjustable weight that can be moved up and down the bar, or one adjustable pivot, to adjust the periods of swing.

Kater’s pendulum is a reversible free-swinging pendulum invented in 1817.  For about a century, until the 1930s, this type of pendulum and its various refinements remained the standard method for measuring the strength of the Earth’s gravity during geodetic surveys.


In 1685, Tito Livio Burattini proposed one of the first formal definitions of the second as

1/86,400th of a solar day,


in his treatise ‘Misura Universale‘ on Metrology – the science of measurement.

The astronomical second was born.

From the time of its invention by Christiaan Huygens in 1656 until the 1930s, the pendulum clock was the World’s most precise timekeeper.  Over the 18th and 19th centuries, pendulum clocks were in widespread use, whether in homes, factories, offices and railroad stations.  They served as the primary time standards for scheduling daily life, work shifts, and public transportation.  Their greater accuracy allowed the faster modern pace of life to develop, and to bring in the Industrial Revolution.

You might find a second here…


A picture showing the Earth-Moon binary system.
Earth-Moon System: Over time, the Moon’s gravitational pull applies a steady brake to the Earth’s rotation. Source: ESA


For a number of reasons, however, the rotation of the Earth is not a reliable standard:

  • churning magma in the planet’s core,
  • growth and shrinkage of sea ice, 
  • wind battering mountains,
  • gravitational pull of the Moon and
  • resulting tidal shifts.


All these impose a steady brake on the Earth’s spin.  The combined effects lead to microseconds of variation in the duration of its daily rotation, making the days of 2013 roughly two milliseconds longer than the days of 1900.

Because Earth’s rotation is irregular, the value of a second based upon its rotation is also in turn ever so slightly irregular.  Leap seconds – and leap years – must be added as basic ways to keep the clock in sync with the Earth and its seasons.

In 1832, German mathematician Gauss proposed using the second as the base unit of time in his millimetre-milligram-second system of units.  In 1862, the British Association for the Advancement of Science $ ($BAAS$ )$ stated that:

“All men of science are agreed to use the second of mean solar time as the unit of time.”


During the 1940s, the  internationally-adopted MKS system of units defined the second as

1/86,400th of a mean solar day.


But, such imprecision became problematic when Quantum Mechanics and Einstein’s Theory of Relativity broke rank from 20th-century classical physics.  Experimental verification of these theories demanded a steadier unit of time, as did emerging technologies, like radio broadcasting and electricity distribution.

Something had to be done.


Atomic Second

In January 1945, Columbia University professor and Nobel Laureate Isidor Rabi outlined the engineering blueprints for the most accurate clock in the universe, tuning in on the radio frequencies at the very hearts of atoms, and beating in harmony with the ‘cosmic pendulum.’  Within a few years, the U.S. National Bureau of Standards had constructed a prototype atomic clock, and by 1955, England’s National Physical Laboratory unveiled the first caesium-based model, which ultimately changed the way we measure time.

A black and white photograph showing Jack Parry and Louis Essen standing next to the World's first caesium-133 atomic clock.
Essen and Parry with the 1955 Caesium Atomic Clock at the National Physical Laboratory, UK. It kept time accurate to a second in 300 years.

English physicist Louis Essen then became interested in the possibility of using the frequency of atomic spectra to improve time measurement.  Atoms have very precise resonances, each associated with one particular frequency which is a fundamental constant of Nature.  An atom will always have the same transition frequency anywhere in the Universe and so by starting from an atom, we have a fundamentally constant reference for time-keeping.

Caesium, the element most commonly used in high-precision atomic clocks, is nudged into an excited state at a microwave frequency of just under 9.2 billion cycles per second. In a caesium-based atomic clock, each cycle can be thought of as a pendulum swing.

The feasibility of measuring time using caesium as an atomic reference had been demonstrated by the U.S. National Bureau of Standards.  In 1955, Essen and Jack Parry developed the first practical atomic clock by integrating the caesium atomic standard with conventional quartz crystal oscillators to allow calibration of existing time-keeping.

A diagram of Essen's atomic clock.
Essen’s Clock Schematics: Tying time to the atom, the clock attained unprecedented precision. Source: RSC

Essen’s clock was a two-metre-long horizontal apparatus with a source of caesium atoms on one end, a microwave cavity in the middle probing the atoms’ frequency and a sensitive detector at the other end.  When it was first put in to operation, it was accurate to one millisecond a day – equal to one second in about 300 years.

In 1956, the second was redefined in terms of a year – the period of the Earth‘s revolution around the Sun, for a particular epoch because the Earth’s rotation on its own axis is not sufficiently uniform as a standard of time.

The second was thus defined as:

the fraction 1/31,556,925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time.

Later, the SI second, referred to as ‘atomic time’, was verified to be in agreement, within 1 part in 1010, with the second of ephemeris time, determined from lunar observations.

You might find a second there…


Ephemeral Time

The 1960 Système International definition abandoned any explicit relationship between the scientific second and the length of a day, as most people understand the term.  With the development of the atomic clock, it was decided to use atomic time as the basis of the definition of the second, rather than the revolution of the Earth around the Sun.

A schematic drawing showing a modern caesium fountain.
NIST-F1 Caesium Fountain Source: NPL

In October 1967, after more than a decade of negotiation, representatives from thirty-six countries convened in Paris for the 13th General Conference on Weights and Measures. Within a week, they had hammered out, in a single sentence, a new basis for the international second:

“The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyper-fine levels of the ground state of the caesium-133 atom.”

The base unit of time became decoupled from the uneven pirouette of Earth, defined instead by an intrinsic atomic property.

During the 1970s, physicists realised that gravitational time dilation caused the second produced by each atomic clock to differ depending on its altitude.  A uniform second was produced by correcting the output of each atomic clock to mean sea level, lengthening the second by about 1 x 10-10 s.

The correction was applied at the beginning of 1977 and formalised in 1980.  In relativistic terms, the SI second is defined as the proper time on the rotating geoid.

The 1997 revised definition implies that the ideal atomic clock contains a single caesium atom, at rest, emitting a single frequency.  In practice, the definition means that high-precision realisations of the second should compensate for the effects of the ambient temperature (black-body radiation) within which atomic clocks operate, and extrapolate accordingly to the value of the second at a temperature of absolute zero.

We are constantly redefining the second.


Fleeting Time

Most of today’s atomic clocks keep time by counting high-frequency microwaves.  To set that frequency, metrologists – as scientists of measurement are known – exploit a law of quantum physics: atoms become excited, and their structure changes when they are exposed to discrete amounts of energy.

The amount of energy required to cause an atom’s transition from one particular state to another is immutable.

The atomic clock operating in the microwave region is nowadays facing a challenge by atomic clocks operating in the optical region.

According to Ludlow et al., 2006:

“In recent years, optical atomic clocks have become increasingly competitive in performance with their microwave counterparts.  The overall accuracy of single-trapped-ion-based optical standards closely approaches that of the state-of-the-art caesium fountain standards.  Large ensembles of ultracold alkaline earth atoms have provided impressive clock stability for short averaging times, surpassing that of single-ion-based systems.  So far, interrogation of neutral-atom-based optical standards has been carried out primarily in free space, unavoidably including atomic motional effects that typically limit the overall system accuracy.  An alternative approach is to explore the ultranarrow optical transitions of atoms held in an optical lattice.  The atoms are tightly localized so that Doppler and photon-recoil related effects on the transition frequency are eliminated.”

In 2013, Ludlow et al. write in ‘An Atomic Clock with 1018 instability’:

“Atomic clocks have been transformational in science and technology, leading to innovations such as global positioning, advanced communications, and tests of fundamental constant variation.  Next-generation optical atomic clocks can extend the capability of these timekeepers, where researchers have long aspired toward measurement precision at 1 part in 1018.  This milestone will enable a second revolution of new timing applications such as relativistic geodesy, enhanced Earth- and space-based navigation and telescopy, and new tests on physics beyond the Standard Model.”

But… Where might you find the perfect second?

Really though?


The Perfect Second

A photograph of an optical clock.
Optical clocks use lasers to measure the atoms’ frequencies. Source: NPL

A number of metrology labs around the World have been developing a new generation of atomic timepieces, known as optical, or optical-lattice, clocks.  Because these clocks rely not on microwaves but on lasers, which operate at far higher frequencies, they can split each second into more intervals.

The latest most accurate timepiece is a strontium fountainAt the heart of the clock, which occupies two rooms, is a single ion of strontium – a pliable metal known for its ruby incandescence in fireworks, and has number thirty-eight on the Periodic Table.

The ion is trapped by lasers and held perfectly centred in a small vacuum, where it is shielded from magnetic fields and cooled to a fraction of a degree above absolute zero.  The ion itself must remain as isolated as possible from the external universe.

The result is a new kind of atomic clock, and one of the most accurate timekeeping devices ever created.

The single-ion clock measures the four hundred and thirty trillion light waves per second required to energise a strontium atom.  It converts this into four hundred and thirty trillion “ticks,” parsing time more finely than any of today’s microwave clocks.

A recent test by the National Institute of Standards and Technology demonstrated an optical clock, running on the rare-earth metal ytterbium, that breaks every second into more than five hundred trillion intervals of a second.

10-1s dsdeci-
10-6smu smicro-


A second can make a World of difference.


Global Positioning System


Exquisitely precise timing is built into every aspect of modern infrastructure.  From G.P.S. technology to smartphones and computer networks, the Internet and electrical power, a whole range of applications require synchronisation down to the billionth of a second.

The steady backbeat of atomic clocks is what makes them work.

For example, we look at global positioning systems.  When turned on, a G.P.S. receiver triangulates its location using signals from overhead satellites.  These satellites, outfitted with small atomic clocks, stamp every signal transmission down to the nanosecond, or billionth of a second. 

Because the speed of the satellite’s signal is known – approximately a foot per nanosecond – by measuring the precise amount of time it spends in transit to the receiver, a ground location can be derived using the satellites as reference points.

If we are only capable of measuring seconds down to the millionths – the length of time it takes a signal to travel a thousand feet, G.P.S. estimates could be off by miles.  It would be akin to designing a microchip with a measuring tape.


Today’s optical clocks will necessitate ever another definition of the second – one based on laser frequencies and, potentially, an element other than caesium. The question of which particular element will define the next second – strontium or ytterbium? – remains open.

A new definition may arise at the 2019 General Conference on Weights and Measures, or even the one after that, in 2023.

Atomic time was 60 years old this month.


Leap Seconds

A leap second is a one-second adjustment that is occasionally applied to Coordinated Universal Time (UTC) to remain in keeping with a time of day that is close to the mean solar time, or UT1.  Because they depend on measurements of the Earth’s rotation, which varies unpredictably, leap seconds occur at irregular intervals.

Leap seconds are announced only six months in advance, which means computers and software cannot be supplied with leap seconds programmed in, and they must be inserted manually leaving plenty of room for potential errors in modern financial  and navigation systems, as well as in communications networks.

A computer screen capture showing the 2012 leap second. It reads as follows: "Right now, the official U.S. time is: 23:59:60 Saturday, June 30, 2012 Accurate within 0.2 seconds".
Screen capture of the UTC clock from time.gov

Since the implementation of this system of correction in 1972, 25 such leap seconds have been inserted.  The most recent one happened on June 30, 2012 at 23:59:60 UTC.

The “leap second” means the last minute of June 2015 will have 61 seconds in it.  While 23:59:59 usually becomes 00:00:00, the leap second will ensure the time becomes 23:59:60.

There, you see!  I told you I would find a second…