Take a flying leap second

By Phil Plait | December 31, 2008 12:18 pm

I hope you liked 2008. Because you’re going to get an extra 0.0000031689% of it today.

That is, on top of the leap day we had on February 29, there’s a leap second getting added tonight. 2008 is the year that keeps on giving.

Astronomical clock

We have leap days because the length of the Earth’s day isn’t an even fraction of the year, and we add a day in every fours years to help even it out (though in reality it’s a LOT more complicated than that). But why do we add a single second?

OK, fair warning: this simple question will lead you down a maze of twisty passages all of which look alike. But first off, for those impatient readers, here’s the simple answer: the length of the day based on the Earth’s spin changes, but the length of the day based on atomic clocks doesn’t, so every now and again we have to adjust them to make them match, adding in a second to align them better.

However, that’s no fun. Jumping into the gory details; that’s fun. And you know I love this stuff, so let’s take a closer look. A much closer look.

Doctor Who schools you on time

There are a zillion ways to measure time. In our daily lives we have the day, the year, the second. The first two are based on actual events: the rotation of the Earth, and the time it takes to go around the Sun (and, of course, the closer you look at them, the more fiercely complicated they get, too).

The "second", though, is arbitrary; it’s a human-designed length of time. We made it up. In general, you can think of a second as being 1/86,400th of a day. But scientists don’t like to do that; for one thing, it’s not sciencey enough. For another, the length of the day changes.

[UPDATE: What I wrote below is technically correct, but I decided to be a little more detailed in a followup post. Please read that when you finish this.]

If the Earth were a solid body with nothing nearby, it would merrily spin at the same rate forever. But it’s not alone: the Moon and Sun are breathing down our necks, so to speak. The gravity of these two guys pulls on the Earth, stretching it and messing with its rotation (again, it’s complicated, but fascinating). If the Earth were a solid sphere, the slowing caused by the Sun and Moon would be constant. However, the Earth is layered in solid and liquid and sorta-kinda-liquid sections (the mantle is more like a thick plastic than a liquid), and these change how the Earth spins. Instead of gradually slowing down, the rate jumps and skips. Even earthquakes can change the Earth’s rotation; the huge seismic event in December 2004 that caused the tsunami in Indonesia shortened the length of the Earth’s day by about 3 microseconds. That ain’t much, sure, but it happened, and was measurable.

gears of a clock

Even weather affects the Earth’s rotation! Obviously, the length of the day is not the best standard of measurement to use for time if you want to be really anal and get out to the tenth decimal place.

That’s why scientists decades ago changed the basic unit from the day to the second, and then decided to base the length of the second on something that won’t change over time. What they needed was a cosmic metronome, and light itself is a good one. It’s a wave, so it has a frequency — how many wavecrests pass through a point in space every second. If you’re on the beach, and a wave crashes ashore twice per minute, then it has a frequency of once every 30 seconds, or 1/30 = 0.0333.

We can flip that definition over, and instead of saying the frequency of some wavelength of light is how many crests pass a point in space every second, we say the unit of time called the second is when a given number of wavecrests pass by that point in space. There’s nothing magic here; it’s just a definition. So let’s do that.

Doctor Who’s fob watch

We need a really solidly stable wavelength we can measure. It turns out that a cesium atom gives us just that. The outer electron in a normal cesium-133 atom will sometimes spontaneously flip over, in a sense swapping north and south poles. This is called the hyperfine transition, for those keeping notes at home. When the electron does that, it gives off a very specific wavelength of light (in the microwave region with a wavelength of roughly 3 centimeters). That corresponds to a frequency of 9,192,631,770 wavecrests per second.

Since cesium atom electron spin-flips are so very precise, we can measure them very accurately, and use them as a basis for our clocks (and when you hear the term "atomic clock", that’s what it means). All we have to do is invert our measurement, and then say:

One standard second is the length of time corresponding to 9,192,631,770 periods of the radiation emitted by the hyperfine transition of an unionized cesium atom in the ground state.

Woohoo! OK, sure, that sounds complicated, but it’s actually very precise and measurable and scientists get all charged up about it. All you have to do is nod your head and accept it. The bottom line is, we have a very precise definition of what a second is, and it’s not based on the Earth’s messy spin. This definition was ratified in 1967 during the Thirteenth General Conference on Weights and Measures. Yes, there’s a meeting for that. I can imagine all the scientists and engineers sitting around during talks at that conference constantly checking their watches. That image makes me smile.

So anyway, now we’re finally ready to understand why we have leap seconds! We have the superprecise scientific definition of a second, and we have the sloppy one we use in everyday life based on the Earth’s spin. But the Earth’s spin is changing! On average it’s slowing down, and that difference builds up. [Don’t forget to read my followup post!] Eventually, when the difference between the day measured by the Earth’s rotation and the one based on the cesium atom gets to be more than 0.9 seconds, a leap second is added in to the day to match them up better.


Clock at midnight

The last time this was done was in December 2005, and it’s happening tonight. That means that officially, we get the following weird sequence of events: The official clock will be ticking tonight, counting down to the New Year. Just before midnight it will read 23 hours 59 minutes 59 seconds. But instead of clicking over to 00 hours 00 minutes 00 seconds on January 1, it will first read 11 hours 59 minutes 60 seconds on December 31! Weird. Imagine your bedside alarm clock going from 11:59 to 11:60 for one second before flipping over to 12:00 and you’ll get the idea.

So that’s the tale of the leap second. Ironically, if you’ve read this far, you’ve blown several minutes of your life, and the extra second tonight won’t make up for it. But now you know why you get that extra second, and you can savor it. Take an extra sip of champagne, or kiss that Significant Other a moment longer, or just take 9,192,631,770 oscillations of a cesium-133’s atom to ponder what 2009 will be like… even if the coming year is a wee bit shorter than this one.

My, how time flies.

Images courtesy of zoutedrop’s Flickr stream, neilspics’ Flickr stream, and judepics’ Flickr stream.

CATEGORIZED UNDER: Astronomy, Cool stuff, Science

Comments (58)

  1. SO, when we do the countdown we have to say, “10, 9, 8, 7,6,5,4,3,2,1,1…Happy New Year?”

    Great breakdown on the reason for all this. Thanks!

  2. Wow! A whole second just for me! Let’s see, I’m going to… Oops, already used it.

    Oh, great article. 😛

  3. Great article, Phil. :)
    My! My! Time Flies! — http://www.youtube.com/watch?v=P57aSW47rY8

    (Make sure to do the high-quality one if you can.)

  4. Paul Clapham

    I saw the phrase “unionized cesium atom” and just for a moment I wondered what would happen if the cesium atoms all went out on strike… and then I realized what it really meant.

  5. mike

    Yeah, I was wondering how one gets cesium atoms to vote as well.

    Perhaps a better term is “neutral.” Or perhaps “uncharged.” 😀

  6. What time does the International Space Station go on? I guess they’ll be having a New Years party every ninety minutes or so…

  7. Glenn

    I can’t believe nobody picked this nit yet. The leap-second gets added at UTC 11:59:60, not New York civil time, so if you “celebrate” when the ball drops, you’ll be wrong by several hours.

  8. The Jigsaw Man

    Technically correct, (the best kind of correct) but the timepieces in NYC are not going to actually COUNT that extra second at 7:59:60(local), they will wait until 11:59:60(local).

    Good enough for most of us, and it saves me having to put on the lampshade too early.

  9. billsmithaz

    > a maze of twisty passages all of which look alike.

    I’ve barely even begun reading this post, but had to drop a comment giving HUGE nerd-props for the Zork reference.

    Infocom FTW!

  10. jasonB

    That top clock is gorgeous. Completely unreadable, but gorgeous.
    I’m now going to contemplate how to enjoy my extra second.

  11. fracai

    @ The Jigsaw Man

    Hah, I love it. Especially because the NYC clocks will therefore be out of sync with the rest of the world, by 1 second, for 5 hours!

  12. John

    I think we should count down 9,1,9,2,6,3,1,7,7,0 then the extra second will have been spent on the actual measure of the second being added and all things will be right with the world again……Happy New Cesium Moment!!!!

  13. IVAN3MAN

    Dr. Phil Plait:

    Even earthquakes can change the Earth’s rotation; the huge seismic event in December 2004 that caused the tsunami in Indonesia slowed the Earth’s spin by about 3 microseconds. That ain’t much, sure, but it happened, and was measurable.

    Er… Phil, I think that you have misread the article that you linked to: It was the Earth’s length of day that was shortened by -2.767 microseconds, not its speed of rotation that was slowed down; shortening of the Earth’s day by that amount would actually mean that the Earth’s rotation had increased by +2.767 microseconds!

    I would have mentioned this sooner, but I wanted to check the facts first! :-)

  14. davidlpf

    I thought time was a wibbly wobbly sort of thing.

  15. Ivan

    It will also cause your Zune not to work! Hooray!

  16. Knurl

    If you have a shortwave radio you can listen to it happen!!! (At 7:59:60 EST, as has been pointed out)

    NIST (The National Institute of Standards and Technology) operates the standard time and frequency radio stations WWV (Ft. Collins, CO) and WWVH (Hawaii). WWV operates on 2.5, 5, 10, 15, and 20 MHZ (or 2500, 5000, 10,000, 15,000, and 20,000 KHZ). WWVH operates on the same frequencies, except not on 20 MHZ (20,000 KHZ).

    If you don’t have a shortwave receiver but know a HAM operator (HF, not VHF or UHF) give ’em a call!! Most are happy as hell to strut their stuff.

    NIST also gives geoalerts at 19 minutes past the hour on WWV and at 46 minutes past the hour on WWVH. WWV used to have the solar and terrestrial indicies (solar flux, Boulder A and K indexes) at 18 minutes past the hour, but I think they stopped. I haven’t been in the game for several years, but I think I’ll pull out my old Radio Shack DX-440 for this one. If it still works, I’ll let you know about the indicies. Either way,


    (Er, NEW YEAR. I’ve been drinking with my boss since noon, and he’s paying the bill.)

  17. JoeSmithCA

    “Ironically, if you’ve read this far, you’ve blown several minutes of your life, and the extra second tonight won’t make up for it.”

    I disagree, I find your articles informative and entertaining. I consider that time as spent, not blown :)

    “If the Earth were a solid body with nothing nearby, it would merrily spin at the same rate forever. ”

    Will it still be spinning at the same rate between ~10^32 and ~10^35 years from now? :)

  18. Good catch, IVAN3MAN. I fixed it, thanks.

  19. GK4

    Phil, that’s a lot of wibbly-wobbly timey-wimey … stuff. Fantastic!

  20. Eric TF Bat

    At the New Year’s Eve Party I attended last night (I’m writing this from Australia, which is the future) we counted down thus:

    10, 9, 8, 7, 6, 5, 4, pi, 3, 2, 1 … Happy New Year!

    We have decided that pi should have honourary integer status for the year. You know – so Indiana doesn’t feel too stupid.

  21. wb4

    Isn’t it at 6:59:60 EST? I believe EST is 5 hours behind UT, not 4 hours.

  22. JoeSmithCA

    @wb4, I believe the variant of UT you’re referring to is UTC (Coordinated Universal Time) in which you are correct Eastern Standard Time(EST) is 5 hours less than UTC.

  23. Good job and thanks. I wanted to write up something about the leap second, but you did a much, much, much better job than I could have done. 😀

  24. Cesium? Harumpf! Everyone knows that a beryllium clock is much more accurate and can be used to fix a TARDIS Type 40 to boot!

  25. Thandarr theWizard

    This really annoys me. I had to reset my clocks already twice this year because of Daylight Savings Time, and now this!

  26. SLC

    Just to make things more complicated, as the Earths’ rotation slows down, clocks will actually run faster because of the reduction of time dilation as predicted by special relativity.

  27. This was one of the most interesting, neat-o BA entries in a long time (not to slight the recent entries of course)…..Vintage awesomeness, and worthy of the title of “Things that make you go Hmmm”.

  28. quasidog

    You pointed out that other factors, like earthquakes can adjust the speed-up or slowdown of Earth spin, tsunamis, weather etc. I didn’t realise that.

    Just how accurate is the measurement of the current slowing process? Clearly then it is not constant, and certain factors will outwiegh certain others, like the tidal forces of the sun and moon, but is this still a science in progress? How many facts about this come into play, and is there room for other facts that have not been discovered yet ? How do meteorite impacts effect it? What about the really big ones that were believed to have assisted in wiping out the dinosaurs ? What if other such impacts happen in the future, considering the angle at which they come in? In other words, is there room for the rate to be adjusted by a great deal .. or even well into the other direction ?

    You mentioned on average the spin rate of the earth is slowing down, so does the leap second rate get adjusted with all these other natural events .. relative to the cesium atoms’ light emission periods?

    I know I am being pedantic but it amazingly interesting. LINKS !! :)

  29. IVAN3MAN

    Phil Plait, you’re welcome! BTW, splendid post on “Take a flying leap second”! The two things that interest me most are Space and Time!

    At the time of writing this, the New Year is almost upon us, here in the U.K., in 3… 2… 1… HAPPY NEW YEAR, PHIL! 😀

  30. I just finished refreshing my computer clock immediately before and after the leap second… and it was EXACTLY ONE SECOND OUT!!!


  31. IVAN3MAN

    Well, at 00:33 GMT, I’ve broken my New Year’s resolution not to blaspheme for at least 24 hours! 😐

  32. @billsmithaz: Zork? You’re about 3 years too late. ITYM Colossal Cave Adventure 😐

  33. JeffB

    More wobbly bits: how does the official time definition account for relativistic time dilation? For example – the clocks in the GPS satellites appear to run faster that those on the ground – so doesn’t it matter exactly where those 9,192,631,770 cycles of the hyperfine transition radiation (from the free agent cesium atoms) are counted?

    Oh, wait – now I see this line in the article – “All you have to do is nod your head and accept it.” OK… Happy New Year!

  34. You just really wanted an excuse to stick some Doctor Who caps in, didn’t you?

  35. Steve Morrison

    @Paul Clapham:

    Isaac Asimov once wrote an essay called “To Tell a Chemist” where he noted that if you ask a non-chemist to pronounce the word “unionized”, you’ll get a three-syllable answer, but a chemist will give you the four-syllable pronunciation!

  36. KC

    >I can’t believe nobody picked this nit yet. The leap-second gets added at UTC 11:59:60, not >New York civil time, so if you “celebrate” when the ball drops, you’ll be wrong by several >hours.

    You get the last official “Killjoy” award for 2008! :-) While you are technically correct I think it is cool to symbolically represent the leap second. At one point, I wish I could remember when, they paused the Time Ball in Times Square for one second a number of years ago – I thought that was really neat even though the second had already been added around 7:00pm EST. Unfortuantely they no longer do that.

  37. KC

    >For example – the clocks in the GPS satellites appear to run faster that those on the ground – >so doesn’t it matter exactly where those 9,192,631,770 cycles of the hyperfine transition >radiation (from the free agent cesium atoms) are counted?

    Someone please correct me if I’m wrong but remember that GPS satellites are a way of distributing time signals accurately…but atomic time doesn’t originate in the satellites – atomic time is created by averaging hundreds of atomic clocks located in climate controlled vaults all over the world.

    One of the best ways of measuring the rotation of the Earth is using radio telescopes to observe distant radio sources…accuracy of variation measurements are +/-0.2 milliarcseconds.

  38. Andy Perrin

    My question is a variant on JeffB’s. Clocks that are at different elevations will tick at different rates because of gravitational time dilatation, so what I want to know is at what point does it not make sense to try to measure time more accurately, given that if you just go to a new elevation, your watch will be wrong? To put it another way, over typical earthly distances, how large is the relativistic correction compared to corrections for the Earth’s rotation and other factors?

  39. Sili

    Steve Morrison,

    The joke is that if you write the words “unionised” and “mole” on the blackboard, and people start talking about organised labour and small, blind, furry animals, they’re not chemists.

  40. Ryan

    Zune’s all over the world crashed yesterday. Coincidence?

  41. Robert Gift

    For a Good Time, call 499-7111.
    (I used to write this on men’s room walls!)
    (Now Colorado requires 10-digit dialing for local calls.)

    I called yesterday and IT WAS BUSY!

    Assuming people like those who read this would cause such a problem, I had also tuned to 5.0 mHz.

    So, what did you do with the extra time? Squander it?

    My girlfriend’s father worked at NBS – National Bureau of Standards. In the early 1970s I got to visit the atomic clock.
    I had a great time!

  42. Joshua Zucker

    “unionized cesium atom … scientists get all charged up about it.”

    LOL HA HA HA ha ha ha … um … OK, well, I thought it was hilarious.

  43. I would have preferred that the extra second had come after Bush leaves office.

  44. Cool read! These are the little things of everyday life we just don’t normally think about.

  45. Hello, Very Nice Article, Check out this post(link below) for a more detailed explanation(scientific explanation) of this extra second. And also, why the earth rotation is slowing down? Take a look.

    Link: http://hostintruder.wordpress.com/2008/12/28/extra-second-added-to-year-2008/

    Hope it helps!!

  46. sutureself

    ok, now can someone please tell me why an observer from off earth will see the earth complete its passage around the sun in 366+ days, while the earthly year is 365+?

    I know that living on earth is expensive, but it does include a free trip around the sun every year. If it takes over a year to get around, does that mean I’m getting gypped?

  47. emily

    love the human nature/the family of blood who pics, made me smile

  48. Steve

    My birthday falls in every leap year! Man I’m 20 human years but only had 5 birthdays LOL.

    Nice read BTW :)

    Here’s the ste I was reading that led me to your’s: http://gpswatchreviews.org/


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