Why the leap second?

So, at the new year celebration with friends, one friend, Trish, asked, "why do we have a leap second?" I gave a vague answer, mostly because I'd just downed the last of my DW's rum and coke; she wasn't there due to an unfortunate sledding accident recently discussed, and she wanted me to drink some "yummy" drinks for her. I know she likes rum and coke, so I had one. Ugh (the rum was pretty good, but the coke was horrid, as are all colas). I had to be goaded into finishing it; I did as I do with most alcoholic drinks...I downed it so I didn't have to taste it. So, I was a little flighty.

Let me more properly answer this question here...

First, we need to discuss how we keep time. One of the many ancient ways of keeping time was based on the position of the sun, which is dependent on the rotation of the earth. Everyone "knows" that a day is one full rotation of the earth and that the the length of a day is 24 hours. This is, in fact, how a day is defined by the National Institute of Standards: A day is exactly 86,400 seconds long (60 seconds/minute * 60 minutes/hour *24 hours/day).

A second is now thusly defined: The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.

Interestingly, even this seemingly super-precise definition isn't quite good enough. According to Einstein's theory of general relativity, the length of time a second takes (huh?) depends on how far into a gravity well the clock is. So, a clock in Earth orbit will keep time at a slightly different rate from one at sea level (the orbital clock will, in about 10,000 years, gain a second on the sea level clock; relativity has been tested by GPS satellites, which need very precise time). So, whenever we talk of counting seconds, we are speaking of an ideal atomic clock at the geoid (just follow the link; there isn't enough space to explain everything).

So, we now have a day that is exactly 24 hours long. However, the earth itself doesn't care how we define a "day". Therefore, for science purposes, we define a "sidereal day" based on the position of the "fixed" stars. That is, we assume the earth's position does not change relative to very distant stars (obviously this is incorrect, but is pretty good). That is, there is rotation of the Earth, but not translation. We define the sidereal day as one full rotation of the earth such that the position of a star, say Alpha Centuari, is in the exact same position as it was the day before as viewed from the same point on the earth. This takes 23 hours, 56 minutes, and 4.090530833 seconds. For now.

Clearly our two precise definitions of time do not agree. Nor is the word "day" in every-day usage self-consistent. So?

Well, it gets even worse. Everyone "knows" that the length of a year is 365 days, except leap years, which are 366 days long. Also everyone knows that a year isn't exactly 365 days, which is why we need leap years (because otherwise our calendars would be wrong relative to our expectations). The amount of time it takes for the earth to complete one orbit around the sun is actually about 365.242 days. You'll notice that this is NOT 365.25 days, which is what you would expect given that a leap year happens every four years. Which is why a leap year does NOT happen every four years. If that were the case, three extra days would be added every 400 years. Therefore, any century year (1800, 1900, 2000, 2100, etc.) that is not divisible by 400 is not a leap year, even though it is divisible by 4. 2000 was a leap year, and 2400 will be a leap year. 1600 was the last leap year before 2000.

So, what does any of this have to do with leap seconds?

Well, it all points to the complication of using either observed, earthly phenomena (the position of the sun or stars in the sky) or precisely defined times (electron movement in a caesium atom) as a way to keep track of scientifically interesting stuff as well as day-to-day stuff with the same clocks. An atomic clock that uses the definition of the second as shown above will eventually tell you that it's noon when it has been dark for hours. That's obviously not useful.

And I haven't even spoken of the fact that the Earth's rotation is slowing due to tidal interactions with the moon, of the fact that Earth's axial tilt precesses with respect to the fixed stars. or...

Because the Earth's rotation rate is changing ever-so-slightly, we need a way to keep our clocks up-to-date. We wouldn't want to have the situation of having to suddenly add a 1/2 day to our calendars because we let our precise clocks get so out-of-sync with our perceived time; this would be much more distressing to the world than adding a second every few years. So, since 1972, we've been adding a leap second (so far, they've all been positive, but it's possible that at some time, we'll end up losing a second from our year. We'll probably get many protests when that happens). Since 1972, we've added 24 leap seconds to our clocks, sometimes in December, sometimes in June.

Note that leap seconds and leap years only share the name "leap" and the fact that our planet does not behave precisely according to our time keeping devices. A leap second can be added in any year whether it's a leap year or not, leap seconds are added irregularly while leap years are very predictable, and they account for different phenomena.