The leap second: Because our clocks are more accurate than the Earth

We've recently been treated to that extra day in February that reminds us that 2016 is a leap year. Introduced by Julius Caesar, the leap day is necessary because the orbital year is not exactly equal to the 365 days of our calendar year. Without the adjustment, this year’s spring-like Christmas would eventually become routine even without climate change. After a few more generations, the snows of July would give way again to sweltering afternoons. Given enough time, the seasons would march across the calendar.

In order for the months to retain their traditional characters, the leap day is inserted every four years (with some exceptions). It keeps the calendar in sync with our expectations for the seasons.

But throwing an occasional day at the problem isn't enough. Just as a watch requires periodic adjustments to keep it in agreement with the real time, we need to make occasional tweaks to our global watch. But what is this global watch, and what is the “real” time that it needs to agree with?

The global timepiece is the Earth itself, or rather its rotation. This rotation creates the apparent motion of the Sun across the sky, which is the basis of our ancient notions of the time of day. The “real" time is the atomic time: an objective reference, passing with perfect uniformity, defined and tended to by technicians around the world.

For centuries, we expended ingenuity on creating timekeeping machines that, with ever increasing accuracy, allowed us to track the march of the heavens. Today, our clocks are so precise that it's the Earth that fails to stay in synchrony with them. We need an additional adjustment now and then: the leap second.

This adjustment, obviously, is not made to the planet, but to the human system of time that we have constructed to be our Earthly clock. Called the Coordinated Universal Time and known as UTC, it's equal to the Greenwich Mean Time and serves as the basis for all the world's time zones. UTC is an atomic-precision time but, rather than tick away for eternity without meddling, it's adjusted to reflect the rotational position of the Earth.

Let's say that, in your local time zone, noon marks the Sun’s zenith. With UTC, noon will still mark the Sun's zenith for your descendants. And, to make sure that happens, we need to sporadically insert leap seconds into our years. Despite the leap second’s ability to keep the Sun in sync with the clock, however, it has its detractors, which we'll hear from below.

Before we get to them, it's worth looking into why we need the leap second at all. Why doesn't our planet rotate at a constant rate? And why is the irregularity unpredictable, requiring the apparently capricious insertion of leap seconds according to the dictates of a mysterious conclave of time lords?

Random lurches in angular momentum

The use of the term “insertion” is deliberate. Since the introduction of leap seconds in 1972, we have only found it necessary to add them, never to subtract. This is because the main non-uniformity in the Earth’s rotation is a constant slowing down due to the braking action of the tides. Although constant, this braking is gradual: the length of the day has increased by about two milliseconds over the past two centuries. So don't worry—there is no chance of the Earth standing still any time soon.

Tidal friction transfers spin angular momentum into orbital angular momentum of the Earth–Moon system. This causes the Moon to move away from the Earth and the lunar month to become longer. Over geological time scales, this gradual slowing causes the number of days per year to decrease significantly. We find the record of this in the growth patterns of ancient corals, which means that Jurassic dinosaurs probably experienced 23-hour days and 385 sunsets per year.

Superimposed on this gradual slowing down are other fluctuations in the length of the day, which occur on time scales from decades to hours. Their causes are complex and chaotic; therefore the schedule of future leap seconds is inherently unpredictable. The last leap second was inserted on June 30, 2015; when the next one will be needed is unknown.

What can cause the length of the day to vary? Although there are many different processes at work, they all lead to redistributions of mass in or on our planet. These redistributions shift the speed of the Earth's rotation. This will not surprise you if you have ever seen a figure skater perform. As the spinning skater draws his arms in, he (or she) speeds up; and as he extends his arms, he slows down.

It's a great demonstration of the conservation of angular momentum, a fundamental law of nature that is a consequence of the symmetry of space.

A spinning body’s angular momentum is calculated, roughly, by adding up the orbits of all of its bits of mass. More dense bits count for more in the sum, and bits farther from the spin axis count for more than those near the axis. As long as no torque, or twisting force, acts on the body, its angular momentum cannot change: it is conserved. In our skating example, the only appreciable torque is the friction at the contact points between the skates and the ice, very near the “south pole” of the rotating body.

This small bit of friction should gradually slow the skater down. So how does he speed up? As he draws in his arms, he is redistributing mass towards his axis of rotation; since this mass now contributes less to the total angular momentum, the spin must increase for the momentum to remain unchanged.

The same is true of the Earth: if some process transports mass closer to the center of the planet, then it will spin faster and our day will become shorter. If the redistribution is not symmetrical, then the planet will wobble—something else that we've observed.

Geology, gravity and... tree sap?

It turns out that there is plenty of activity, from deep within the planet out to its atmosphere, that creates net redistributions of mass along the Earth's radius. The core and mantle flow in patterns that are largely unobservable and unpredictable; indeed one of the ways this motion can be detected is through measurement of the Earth’s spin. Earthquakes also shift the crust.

The seas contribute: cold water is denser than warm, and seasonal motions of the oceans change the length of the day. The ongoing melting of glaciers, due to climate change, has created a measureable speeding up of the Earth’s rotation, as the “arms” of ice are drawn inward to the sea, and thus toward the axis.

The technology that we use to determine the length of the day has gotten so precise that the signal from the rising of sap in trees (along with other variations in the biomass) has reached the threshold of detectability.

There is an additional mechanism, not available to the figure skater, that affects the length of the day. If the atmosphere or the oceans pick up a predominant flow either east or west, and therefore attain some non-zero total angular momentum, this must be balanced by a compensating change in the spin of the solid Earth.

The action of winds and ocean currents on the length of the day has been subjected to modeling and calculation for some time. Long-time variations in the spin rate, over decades and centuries, have been known about since the early nineteenth century. But only in recent years has measurement become sophisticated enough to see the minute seasonal and daily effects on the speed of the Earth’s rotation.

Responsibility for monitoring the length of the day largely rests with the International Earth Rotation Service, an organization with a name almost as cool as the Office of Planetary Protection. Several observational techniques are used, but the primary method measures the arrival of microwave pulses from extragalactic objects at widely separated observatories. Measurement is delicate—the observatories themselves are attached to the Earth, and move along with its tidal bulge, a displacement that must be accounted for.

Regardless of the challenges, the results are fed into a time system called UT1, which tracks the mean solar day. When the difference between it and UTC exceeds 0.9 seconds, the IERS declares that a leap second shall be deployed.