Monday, 18 January 2010

One Small Leap

First, I would like to explain the concept of the leap second. At first the definition of a second was 1/86400 of a solar day. This was not a good enough standard, so the definition was later changed to the somewhat less comprehensible length 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. This gave some new problems since the solar day became approximately 1.7ms longer every century, the reason being that the earth's rotation is slowing down. To counter this sometimes an extra second is added June 30 or December 31. This added second is called a leap second. Worth mentioning is that the decreasing rotation varies based on unpredictable factors like the motion of mass in the center of the earth, which means we have no formula to calculate when the next leap second needs to be added. Instead the leap second is added when the difference between solar day time and the measured time gets too large (0.9).

This gives us some strange effects, especially when trying to calculate the difference between two points in time, where one or more leap seconds have been inserted. Imagine that a leap second was added on December 31 at 11.59.60p.m. The last minute of the year is made one second longer. This means that if were to count the seconds between 8 a.m. December 31 and 8 a.m January 1, we would get a count of 86401. If we were to count the hours instead though, the result would be 24 which, if we translate it into seconds, is 86400 and we just lost a second in the process. (This makes for some strange effects when dealing with date differences in computer systems, but that is not the topic here).

How can this be? Well, it all comes down to the difference between elapsed time and our daily measured time. The reason for the added second is to get our clocks synchronized with the solar time. The elapsed time would be 86401s = 1440m1s = 24h0m1s = 1d0h0m1s, and our clocks are calibrated so that we remove one second from the measurement of time. So what we actually do with the leap second is not to add a second, but instead hide it, delaying the coming of the next day.

We sweep one second under the rug, a little ashamed that we cannot cope with it any other way. Life goes on but the seconds we hide away will always be there in the past as a testimony that not everything can be exact.

1 comment:

  1. Things can be exact, but to do so requires being painstakingly precise about the ambiguous meanings of words like "second" and "day". Precision demands complication, for simplicity will not adequately describe reality.

    A major problem is the lack of international agreement in laws regarding the notion of time.