tag:theconversation.com,2011:/global/topics/leap-second-18331/articlesLeap second – The Conversation2022-11-21T02:42:13Ztag:theconversation.com,2011:article/1949222022-11-21T02:42:13Z2022-11-21T02:42:13ZIt’s time-out for leap seconds: an expert explains why the tiny clock adjustments will be paused from 2035<figure><img src="https://images.theconversation.com/files/496357/original/file-20221121-18-vwota1.jpeg?ixlib=rb-1.1.0&rect=54%2C99%2C5952%2C3908&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><span class="source">Shutterstock</span></span></figcaption></figure><p>Meeting in Versailles, France, on Friday, the Bureau International des Poids et Mesures (BIPM) has <a href="https://www.nytimes.com/2022/11/19/science/time-leap-second-bipm.html">called time-out</a> on “leap seconds” – the little jumps occasionally added to clocks running on Coordinated Universal Time (UTC), to keep them in sync with Earth’s rotation. </p>
<p>From 2035, leap seconds will be abandoned for 100 years or so and will probably never return. It’s time to work out exactly what to do with a problem that has become increasingly urgent, and severe, with the rise of the digital world.</p>
<h2>Why do we have leap seconds?</h2>
<p>Roll back to 1972, when the arrival of highly accurate atomic clocks laid bare the fact that days are not exactly 86,400 standard seconds long (that being 24 hours, with each hour comprising 3,600 seconds).</p>
<p>The difference is only in milliseconds, but accumulates inexorably. Ultimately, the Sun would appear overhead at “midnight” – an indignity metrologists (people who study the science of measurement) were determined to prevent. Complicating matters further, Earth’s rotation, and thus the length of a day, actually varies erratically and can’t be predicted far in advance.</p>
<p>The solution arrived at was leap seconds: one-second corrections applied at the end of December and/or June on an ad hoc basis. Leaps were scheduled to ensure the timekeeping system we all use, Coordinated Universal Time (UTC), is never more than 0.9 seconds away from the Earth-tracking alternative, Universal Time (UT1).</p>
<p>But all this was before computers ruled the Earth. Leap seconds were an elegant solution when first proposed, but are diabolical when it comes to software implementations.</p>
<p>This is because a leap second is an abrupt change that badly breaks key assumptions used in software to represent time. Base concepts such as time never repeating, standing still, or going backward are all at risk – as well as other quaint notions like each minute lasting exactly 60 seconds. </p>
<h2>Leaping into danger</h2>
<p>Question: what’s worse than mixing computers and leap seconds? Answer: mixing billions of interconnected networked computers, all trying to execute a leap second jump at (theoretically) the same time, with a great many failing in a wide variety of ways. </p>
<p>It gets better: most of those computers are learning about the impending leap second from the network itself. Better still, almost all are constantly synchronising their internal clocks by communicating over the internet to other computers called time servers, and believing the timing information these supply.</p>
<p>Imagine this scene then: during leap-second madness, some time-server computers can be wrong, but client computers relying on them don’t know it. Or they can be right, but client computer software disbelieves them. Or both client and server computers leap, but at slightly different times, and as a result software gets confused. Or perhaps a computer never receives word that a leap is happening, does nothing, and ends up a second ahead of the rest of the world. </p>
<p>All of this and more was seen in the analysis of timing data from the last <a href="https://data.research.uts.edu.au/publication/2e573e44ae983b08f3e03f50540d059e/ro-crate-preview.html">leap-second event</a> in 2016. </p>
<p>The ways in which computer confusion over time can impact networked systems are too numerous to describe. Already there are documented cases of significant outages and impacts arising from the most recent leap second events. </p>
<p>More broadly though, consider the networked critical infrastructure our world runs on, including electricity grids, telecommunications systems, financial systems, and services such as collision avoidance in shipping and aviation. Many of these rely on accurate timing at millisecond scales, or even down to nanoseconds. An error of one second could have huge and even deadly impacts. </p>
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<span class="caption">Russia voted against the decision to abandon leap seconds, in part because this will require a major update to its global navigation satellite system, GLONASS, which incorporates leap seconds.</span>
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<h2>Time’s up!</h2>
<p>In recognition of the growing costs to our computer-based world, the idea of doing away with leap seconds has been on the table since 2015.</p>
<p>The International Telecommunications Union, the standards body that governs leap seconds, pushed back a decision several times. But pressure continued to grow on multiple fronts, including from major tech players such as Google and Meta (formerly Facebook). </p>
<p>The majority of international participants in the vote, including the US, France and Australia, supported the recent decision to drop the leap second.</p>
<p>The Versailles decision is not to abandon the idea of keeping everyday timekeeping (UTC) aligned with Earth. It’s more a recognition that the disadvantages of the current leap second system are too high, and getting worse. We need to stop it before something really bad happens!</p>
<p>The good news is we can afford to wait the suggested 100 years or so. During this time, the discrepancy may grow to as much as a minute, but that’s not very significant if you consider what we endure with daylight savings time each year. The logic is that by dropping the leap second right now, we can avoid its dangers and allow plenty of time to work out less disruptive ways to keep time aligned.</p>
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Read more:
<a href="https://theconversation.com/a-brief-history-of-telling-time-55408">A brief history of telling time</a>
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<h2>How could we deal with this down the track?</h2>
<p>An extreme approach would be to fully adopt an abstract definition of time, abandoning the long-held <a href="https://www.nytimes.com/2022/11/14/science/time-leap-second.html">association between time</a> and Earth’s movements. Another is to make larger adjustments than a second, but far less frequently and with far better preparation to limit the dangers – perhaps in an age where software has evolved beyond bugs.</p>
<p>The decision of how far we’re willing to let things drift before a new approach is decided upon has its own deadline: the next meeting of the Bureau International des Poids et Mesures is set for 2026. In the meantime, we’ll be stuck with leap seconds until 2035. </p>
<p>Since the Earth has surprisingly begun to <a href="https://theconversation.com/the-length-of-earths-days-has-been-mysteriously-increasing-and-scientists-dont-know-why-188147">spin faster</a> in recent decades, the next leap second may, for the first time, involve removing a second to speed up UTC, rather than adding a second to slow it down. </p>
<p>Software for this case is largely already in place, but has never been tested in the wild – so be prepared to leap into the unknown.</p>
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Read more:
<a href="https://theconversation.com/scientists-are-hoping-to-redefine-the-second-heres-why-157645">Scientists are hoping to redefine the second – here's why</a>
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<p class="fine-print"><em><span>Darryl Veitch has received funding from the ARC for network timing research. </span></em></p>The majority of nations voted to scrap leap seconds – the little jumps added to UTC time to keep it aligned with Earth’s rotation. What can we expect moving forward?Darryl Veitch, Professor of Computer Networking, University of Technology SydneyLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1881472022-08-05T04:10:26Z2022-08-05T04:10:26ZThe length of Earth’s days has been mysteriously increasing, and scientists don’t know why<figure><img src="https://images.theconversation.com/files/477777/original/file-20220805-17816-qkr00w.jpeg?ixlib=rb-1.1.0&rect=33%2C53%2C4459%2C2701&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><span class="source">Shutterstock</span></span></figcaption></figure><p>Atomic clocks, combined with precise astronomical measurements, have revealed that the length of a day is suddenly getting longer, and scientists don’t know why.</p>
<p>This has critical impacts not just on our timekeeping, but also things like GPS and other technologies that govern our modern life.</p>
<p>Over the past few decades, Earth’s rotation around its axis – which determines how long a day is – has been speeding up. This trend has been making our days shorter; in fact, in June 2022 <a href="https://www.timeanddate.com/news/astronomy/shortest-day-2022">we set a record</a> for the shortest day over the past half a century or so. </p>
<p>But despite this record, since 2020 that steady speedup has curiously switched to a slowdown – days are getting longer again, and the reason is so far a mystery.</p>
<p>While the clocks in our phones indicate there are exactly 24 hours in a day, the actual time it takes for Earth to complete a single rotation varies ever so slightly. These changes occur over periods of millions of years to almost instantly – even earthquakes and storm events can play a role.</p>
<p>It turns out a day is very rarely exactly the magic number of 86,400 seconds. </p>
<h2>The ever-changing planet</h2>
<p>Over millions of years, Earth’s rotation has been slowing down due to friction effects associated with the tides driven by the Moon. That process adds about about 2.3 milliseconds to the length of each day every century. A few billion years ago an Earth day was only about <a href="https://www.science.org/content/article/average-earth-day-used-be-less-19-hours-long#:%7E:text=In%20timely%20news%2C%20scientists%20have,24%20hours%2C%20The%20Guardian%20reports">19 hours</a>.</p>
<p>For the past 20,000 years, another process has been working in the opposite direction, speeding up Earth’s rotation. When the last ice age ended, melting polar ice sheets reduced surface pressure, and Earth’s mantle started steadily moving toward the poles.</p>
<p>Just as a ballet dancer spins faster as they bring their arms toward their body – the axis around which they spin – so our planet’s spin rate increases when this mass of mantle moves closer to Earth’s axis. And this process shortens each day by about 0.6 milliseconds each century.</p>
<p>Over decades and longer, the connection between Earth’s interior and surface comes into play too. Major earthquakes can change the length of day, although normally by small amounts. For example, the Great Tōhoku Earthquake of 2011 in Japan, with a magnitude of 8.9, is believed to have sped up Earth’s rotation by a relatively tiny <a href="https://www.space.com/11115-japan-earthquake-shortened-earth-days.html">1.8 microseconds</a>. </p>
<p>Apart from these large-scale changes, over shorter periods weather and climate also have important impacts on Earth’s rotation, causing variations in both directions.</p>
<p>The fortnightly and monthly tidal cycles move mass around the planet, causing changes in the length of day by up to a millisecond in either direction. <a href="https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/2013JB010830">We can see tidal variations</a> in length-of-day records over periods as long as 18.6 years. The movement of our atmosphere has a particularly strong effect, and ocean currents also play a role. Seasonal snow cover and rainfall, or groundwater extraction, alter things further. </p>
<h2>Why is Earth suddenly slowing down?</h2>
<p>Since the 1960s, when operators of radio telescopes around the planet started to devise techniques to <a href="https://www.esa.int/Science_Exploration/Space_Science/Observations_Very_Long_Baseline_Interferometry_VLBI">simultaneously observe cosmic objects like quasars</a>, we have had very precise estimates of Earth’s rate of rotation.</p>
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<figcaption><span class="caption">Using radio telescopes to measure Earth’s rotation involves observations of radio sources like quasars. NASA Goddard.</span></figcaption>
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<p>A comparison between these estimates and an atomic clock has revealed a seemingly ever-shortening length of day over the past few years.</p>
<p>But there’s a surprising reveal once we take away the rotation speed fluctuations we know happen due to the tides and seasonal effects. Despite Earth reaching its shortest day on June 29 2022, the long-term trajectory seems to have shifted from shortening to lengthening since 2020. This change is unprecedented over the past 50 years.</p>
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Read more:
<a href="https://theconversation.com/we-found-the-first-australian-evidence-of-a-major-shift-in-earths-magnetic-poles-it-may-help-us-predict-the-next-155040">We found the first Australian evidence of a major shift in Earth's magnetic poles. It may help us predict the next</a>
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<p>The reason for this change is not clear. It could be due to changes in weather systems, with back-to-back La Niña events, although these have occurred before. It could be increased melting of the ice sheets, although those have not deviated hugely from their steady rate of melt in recent years. Could it be related to the huge volcano explosion in Tonga <a href="https://www.abc.net.au/news/2022-08-03/tonga-volcanic-eruption-could-temporarily-warm-the-earth/101297676#:%7E:text=A%20NASA%20study%20examining%20atmospheric,enough%20to%20worsen%20climate%20change">injecting huge amounts of water into the atmosphere</a>? Probably not, given that occurred in January 2022. </p>
<p><a href="https://www.timeanddate.com/news/astronomy/shortest-day-2022">Scientists have speculated</a> this recent, mysterious change in the planet’s rotational speed is related to a phenomenon called the “Chandler wobble” – a small deviation in Earth’s rotation axis with a period of about 430 days. Observations from radio telescopes also show that the wobble has diminished in recent years; the two may be linked. </p>
<p>One final possibility, which we think is plausible, is that nothing specific has changed inside or around Earth. It could just be long-term tidal effects working in parallel with other periodic processes to produce a temporary change in Earth’s rotation rate.</p>
<h2>Do we need a ‘negative leap second’?</h2>
<p>Precisely understanding Earth’s rotation rate is crucial for a host of applications – navigation systems such as GPS wouldn’t work without it. Also, every few years timekeepers insert leap seconds into our official timescales to make sure they don’t drift out of sync with our planet.</p>
<p>If Earth were to shift to even longer days, we may need to incorporate a “negative leap second” – this would be unprecedented, and <a href="https://arstechnica.com/science/2022/08/record-short-days-could-speed-up-debate-on-leap-seconds/">may break the internet</a>.</p>
<p>The need for negative leap seconds is regarded as unlikely right now. For now, we can welcome the news that – at least for a while – we all have a few extra milliseconds each day.</p>
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Read more:
<a href="https://theconversation.com/curious-kids-could-the-earth-ever-stop-spinning-and-what-would-happen-if-it-did-174132">Curious Kids: could the Earth ever stop spinning, and what would happen if it did?</a>
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<img src="https://counter.theconversation.com/content/188147/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Matt King receives funding from the Australian Research Council, the Department of Climate Change, Energy, the Environment and Water, the Department of Industry, Science and Resources, and the Australian National Collaborative Research Infrastructure Strategy (NCRIS). He has previously received funding from the Centre for Southern Hemisphere Oceans Research. </span></em></p><p class="fine-print"><em><span>Christopher Watson receives funding from the Australian National Collaborative Research Infrastructure Strategy (NCRIS) and the Australian Research Council.</span></em></p>The length of a day has critical impacts on our technologies, navigation, and more.Matt King, Director of the ARC Australian Centre for Excellence in Antarctic Science, University of TasmaniaChristopher Watson, Senior Lecturer, School of Geography, Planning, and Spatial Sciences, University of TasmaniaLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/705832016-12-29T20:58:33Z2016-12-29T20:58:33ZWait a moment: 2016 goes a little longer thanks to a leap second<figure><img src="https://images.theconversation.com/files/150726/original/image-20161219-24276-l7zapx.JPG?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">That time is it on Earth?</span> <span class="attribution"><a class="source" href="http://www.measurement.gov.au/Pages/default.aspx">National Measurement Institute</a></span></figcaption></figure><p>To the time-poor of the world: take heart, for 2016 is a generous year. Not only were you granted a leap day on 29 February, you will soon score a New Year’s Eve countdown bonus, a <em>leap second</em>, to hold off 2017 for a final sip or regret.</p>
<p>Whereas leap years add a day to align the calendar with the seasons, <a href="https://www.nist.gov/pml/time-and-frequency-division/leap-seconds-faqs#often">leap seconds</a> align our everyday clocks with the Sun’s position in the sky, that is, with the Earth’s rotation.</p>
<p>Currently our planet takes roughly 86,400.00183 seconds (on average) to turn, instead of the expected 86,400 seconds you get by multiplying 24 hours by 60 minutes by 60 seconds. This may not sound like a great difference, but it amounts to a full second every 18 months. If left unchecked, it would become noticeable over time, and ultimately become problematic.</p>
<p>How did we get into this awkward situation? Why not just define a second so that there are exactly the right number? This sensible idea was tried in 1874, but hit a snag: the Earth keeps changing. </p>
<p>In terms of today’s standard <a href="http://www.bipm.org/en/measurement-units/">SI</a> second (defined via atomic physics), the above discrepancy is due to the fact that the day is losing about 0.0015 seconds per century, due largely to tidal friction. </p>
<p>Not only that, it also changes quite erratically due to mass redistribution.
For example, it is slowed by oceanic thermal expansion due to global warming, just as a playground spinning seat slows, via the conservation of angular momentum, when you place your body farther from the centre.</p>
<p>Leap seconds are used to make sure our usual timekeeping system, Coordinated Universal Time (<a href="https://en.wikipedia.org/wiki/Coordinated_Universal_Time">UTC</a>), never gets more than 0.9 seconds away from the Earth-tracking alternative, Universal Time (<a href="https://en.wikipedia.org/wiki/Universal_Time">UT1</a>).</p>
<p>But unlike leap years, leap seconds cannot be calculated centuries in advance. Because the Earth moves erratically, it must be observed closely, and leap seconds scheduled on an as-needed basis. </p>
<p>In UT1, seconds actually vary in duration, being stretched and compressed to match the Earth’s variations. In UTC, all seconds are standard SI seconds, which is much simpler, but it means that if you want to slow down or speed up UTC, there is no alternative but to jump. </p>
<p>All the leap seconds so far have been “positive”, meaning that an extra second is inserted, corresponding to jumping the clock back, and so slowing it down. </p>
<h2>Time’s up for the leap second?</h2>
<p>The leap second system has been with us since 1972. It represents an important chapter in the entangled history of civilian timekeeping, and of the definition of the second itself. Its days, however, may well be numbered. </p>
<p>For a number of years, support has been growing within the <a href="http://www.itu.int/en/Pages/default.aspx">International Telecommunications Union</a>, the standards body governing leap seconds, to abolish it. </p>
<p>The chief reason is complexity. Simply put, hardware and software can and do get things wrong. And the potential impacts are serious, from failures in navigation leading to collisions, to erroneous financial transactions, computer crashes and the inability to specify UTC times reliably into the future, because the leap second times are not yet known! </p>
<p>Because UTC jumps back at a leap second, effectively the second before the leap is repeated. Managing such “time travel” is inherently complex and error prone, so much so that in many cases the recommended action is to simply shutdown the system and restart it after the leap.</p>
<p>A dramatic illustration of the problem can be found in the internet. All computers have software clocks that generally rely on communication with time servers over the network to synchronise to UTC. Network timekeeping is a core internet service, and at its heart are the <a href="https://ntpserver.wordpress.com/2008/09/10/ntp-server-stratum-levels-explained/">Stratum-1 servers</a>, which have direct access to reference hardware such as atomic clocks. </p>
<p><a href="http://crin.eng.uts.edu.au/%7Edarryl/Publications/LeapSecond_camera.pdf">We collected data</a> from around 180 such servers around the world during the June 2015 leap second event, and assessed them from two points of view. </p>
<p>First, the clocks themselves: did they jump cleanly and sharply exactly as required?</p>
<p>Second, at the protocol level, that is with respect to the messages the servers send to the computers that rely on them: did they inform them properly of the upcoming leap?</p>
<p>Overall, we found that, at most, 61% of the servers were performing correctly. Many of the servers are well known and highly utilised, potentially impacting thousands of clients, possibly resulting in security vulnerabilities. </p>
<p>An expanded experiment is currently underway for the 2016 event, involving almost 500 servers, including from the widely used <a href="http://www.pool.ntp.org/en/">ntppool</a> project. </p>
<p>This is part of a broader network timing project at UTS led by myself together with Dr Yi Cao, which aims to refashion the global system, and in particular to make it scale in a trusted way to the <a href="https://theconversation.com/au/topics/internet-of-things-1724">Internet of Things</a>.</p>
<p>Finally, we must point out that leap seconds occur simultaneously across the globe, and it can’t be midnight everywhere.</p>
<p>Thus, as I confirmed with Dr Michael Wouters, responsible for Australia’s reference time at the <a href="http://www.measurement.gov.au/Pages/default.aspx">National Measurement Institute</a>, for us it will occur at 11am AEDT on January 1, 2017. Save the last sip till then.</p><img src="https://counter.theconversation.com/content/70583/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>This work was supported by the Australian Research Council and Symmetricom. </span></em></p>2016 has been a long year, but it’ll be made slightly longer care of a leap second. But why do we need such things?Darryl Veitch, Professor of Computer Networking, University of Technology SydneyLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/540322016-02-25T17:40:03Z2016-02-25T17:40:03ZLeap day: fixing the faults in our stars<figure><img src="https://images.theconversation.com/files/112786/original/image-20160224-16429-bu1c2l.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">An unusual date that comes to us from the heavens.</span> <span class="attribution"><a class="source" href="http://www.shutterstock.com/pic-358273034.html">Date image via shutterstock.com</a></span></figcaption></figure><p>The number 2016 divided by 4 equals 504, exactly – with no remainder, which makes the year 2016, like the upcoming years 2020, 2024 and 2028 (and beyond), a leap year. We will get an “extra” day, February 29. </p>
<p>This pattern will repeat until 2100, when the cycle breaks. Though 2100 is exactly divisible by 4, there is an exception – for years whose number is exactly divisible by 100. (On top of that, there’s another exception – for years exactly divisible by 400. So 2400 <em>will</em> be a leap year. Mark your calendars now.)</p>
<p>Where do these quadrennial liberties with our calendar originate? </p>
<p>In the stars, of course.</p>
<h2>Celestial rhythms</h2>
<p>One of the simplest joys of life is to watch the stars, night after night, month after month, year after year. They become old friends. They spend a season, and then move on. Or rather, it is we who move on – ever advancing around the sun toward next week’s deadlines, new constellations, new fashions and new ideas.</p>
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<a href="https://images.theconversation.com/files/112788/original/image-20160224-16416-1m6rjfu.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/112788/original/image-20160224-16416-1m6rjfu.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/112788/original/image-20160224-16416-1m6rjfu.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=900&fit=crop&dpr=1 600w, https://images.theconversation.com/files/112788/original/image-20160224-16416-1m6rjfu.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=900&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/112788/original/image-20160224-16416-1m6rjfu.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=900&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/112788/original/image-20160224-16416-1m6rjfu.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=1131&fit=crop&dpr=1 754w, https://images.theconversation.com/files/112788/original/image-20160224-16416-1m6rjfu.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=1131&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/112788/original/image-20160224-16416-1m6rjfu.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=1131&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Orion, the annual visitor.</span>
<span class="attribution"><a class="source" href="https://commons.wikimedia.org/wiki/File:Orion_3008_huge.jpg">Mouser</a>, <a class="license" href="http://creativecommons.org/licenses/by-sa/4.0/">CC BY-SA</a></span>
</figcaption>
</figure>
<p>I imagine myself late one night, eight months from now, remembering the overfull recycling bin, at midnight on trash day. As I try to quietly dump wine bottles into the yellow-topped container, there striding over the eastern skyline is <a href="http://www.space.com/16659-constellation-orion.html">Orion</a>. Back again is my ancient friend, telling me that winter is near, and that I have ridden this miraculous rock almost another full lap around my home star. <a href="http://earthsky.org/brightest-stars/blue-white-rigel-is-orions-brightest-star">Rigel</a> shimmers its blue-white light, the twinkle in the eye (the knee, actually) of a companion who has visited me, annually, every place on Earth I have lived since childhood. Even to the Southern Hemisphere, the steady Orion came for a summer visit – cartwheeling upside down, feet over hands.</p>
<p>It is from these celestial cycles that our concepts of time originate, and, ultimately, from which we gain the leap day.</p>
<p>The <em>sidereal year</em> is the length of time it takes for the Earth to return to the same place with respect to the <a href="http://www.william-shakespeare.info/act3-script-text-julius-caesar.htm">“fix’d” and “constant” stars</a>, so that Orion appears exactly in the same place in the sky, at exactly midnight, 365.2563 days later. Stellar friends like that don’t stand you up; they keep their appointments to seven-digit precision (and more).</p>
<figure class="align-left zoomable">
<a href="https://images.theconversation.com/files/112790/original/image-20160224-18284-klc76h.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/112790/original/image-20160224-18284-klc76h.png?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/112790/original/image-20160224-18284-klc76h.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=326&fit=crop&dpr=1 600w, https://images.theconversation.com/files/112790/original/image-20160224-18284-klc76h.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=326&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/112790/original/image-20160224-18284-klc76h.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=326&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/112790/original/image-20160224-18284-klc76h.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=410&fit=crop&dpr=1 754w, https://images.theconversation.com/files/112790/original/image-20160224-18284-klc76h.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=410&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/112790/original/image-20160224-18284-klc76h.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=410&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Right over the equator: A diagram showing the sun’s position relative to the Earth at the vernal equinox.</span>
<span class="attribution"><a class="source" href="https://commons.wikimedia.org/wiki/File%3AHeliocentric_rectangular_ecliptic.png">Tfr000</a>, <a class="license" href="http://creativecommons.org/licenses/by-sa/4.0/">CC BY-SA</a></span>
</figcaption>
</figure>
<p>Our Western calendar is tied to the <em>tropical year</em> – the time between successive <a href="http://solar.physics.montana.edu/ypop/Classroom/Lessons/Sundials/equinox.html">vernal equinoxes</a>. At that moment, the sun’s position in the sky is exactly where the ecliptic (the plane of the solar system and the path that the planets take as they move through the constellations) crosses the celestial equator (the projection of the Earth’s own equator onto the celestial sphere). Straddling the celestial equator, the sun splits its time exactly between the day side and the night side of the Earth. It returns to that place again in roughly 365.24219 days. Roughly.</p>
<p>Now you can see where those alternating “divisible by 4, 100 and 400” leap year rules originate. </p>
<h2>Making up the differences</h2>
<p>At the end of 365 days, there are still 0.24219 days (just shy of six hours) to go before Earth gets back to the equinox line. </p>
<p>After four years, however, this fractional 0.24219 of a day adds up to 0.96876, which is pretty close to one full day. If we were using only a 365-day calendar, the stars, and more importantly the months, corresponding to the seasons – crucial for agricultural societies – would slip behind. This was apparent to the Romans in the first century, as well as to the Olmecs and the <a href="http://www.livescience.com/25662-how-mayan-calendar-works.html">Maya</a> on the other side of the world.</p>
<p>Thus decreed Julius Caesar in 46 B.C.: that every four years an extra day would be added to February. It was called the Julian calendar. But adding one day every four years, in order to make up for that 0.96876 of a day in orbital spare change, is overcompensating. Caesar’s “every four” leap year prescription adds 0.03124 of a day too much. This makes the Julian calendar run fast by just over 600 seconds per year. </p>
<figure class="align-right zoomable">
<a href="https://images.theconversation.com/files/112789/original/image-20160224-18284-8uyemr.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/112789/original/image-20160224-18284-8uyemr.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/112789/original/image-20160224-18284-8uyemr.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=809&fit=crop&dpr=1 600w, https://images.theconversation.com/files/112789/original/image-20160224-18284-8uyemr.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=809&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/112789/original/image-20160224-18284-8uyemr.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=809&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/112789/original/image-20160224-18284-8uyemr.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=1016&fit=crop&dpr=1 754w, https://images.theconversation.com/files/112789/original/image-20160224-18284-8uyemr.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=1016&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/112789/original/image-20160224-18284-8uyemr.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=1016&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Exception after exception: Christopher Clavius, in a line engraving by E de Boulonois.</span>
<span class="attribution"><a class="source" href="https://commons.wikimedia.org/wiki/File:Christopher_Clavius._Line_engraving_by_E._de_Boulonois._Wellcome_V0001150.jpg">Wellcome Trust</a>, <a class="license" href="http://creativecommons.org/licenses/by/4.0/">CC BY</a></span>
</figcaption>
</figure>
<p>Like with the spare coin jar in our house, small change like that takes a while to add up. It wasn’t until the age of Pope Gregory XIII, in 1582, that this mismatch was becoming a problem. After consultation, presumably with God, but particularly with his astronomer, <a href="http://galileo.rice.edu/sci/clavius.html">Christopher Clavius</a>, <a href="http://www.bluewaterarts.com/calendar/NewInterGravissimas.htm">the pope adopted Clavius’ clever solution</a>. </p>
<p>The Julian calendar runs fast by 0.03124 of a day every four years; multiply both sides by 100, and see an excess of about three days after 400 years. Clavius’ solution was to make centuries exceptions – but that would lose too much, <em>four</em> days in 400 years, not three. So Clavius added one back, once every 400 years, starting in 1600.</p>
<p>This Gregorian calendar, which we use today, has the following rules:</p>
<ul>
<li>Every year divisible by 4: add February 29</li>
<li>Every century (1800, 1900, 2000, 2100): do not add February 29</li>
<li>Every century divisible by 400: add February 29</li>
</ul>
<h2>Still finer measurements</h2>
<p>Even with this refinement, there is still orbital change left over. But now we are talking about temporal shavings that are quite small. At this level of precision, <a href="http://tycho.usno.navy.mil/leapsec.html">other wobbles</a> in the relation of the Earth’s rotational period (the day) and its revolution period (the year) have to be <a href="http://thephoenix.com/boston/news/57080-beat-the-clock/">taken into account</a>.</p>
<figure class="align-left zoomable">
<a href="https://images.theconversation.com/files/112791/original/image-20160224-15614-7njtc9.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/112791/original/image-20160224-15614-7njtc9.png?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/112791/original/image-20160224-15614-7njtc9.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=163&fit=crop&dpr=1 600w, https://images.theconversation.com/files/112791/original/image-20160224-15614-7njtc9.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=163&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/112791/original/image-20160224-15614-7njtc9.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=163&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/112791/original/image-20160224-15614-7njtc9.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=205&fit=crop&dpr=1 754w, https://images.theconversation.com/files/112791/original/image-20160224-15614-7njtc9.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=205&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/112791/original/image-20160224-15614-7njtc9.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=205&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">When a leap second is added, digital clocks tick past 23:59:59 but don’t go directly to 00:00:00.</span>
<span class="attribution"><a class="source" href="https://commons.wikimedia.org/wiki/File:Leap_second.png">Twid</a></span>
</figcaption>
</figure>
<p>Keeping track of minute effects like this is the job of the <a href="http://hpiers.obspm.fr/">International Earth Rotation and Reference Systems Service</a>, which controls the addition (or deletion) of leap seconds. For example, a second was added to <a href="http://www.nhc.noaa.gov/aboututc.shtml">Coordinated Universal Time</a> by the service on <a href="http://www.bbc.com/news/science-environment-33313347">June 30, 2015</a>, due largely to the slowing of the Earth’s rotation by the gravitational pull of the moon. </p>
<p>There are other sources of calendar slip: the <a href="https://www.ngdc.noaa.gov/hazard/11mar2011.html">8.9 magnitude earthquake that triggered the Japanese tsunami on March 11, 2011</a>, for example, shifted the planet’s mass distribution enough to decrease the length of a day by 1.8 microseconds. This will add up to about a second after 1,500 years.</p>
<h2>Using that ‘extra’ time</h2>
<p>Personally, I think we should make February 29, leap day, a global holiday. It should be considered a gift to ourselves, like taking that accumulated spare change to the grocery store coin-counting machine, and trading it for some easier-to-spend bills. It should be a day of celebration, a reward for saving that quarter of a day over the last four years, to be spent on something frivolous. Or it could be a special day to realign our sense of hourly routines, weekly trash pickups, the race to fulfill monthly quotas, to the celestial schedule.</p>
<p>Without that extra day every fourth year, our ancient friends would begin to miss their annual appointments, and start to fall behind in wishing us prompt birthday greetings, like forgetful Facebook friends. Without February 29, roughly, every four years, the “constant stars” would cease to be constant.</p><img src="https://counter.theconversation.com/content/54032/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>James Hetrick receives funding from the National Science Foundation. </span></em></p>We will get an ‘extra’ day this year, February 29. Where do these quadrennial liberties with our calendar originate?James Hetrick, Professor of Physics and Analytics, University of the PacificLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/440772015-06-30T20:10:27Z2015-06-30T20:10:27ZTemporal flux: why we need to keep adding leap seconds<figure><img src="https://images.theconversation.com/files/86821/original/image-20150630-5846-zpfab3.jpg?ixlib=rb-1.1.0&rect=82%2C13%2C1426%2C1237&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Time can feel like that sometimes, even if the Earth's rotation isn't slowing down.</span> <span class="attribution"><span class="source">JD/Flickr</span>, <a class="license" href="http://creativecommons.org/licenses/by/4.0/">CC BY</a></span></figcaption></figure><p>Today at precisely 10am Australian Eastern Standard time, something chronologically peculiar will take place: there’ll be an extra second between 09:59:59 and 10:00:00. </p>
<p>This will make 1st July 2015 (or 30th June 2015 in many other parts of the world) one second longer than the length of a standard day. The culprit is a “leap second”, although it’s far from unique. In fact, it’ll be the 26th one we’ve had since they were first introduced in 1972. </p>
<h2>How long is a piece of day?</h2>
<p>Why do we need to add an extra second to the day? Historically the second had been defined as a fraction of the day: one 86,400th of the total time for the sun to return to the same position in the sky. </p>
<p>That was precise enough for most purposes, but by the early twentieth century, astronomers had determined that the Earth’s rotation was not constant. It was actually slowing down. This meant that a second defined in this fashion would slowly lengthen over time. </p>
<p>The development of <a href="http://www.npl.co.uk/60-years-of-the-atomic-clock/">atomic clocks</a> in the 1950s allowed the second to be defined with incredible accuracy, with a variance of only one part in 10<sup>14</sup>. </p>
<p>Thus was the second redefined in 1967 by the <a href="http://www.bipm.org/en/committees/cipm/">International Committee for Weights and Measures</a> in 1967. It was no longer pegged to the Earth’s rotation. Instead it was defined in terms of a very particular physical property of a caesium-133 atom. </p>
<p>This mechanical definition has disconnected the second from the length of the solar day. In fact, the tables turned and the day was subsequently redefined in terms of this newly established atomic second: 86,400 seconds make up a standard day. </p>
<p>The length of the solar day – or the time it actually takes the Earth to complete a rotation – is no longer precisely as long as a standard day, and it has not been for a century. This is because the Earth’s rotation continues to slow. </p>
<p>The main reason it’s lagging is tidal friction from the Moon, which by itself would increase the length of the day by <a href="http://eclipse.gsfc.nasa.gov/LEcat5/secular.html">2.3 milliseconds each century</a>. </p>
<p>However, other geological process on Earth that shift mass around will also have an effect on the rotation rate, since the system mus conserve its total <a href="http://hyperphysics.phy-astr.gsu.edu/hbase/amom.html">angular momentum</a>. This can end up increasing the Earth’s rotation rate as well as decreasing it. </p>
<p>For example, the 2005 earthquake in Indonesia that caused the tsunami also decreased the <a href="http://www.nasa.gov/home/hqnews/2005/jan/HQ_05011_earthquake.html">length of the day by 2.68 microseconds</a>. </p>
<p>So we have to keep adding leap seconds to keep the time of noon at Greenwich (<a href="http://wwp.greenwichmeantime.com/">Greenwich Mean Time</a>) in line with noon as measured by the atomic clock (<a href="http://www.bipm.org/en/bipm/tai/tai.html">International Atomic Time</a>). This guarantees that the solar time (the rise and fall of the sun) doesn’t fall too far out of sync with our clocks.</p>
<h2>Taking time</h2>
<p>The task of adding these seconds was initially taken on by the <a href="http://adsabs.harvard.edu/full/2000ASPC..208..175G">Bureau International de l'Heure</a>, the executive body of the <a href="https://en.wikipedia.org/wiki/International_Time_Bureau">International Commission of Time</a>, which itself was part of the International Astronomical Union (<a href="http://www.iau.org/">IAU</a>). </p>
<p>In 1987 the IAU created a new organisation, the International Earth Rotation and Reference Systems Service (<a href="http://www.iers.org/IERS/EN/Home/home_node.html">IERS</a>). And from 1st January 1988, it became responsible for the leap second. </p>
<p>The leap second itself is an irregular occurrence. Between 1990 and 1999 there were seven leap seconds added. Yet between 2000 and 2009, only two extra seconds were added. In fact, it is so irregular that leap seconds are only announced by the IERS six months in advance. </p>
<p>This is a headache for computer systems. Software that doesn’t know about the leap seconds may see time going backwards and crash. When the previous leap second was added in 2012 the computerised reservation system for the <a href="http://www.news.com.au/travel/travel-updates/flights-back-to-normal-after-system-crash/story-e6frfq80-1226413756216">airline Qantas collapsed</a> and up to 50 flights were delayed. Similar problems affected sites such as <a href="http://www.wired.com/2012/07/leap-second-bug-wreaks-havoc-with-java-linux">Reddit, Foursquare and LinkedIn</a>.</p>
<h2>Temporal flux</h2>
<p>The future of the leap second is currently being debated. The chaos that it can cause on the world’s computer systems may not be worth the continued consistency with the heavens. </p>
<p>The New York Stock Exchange plans to <a href="http://gpsworld.com/june-30-leap-second-worries-markets-internet/">close its after hours trading 30 minutes early</a>. The web services arm of the online retailer Amazon plans to change their definition of the second for the day, such that they retain the 86,400 seconds in a standard day. This would mean that the clocks of Amazon Web Services would be slightly different to civil time.</p>
<p>Does the day to day time used by humans even need to remain linked to astronomical time? If the second retains the definition that it has, the need for leap-seconds will only increase. In 100 years there will need to be one at least one a year. And in a thousand year’s time we will need to add a new leap second every couple of months. </p>
<p>There are already timing schemes that do not follow the civil definition of time, such as the <a href="http://www.bipm.org/en/bipm/tai/tai.html">International Atomic Time</a> and the <a href="https://en.wikipedia.org/wiki/Global_Positioning_System">Global Positioning System time</a>. Computer systems could be linked to either of these. </p>
<p>Thus, this peculiarly long minute on 1st July 2015 serves as a useful reminder that time is no simple thing. We might want it to be pure and ordered, but as long as we live on a giant ball of shifting molten rock orbited by another huge ball of rock, all careening through space around an enormous ball of exploding gas, then it’s inevitable that we’ll need to adjust our clocks from time to time.</p><img src="https://counter.theconversation.com/content/44077/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>David Parkinson receives funding from the Australian Research Council and the University of Queensland, and is affiliated with the Australian Research Council's Centre of Excellence for All-sky Astrophysics.</span></em></p>Keeping time isn’t easy, particularly as the Earth’s rotation is slowing down, so we need to keep adding troublesome leap seconds.David Parkinson, Researcher in astrophysics, The University of QueenslandLicensed as Creative Commons – attribution, no derivatives.