Leap second

A leap second is an occasional one-second adjustment applied to Coordinated Universal Time (UTC) to maintain close agreement with Universal Time (UT1), the measure of time based on the Earth’s rotation. Because the rotation of the Earth is not constant and varies due to climatic, geological, and astronomical factors, UTC—derived from the highly regular International Atomic Time (TAI)—would drift away from mean solar time without such corrections. Leap seconds ensure that the difference between UTC and UT1 never exceeds 0.9 seconds.

The Need for Leap Seconds

UTC underpins international civil timekeeping and is based on the SI second as realised by atomic clocks. These clocks follow TAI, which steadily diverges from solar time because the length of the mean solar day is not constant. In particular, irregularities in Earth’s rotation require periodic adjustments to keep UTC synchronised with UT1. This adjustment takes the form of a positive or, potentially, negative leap second.
Leap seconds have been added since their introduction in 1972. By 2016, 27 leap seconds had been inserted, with the most recent added on 31 December 2016. Decisions on insertion are made by the International Earth Rotation and Reference Systems Service (IERS) and are typically announced around six months in advance.

Historical Development of the Second

The modern second has evolved over many centuries:

• Ancient Origins: Around AD 140, Ptolemy subdivided the solar day sexagesimally, although not in a manner equivalent to the modern second. Medieval Islamic scholars refined this system: by 1000, al-Biruni had subdivided the day into 24 equinoctial hours, each further divided into minutes, seconds, thirds, fourths, and fifths, establishing the second as a defined fraction of the mean solar day.
• Nineteenth-Century Redefinitions: In 1874, the second was adopted as the base unit of time in the CGS system. However, the discovery of irregularities in Earth’s rotation led to redefinitions by the International Astronomical Union (IAU) in 1952 and 1955, first in relation to the sidereal year and then the mean tropical year.
• Twentieth-Century Refinement: In 1956 the second was tied to a specific fraction of the tropical year 1900. This approach remained inadequate for precise measurements, leading to the definitive 1967 SI definition: the second as 9 192 631 770 periods of radiation from the caesium-133 atom. This corresponded closely to the earlier astronomical ephemeris second and represented a shift to a purely atomic standard.

By the mid-twentieth century, the mean solar day had already grown longer than 86 400 SI seconds due to rotational slowing; thus, time standards based on atomic seconds inevitably diverged from UT.

The Introduction of UTC and the Leap Second

UTC was introduced in 1960, combining the stability of atomic time with the need to stay aligned with solar time. Initially, synchronisation was achieved by adjusting the rate of UTC relative to TAI—a practice known as the rubber second. Between 1960 and 1971, frequency offsets and occasional small steps ensured that UTC matched UT2, a smoothed version of UT1.
In parallel, stepped atomic time (SAT) was adopted by certain time services from 1966, employing periodic 0.02-second adjustments to remain within 0.1 seconds of UT2.
The modern leap-second system commenced in 1972. At this point, UTC was already 10 seconds behind TAI, but from 1972 onwards both have run at the same ticking rate, diverging only when leap seconds are added to UTC. Today the difference equals the initial 10 seconds plus the 27 leap seconds inserted since, totalling 37 seconds.

Causes of Variations in Earth’s Rotation

The Earth’s rotation exhibits both long-term and short-term variations:

• Tidal Friction: The dominant long-term mechanism, caused by the gravitational interaction between Earth, Moon, and Sun. It gradually slows Earth’s rotation, lengthening the day by approximately 2 to 3 ms per century.
• Geophysical Processes: Redistribution of mass within Earth’s interior alters its moment of inertia, affecting rotation due to conservation of angular momentum. Changes in mantle convection and core dynamics contribute to secular and periodic variations.
• Glacial Rebound: The gradual rise of land masses previously compressed by ice sheets shortens the day by about 0.6 ms per century, partially offsetting tidal friction.
• Sudden Geological Events: Major earthquakes can cause abrupt shifts. The 2004 Indian Ocean earthquake was estimated to have shortened the day by 268 microseconds.
• Climate Effects: Variations in atmospheric pressure, ocean circulation, and hydrological cycles lead to rotational fluctuations. Recent studies indicate that melting ice mass and associated water redistribution can affect rotation measurably.

Historical modelling by Stephenson and Morrison based on astronomical records from antiquity to the modern era indicates a general increase of the mean solar day by about 1.4 ms per century in recent centuries, shaped by both long-term trends and multi-century oscillations.

Behaviour of the Mean Solar Day

It is incorrect to interpret leap seconds as a measure of Earth’s slowing rotation. Instead, they reflect the accumulated difference between atomic and rotational time. For example, although leap seconds were added frequently between 1972 and 2016, analyses show that the average day length over this period fluctuated and even decreased at times.
In 2020, Earth recorded the 28 shortest days since 1960, each under 86 400 seconds. On 29 June 2022, Earth experienced the shortest day ever measured, approximately 1.59 milliseconds shorter than 24 hours. Rapid rotation during such periods has led to discussions of a negative leap second, a procedure never yet applied.
Recent research, including a 2024 paper in Nature, indicates that redistribution of water from melting ice caps may interplay with core-mantle dynamics, affecting future rotational trends and potentially delaying the need for a negative leap second.

Future of the Leap Second

Leap seconds have proved increasingly problematic in the digital era. Many computer systems and time-critical infrastructures are not designed to handle the extra second smoothly, leading to disruptions, calculation errors, and system failures. These operational challenges intensified debates within international standards bodies.
In November 2022, the 27th General Conference on Weights and Measures resolved to eliminate leap seconds by or before 2035. This transition aims to establish a continuous, uninterrupted UTC that would eventually diverge gradually from UT1 by more than a second, but would avoid the operational difficulties inherent in the leap-second system.
While the long-term strategy for reconciling atomic time with Earth rotation remains under discussion, many experts anticipate new frameworks that accommodate both scientific requirements and modern technological needs.