315 lines
17 KiB
Plaintext
315 lines
17 KiB
Plaintext
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C I R C U M L U N A R
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T R A N S M I S S I O N S
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Issue One May 2021
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==============[ What's the Deal with Leap Seconds? ]===============
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================[ A Brief Overview of Timescales ]=================
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by solderpunk
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ASTRONOMICAL SECONDS
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Why is a second as long as it is, and not a little shorter or a
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little longer? This is a seemingly simple question which leads
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down a deep and delightfully twisted rabbit hole. It's something
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that I wish Neal Stephenson had written an epically long,
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inexplicably compelling 1990s Wired article about, in the spirit of
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his "Mother Earth, Mother Board" or "In the Kingdom of Mao Bell".
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But he didn't, so you're stuck reading this, instead: a brief,
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incomplete, possibly slightly inaccurate overview based on my own
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characteristically obsessive reading on the topic over the past
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week or so.
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For most of the time that the concept of the second has been
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around, its length has been defined implicitly by that of the day.
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Everybody knows the answer to "why is a day as long as it is?" -
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one day is the time it takes the Earth to complete a single
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revolution about its axis. And since there are 60 seconds in a
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minute, 60 minutes in an hour and 24 hours in a day, a second is
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simply one 86,400th of the time it takes the Earth to rotate once.
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Or, if you like, a second is the time it takes for the Earth to
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rotate one 240th of a degree, out of the full 360. End of story,
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right?
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Well, no. This is a perfectly sensible way to define time - for
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some applications, it's the best way to do it. This astronomically
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defined time scale is still in use today in certain contexts. The
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official name of its modern incarnation is Universal Time, or UT
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(technically, there are a few subtly different variants, denoted
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UT0, UT1 and UT2, but we'll gloss over that here). The official
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determination of UT nowadays is based mostly on measurements made
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at observatories tracking the movement of distant radio sources
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across the sky as the Earth rotates. This is easier than making
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precision measurements of the sun, but is still measuring the exact
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same thing.
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EARTH IS A NICE PLACE TO LIVE, BUT IT'S NOT THE BEST CLOCK
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The problem with an astronomical definition of the second is this:
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the Earth doesn't actually rotate at a perfectly constant rate (it
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wasn't until the 19th century that we could build clocks accurate
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enough to notice this). In fact, the Earth's rotation is slowing
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down. Very slowly, of course. Every century, a complete rotation
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takes about 2 milliseconds longer than it used to. The rate of
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slowing down is not steady. Some years the change is more and
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other years it's less. In fact, even though the overall trend is
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one of slowing down, some years the rotation actually speeds up.
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The dynamics of the process are complicated, and we can't make
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accurate long term forecasts. Gravitational interaction between
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the Earth and the moon is the primary driver, but the movement of
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tectonic plates and friction between Earth's surface and its
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atmosphere and oceans have their say, too. The Indian Ocean
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Earthquake in 2004 was powerful enough to shorten the length of a
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day by 2.68 microseconds. There are even periodic variations in
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the rate of rotation that we just don't understand the cause of
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yet. But the take home message is that, whatever the causes,
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astronomical seconds actually have small, random fluctuations in
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their duration over long time spans. If you define the second by
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looking into the skies, no two seconds are exactly the same.
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That's a pretty inconvenient property for the official definition
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of a fundamentally important unit like the second to have. For
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most of the time this definition was used, the fluctuations were
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smaller than we could reliably measure. Certainly, they weren't
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enough to have an impact on everyday life. Nobody was going to be
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late to lunch because of the Earth's unsteady rotation. But by the
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20th century, scientific and technological progress meant these
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tiny fluctuations started to matter, as we began measuring natural
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phenomena and building machines which operated on very small time
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scales. A 10 megahertz radio oscillator, for example, has a period
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of 0.0000001 seconds - only 100 nanoseconds! Gigahertz radiation,
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which is important in radio astronomy and was used for
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communications and radar during WWII decades before it came to
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underpin modern technology like GPS, WiFi, and mobile data
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networks, has periods measured in *picoseconds*. Even very, very
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small variations in the length of a second are enough to make the
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measured frequency of radio waves change, even if the *actual*
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frequency is fixed. Modern technological society simply couldn't
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be built using a wobbly clock like the Earth.
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ATOMIC SECONDS
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Fortunately, in the 1950s, atomic clocks were invented which kept
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time better than any previous mechanism. I'll gloss right over the
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details, but suffice it to say, we came up with a new way to define
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the second which involved measuring the properties of caesium atoms
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instead of looking at things moving through the sky. In 1967, the
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relatively young International System (or SI, for the French
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"Système International") of units redefined the second on this
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basis. The new atomic second was defined such that it had the same
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length as the astronomical second in use before it, as far as
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measurements at the time could tell, but it had the added bonus
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that the length of the second was then fixed and unchanging.
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Caesium atoms at a given temperature "vibrate" (very loosely
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speaking) at a frequency which, as far as we can tell, is
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completely and perfectly stable, and which can be measured very
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accurately in a sufficiently advanced laboratory.
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With the arrival of atomic seconds, a new time scale was also
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defined: International Atomic Time (or TAI, for the French "Temps
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Atomique International"). At midnight on January 1st in 1958, TAI
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and UT were perfectly synchronised. Ever since then, they have
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slowly but surely drifted apart. The seconds of TAI are of
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perfectly unchanging length (as measured by averaging hundreds of
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atomic clocks all over the world), but the seconds of UT fluctuate
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with the Earth's rotation. The accumulated drift up until now is a
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little less than 40 seconds, but it will continue to grow, without
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limit. And while the perfectly uniform seconds of TAI make it the
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perfect tool for some tasks, this drift apart from UT makes it
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problematic for others. If you go outside at noon UT in Greenwich,
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England (or anywhere else at 0 degrees longitude), the sun will
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*always* be high in the sky. This is true today and it will be
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true in a thousand years, Because UT is fundamentally linked to the
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Earth's rotation. TAI, on the other hand, is fundamentally
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divorced from it. Thousands of years in the future, there will
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come a day when, according to TAI, the sun rises in Greenwich at
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midnight.
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This isn't just an abstract concern for the distant future. In the
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late '50s when TAI was defined, it was still common for ships at
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sea to figure out where they were by using a sextant to record the
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position of the sun above the horizon at a certain time and
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consulting a printed table of conversions. For this purpose, ships
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carried the most accurate clocks they could afford, and compared
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them regularly against true UT time using time signals broadcast by
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radio stations all over the world. Celestial navigation works very
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well when using a timescale which is tightly linked to Earth's
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rotation, and hence the position of things in the sky. But if the
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radio time signals switched to broadcasting TAI instead of UT,
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celestial navigation would become increasingly less accurate as TAI
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drifted further out of synch with the Earth and the stars. This
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meant that the "new and improved" TAI time scale wasn't actually an
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improvement for everybody.
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COORDINATING CHAOS
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Instead of broadcasting two different time signals for different
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purposes, which could easily lead to confusion, on January 1st in
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1960 the powers that be (back then that was the International Time
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Bureau, or BIH, for the French "Bureau International de l'Heure",
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but today the torch has been passed to a combination of the
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International Bureau of Weights and Measures, or BIPM, for the
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French "Bureau International des Poids et Mesures" and the
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International Earth Rotation Service, who have the gall to
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abbreviate the *English* version of their name and go by IERS)
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defined yet another time scale, in an attempt to achieve the best
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of both worlds and make everybody happy. Enter Coordinated
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Universal Time, or UTC - at last, something normal people have
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heard of!
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The abbreviation UTC is a strange compromise between the English
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abbreviation CUT and the French abbreviation TUC (for "Temps
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Universel Coordonné"). This is somewhat fitting, because UTC
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itself is a strange compromise time scale between UT and TAI. Like
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TAI, UTC is an atomic time scale. Every second of UTC is exactly
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as long as any other, using the SI standard second based on caesium
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atoms, allowing scientists and engineers around the world to
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calibrate their instruments and reliably measure time intervals and
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frequencies very precisely. But whereas TAI is destined to drift
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ever further away from UT, to the chagrin of sailors and
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astronomers, UTC is kept synchronised closely enough with UT that
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it allows seafarers to perform celestial navigation with sufficient
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accuracy for safe ocean passage. This synchronisation is achieved,
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like all technical compromises, using ugly hacks. It cannot be any
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other way, as UTC is a stubborn attempt to reconcile two desirable
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but fundamentally incompatible properties of a timescale: perfectly
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regular seconds, and synchronisation with a spinning globe whose
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rate of rotation is unpredictably irregular.
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The precise nature of the ugly hack underlying UTC has changed
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somewhat since it was first defined, but for almost 50 years now,
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starting in 1972, the ugly hack of choice has been the leap second.
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The way it works is this. The difference between UTC and UT - a
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quantity denoted DUT - is carefully monitored. Any time it looks
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like that difference is on track to exceed 0.9 seconds, in either
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direction, UTC is kicked back into alignment by either inserting or
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removing a single second on one particular day. This makes UTC the
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*only* time scale where the number of seconds in a day is not
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absolutely fixed at 86,400 by definition. There almost always
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*are* 86,400 seconds in a UTC day, but 86,401 and 86,399 are also
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allowed when necessary to keep the time scale locked to the
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movement of the sun across the sky.
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So far, there have been 27 leap seconds defined, although UTC and
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ATI are today exactly 37 seconds apart - the other 10 seconds come
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from hacks applied before leap seconds were established in 1972.
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All of them to date have been insertions rather than removals.
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They don't happen on a regular, predictable basis, like leap years
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(which are an adjustment for the fact that the time it takes the
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Earth to orbit the sun once, defining a year, is not perfectly
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divisible by the time it takes the Earth to rotate once, defining a
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day). Because the Earth's rate of rotation fluctuates randomly,
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sometimes slowing down and sometimes speeding up, astronomers need
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to be actively on the lookout for excessive values of DUT. When
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it's decided a leap second is needed - it's the IERS who makes that
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call - they are announced at least six months in advance. They're
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allowed to occur on either June 30th or December 31st, and are
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inserted or deleted at midnight UTC (which is the middle of the day
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in some time zones, of course) on those days. At the time of
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writing, the last leap second happened on December 31st, 2016. In
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principle, six months is enough advance warning that nobody doing
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anything which depends on precise time synchronisation should be
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caught by surprise when a leap second rolls around. In practice,
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it's not always so simple.
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INCREASING IMPLEMENTATION BURDEN AND AN UNCERTAIN FUTURE
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Leap seconds have always had their critics, but at the time they
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were adopted, their benefits arguably balanced their associated
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hassle. 50 years later, this hack is starting to show its age.
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The advent of cheap and reliable GPS technology means that
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celestial navigation at sea is now rarely a matter of life or death
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(although some sailors still appreciate the relative simplicity of
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the technology it relies on), removing some of the argument for
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making sure UTC stays in lock step with the Earth's rotation. At
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the same time, the internet has come along: a massive network of
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computers talking to each other, with the frequent need for
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activity on one to be synchronised with activity on another (hence
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tools like the Network Time Protocol, NTP). Computer programmers
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*hate* leap seconds, for the same reason they hate Daylight Saving
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Time: they complicate time calculations (you can't accurately
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calculate the number of seconds between two UTC timestamps without
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consulting a table of when previous leap seconds were inserted) and
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are a frequent cause of confusion and errors, when one system
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implements them differently from another its trying to interoperate
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with.
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Affordances for leap seconds are often added to software as an
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afterthought - if they are added at all. Some systems represent
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the extra second using the timestamp 23:59:60, but others instead
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repeat the timestamp 23:59:59 twice (since some software will fail
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to parse a timestamp ending in :60). Other systems "smear" the
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leap second out over longer time periods, like 24 hours, to avoid
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problems associated with sudden discontinuities. This just leads
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to a whole day of small, slowly varying errors compared to
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non-smearing systems. Some systems, of course, forget to do
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anything at all. Because all the leap seconds to date have been
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insertions rather than removals, it's a safe bet that there's
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plenty of software out there which has worked correctly so far but
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will fail the first time a second is removed. And the Earth's
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rotation is going through a bit of a fast phase right now, so the
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first negative leap second might be looming on the horizon.
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The software interoperability situation at the time of a leap
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second is bad enough that several major stock exchanges simply
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agreed to voluntarily shut down for an hour around midnight UTC in
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2016, rather than risk problems by continuing to trade during the
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leap second. Given that a number of major web services, including
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Amazon, Instagram, Netflix and Twitter, experienced outages around
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this time, this was probably not a bad idea. Of course, simply
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shutting time critical services off for every leap second isn't
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always an option. It's one thing to shut down the New York Stock
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Exchange for an hour, but Air Traffic Control has to stay up 24/7.
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It's no surprise that increasingly many voices in the tech industry
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are calling for leap seconds to be abolished. Plenty of people are
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very unhappy with that idea, of course, not to mention there's no
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consensus on what to do instead.
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It's far from clear what the future holds for the leap second. As
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software continues to eat the world, the headaches leap seconds
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cause are only likely to get worse. The atomic definition of
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second likely isn't going away any time soon, though, and that
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means that getting rid of leap seconds entirely means abandoning
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the millennia old notion that the way we represent time is
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intimately linked with the natural cycle of night and day.
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Assuming we're not willing to do that, there are only two
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alternatives: coming up with a new ugly hack which is somehow less
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problematic, or giving up on a "one size fits all" time scale.
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BUT WAIT, THERE'S MORE!
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If you think this story has been needlessly fiddly and complicated,
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rest assured I have skipped over a tonne of details. If you're
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actually interested to learn more, I highly recommend the article
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"The leap second: its history and possible future", which you can
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easily find on the web (full citation below), along with, as
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always, following Wikipedia links wherever they take you. Along
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the way you can learn the difference between UT0, UT1 and UT2, meet
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other exciting astronomic and atomic time scales like Ephemeris
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Time (ET), GPS Time (GPST) and Terrestrial Time (TT), and discover
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that the SI system of units defined the second based on something
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other than Earth's rotation when it was established in 1960, seven
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years before the caesium definition was adopted.
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- - -[ REFERENCES ]- - -
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Nelson, R., McCarthy, D., Malys, S., Levine, J.M., Guinot, B.,
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Fliegel, H., Beard, R., & Bartholomew, T. (2001). The Leap Second
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- Its History and Possible Future. Metrologia, 38, 509-529.
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"Time-nuttery 101" by Ole Petter Ronningen
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https://efos3.com/TimeNut.html
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"UTC might be redefined without Leap Seconds" by Steve Allen
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https://ucolick.org/~sla/leapsecs/timescales.html
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