Fri. Mar 24th, 2023
The leap second: because our clocks are more accurate than the Earth

We were recently 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 again give way to sweltering afternoons. Given enough time, the seasons would march across the calendar.

To ensure that the months retain their traditional character, the leap day is inserted every four years (with a few exceptions). It keeps the calendar in sync with our expectations for the seasons.

But throwing a day at the problem now and then isn’t enough. Just as a watch requires periodic adjustments to keep it in line with real time, we occasionally need to make adjustments to our global watch. But what is this global watch and what is the “real” time it should correspond to?

The global clock is the Earth itself, or rather its rotation. This rotation creates the apparent movement of the sun across the sky, which is the basis of our ancient beliefs about the time of day. The “real” time is atomic time: an objective reference, perfectly uniformly transient, defined and maintained by technicians all over the world.

For centuries we have spent ingenuity creating timekeeping machines that enabled us, with increasing accuracy, to track the march of the heavens. Today, our clocks are so accurate that it’s the Earth that fails to keep in sync with them. Occasionally we need an extra adjustment: the leap second.

Of course, this adjustment is not made for the planet, but for the human time system that we constructed to be our Earth clock. Called Coordinated Universal Time and known as UTC, it is equivalent to Greenwich Mean Time and serves as the basis for all of the world’s time zones. UTC is an atomic-precision time, but instead of ticking away for eternity without interference, it has been adjusted to reflect the rotational position of the Earth.

Let’s say that in your local time zone, noon marks the zenith of the sun. With UTC, noon still marks the sun’s zenith for your descendants. And in order for this to happen, we need to insert leap seconds into our years sporadically. However, despite the leap second’s ability to keep the sun in sync with the clock, it has its detractors, which we’ll hear about below.

Before we get to them, it’s worth examining why we need the leap second in the first place. Why doesn’t our planet rotate at a constant speed? And why is the irregularity unpredictable, requiring the apparently erratic insertion of leap seconds according to the dictates of a mysterious conclave of time lords?

Random swings in angular momentum

The use of the term “insertion” is intentional. Since the introduction of leap seconds in 1972, we’ve only found it necessary to add them, never to subtract them. This is because the main non-uniformity in the Earth’s rotation is a constant deceleration 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’s no chance the Earth will stand still anytime soon.

Tidal friction transfers the spin angular momentum into the orbital angular momentum of the Earth-Moon system. This causes the moon to move away from the earth and the lunar month lengthens. On 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, meaning that Jurassic dinosaurs probably went through 23 hours a day and 385 sunsets a year.

Adding to this gradual slowdown are other fluctuations in the length of the day, occurring on timescales ranging 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 is needed is not known.

Why can the length of the day vary? While there are many different processes at work, they all lead to mass redistribution in or on our planet. These redistributions shift the speed of the Earth’s rotation. This won’t surprise you if you’ve ever seen a figure skater perform. As the spinning skater pulls 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 results from the symmetry of space.

The angular momentum of a revolving body is roughly calculated by adding together the orbits of all its masses. More dense bits count for more in the sum, and bits farther from the axis of rotation count for more than those near the axis. As long as there is no torque or torque acting on the body, angular momentum cannot change: it is conserved. In our skating example, the only noticeable torque is the friction at the contact points between the skates and the ice, near the “south pole” of the rotating body.

This little bit of friction should gradually slow the skater down. So how does it speed up? As he retracts his arms, he redistributes the mass to 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 goes for 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, the planet will wobble – another thing we observed.

Geology, gravity and… tree sap?

As it turns out, there’s a lot of activity from deep inside the planet to the atmosphere that creates a net redistribution of mass along the Earth’s radius. The core and mantle flow in patterns that are largely imperceptible and unpredictable; indeed one of the ways this motion can be detected is by measuring the rotation of the earth. Earthquakes also shift the crust.

The seas contribute: cold water is denser than warm, and seasonal movements of the oceans change the length of the day. The continued melting of glaciers, due to climate change, has led to a measurable acceleration in the Earth’s rotation as the “arms” of ice are pulled inward towards the sea, and thus towards the axis.

The technology we use to determine the length of the day has become so accurate that the signal from sap rising in trees (along with other biomass variations) 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 oceans pick up a predominant current, either to the east or to the west, and thereby reach a non-zero total angular momentum, this must be compensated by a compensating change in the rotation of the solid Earth.

The effect of winds and ocean currents on the length of the day has been subject to modeling and calculation for some time. Ever since the early nineteenth century, long-lasting variations in spin speed over decades and centuries have been known. But it’s only in recent years that measurement has become sophisticated enough to see the minuscule seasonal and diurnal effects on the rate of Earth’s rotation.

The responsibility for monitoring the length of the day lies largely with the International Earth Rotation Service, an organization with a name almost as cool as the Office of Planetary Protection. Various observing techniques are used, but the primary method measures the arrival of microwave pulses from extragalactic objects at widely separated observatories. Measurements are delicate – the observatories themselves are fixed to the Earth and move with the 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 average solar day. When the difference between UTC and UTC is greater than 0.9 seconds, the IERS declares that a leap second will be deployed.

The opponents of the leap second

The daily life of a large part of humanity depends on the proper functioning of a huge network of computers. Each contains a clock, and these clocks expect the time 23:59:59, or one second before midnight, to be followed by 00:00:00 one second later. When the leap second is added, the convention is to interpolate the impossible time 23:59:60 between the two times mentioned above.

What could go wrong? Well, countless computer programmers may not be aware of the possibility of a leap second to begin with. Every time another leap second arrives, IT departments around the world brace themselves. Critical systems, such as those that handle airline reservations, occasionally crash and take some of their network partners with them.

Some officials say leap seconds are just not worth it. This group believes that our descendants would be fine with the minuscule drift of the afternoon, and that preserving the traditional meanings of the hours is not worth the recurring technological breakdowns. There have been reports of significant tensions, and voices have even been raised at meetings of timekeepers of the international scientific community, where the topic of the possible abolition of the leap second has been raised.

Others are looking for technical solutions, such as the approach of Amazon and Google, which “smudge out” the seconds leading up to the official leap second so that their clocks adjust gradually.

Whatever compromise we eventually agree on on timekeeping, the fact that our civilization has reached the point where we can observe hourly variations in the speed at which our planet rotates should be a source of surprise and pride.

The author would like to thank astronomer Dr. Alice Monet for providing information and stimulating discussion on the leap second.

By akfire1

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