cdybedahl | Leap Seconds

BBC News has an article about the recent (non-)decision about the continued existence or not of leap seconds. They also have an explanation of what leap seconds are. I don't think their explanation is very good, so I'm going to try to write a better one. Here goes.

The whole thing is about measuring time. Humans have done that for a very long time indeed, with steadily increasing accuracy. During the 20th century, the accuracy got sufficiently good that it became important to figure out what, exactly, we were measuring and how we measure it. The "what" part heads off into physics and is irrelevant for this post. "The passage of time" is definition enough right now. The entire leap second thing comes out of "how".

In order to measure something, we need a scale. We need a basis, some sort of ground against which we compare whatever it is we measure. When we measure temperature, we use hundreths of the difference between the temperature where water melts and where it boils (well, some of us do, at least). For measuring time, we use 86400ths (24*60*60) of the time it takes for the Earth to turn around its axis. We call those bits of time "seconds", like we call the bits of temperature "degrees centigrade".

Except it turns out things aren't quite that simple when it comes to time. Without meaning to, we have for at least the past 4000 years been using two different scales to measure time. It's just that the two are so very nearly the same that it wasn't until the mid-20th century that the difference became measurable.

The two scales are these: the Earth's rotation and pure physics. The Earth's rotation is the scale used by a sun clock. This is almost certainly the oldest way to measure time at a smaller scale than entire days. Ram a stick into the ground while the sun shines, and you have a clock. This has some obvious drawbacks, like the fact that the sun doesn't always shine. So somewhere between 2000BCE and 4000BCE someone in the Middle East or China invented the water clock. That's almost as simple as the sun clock: a container of water with a small hole in it. You measure the passing of time by how fast the water dribbles out. This, unlike the sun clock, is a pure physics clock. The time it takes for the water to move is entirely unaffected by the rotation of the Earth. The only things that affect the water clock are gravity and evaporation.

Fast forward to today. The slightly weird fact is that we still use those two scales. Earth-rotation time is no longer measured by watching the shadow from a stick in the ground, but instead by using radio telescopes to watch extremely distant quasars. Pure-physics time is no longer measured by falling drops of water, but by counting extremely rapid variations in Caesium atoms at near absolute zero temperature.

Now, since we can chose arbitrarily how we divide the measurements into pieces, these two scales wouldn't be a problem if it wasn't for one simple fact: the Earth's rotation is slowing down (if you're curious why, look up tidal acceleration on Wikipedia). Since we've defined the length of an Earth-rotation second as a fraction of the time it takes to rotate once, slower rotation means that those seconds get longer. It's like cutting pieces of a cake: if you cut the same number of pieces from a bigger cake, each piece turns out bigger. Since we carve out the same number of seconds from each rotation, if the rotation takes more time each second covers more time. Earth-rotation seconds are not constant in length! Pure-physics seconds, on the other hand, are all exactly the same size.

The official name for the main Earth-rotation time scale is UT1, "Universal Time One". The main pure-physics time scale is called TAI, "Temps Atomique International". The slowing rotation of the Earth makes it so that these two scales are very slowly moving out of sync. Over the course of a few thousand years, they will drift apart so what would be "noon" in TAI will happen while the sun is not in the sky. In UT1, the sun will always be visible while the clock shows daytime hours. Since most times we care what the clock shows it is has to do with human things, UT1 is a more attractive scale for everyday use. But if you're doing the sort of thing where very small bits of time are relevant (like, for example, GPS navigation), you really want your seconds to have constant length. So there TAI is by far the most useful scale.

In order to bridge that gap, a compromise time scale was designed. It's called UTC, "Coordinated Universal Time" (the acronym doesn't work out due to Anglo-French rivalry). In UTC, every second is exactly as long as a TAI second, so it too slowly drifts compared to UT1. But in UTC, when the difference compared to UT1 becomes larger than 0.9 seconds, one second is added or skipped to bring them back closer together. And those, finally, are leap seconds. Those seconds that are added to or taken from UTC in order to keep it mostly synchronized with UT1 while still having constant-length seconds. In reality, there have only been seconds added, but in theory there could in the future be a need to skip one.

Anyway. To summarize, we have these three scales for measuring time:

UT1, which measures the Earth's gradually slowing rotation and has non-constant-length seconds.

TAI, which measures ridiculously exact subatomic events and gradually gets out of sync with the sun.

UTC, which has constant-length seconds and tracks the sun, at the cost of occasionally having minutes with 61 or 59 seconds in them.

As far as I know, every country in the world uses the UTC scale for their official civil time. We modify it with time zones, so for example Stockholm time is UTC plus one hour (for now, we disregard the horror that is daylight savings time). A leap second is due to be added to UTC at the end of June this year, so in the small hours of 1st July I will be able to see the clock go 00:59:58, 00:59:59, 00:59:60, 01:00:00, 01:00:01, if I have a good enough clock.

So that's what leap seconds are. The reason they're being mentioned in the news at the moment is that there is a suggestion that they be abolished. As far as I've been able to figure out, the suggestion comes from the US delegation to the body that decides these things (ITU) and their argument boils down to "Leap seconds are too hard!". They've expressed a fear that high-end navigation equipment and other stuff that relies on very exact time might malfunction at leap seconds. Note "might". The obvious counter-arguments would seem to be "We've had 34 of them so far and there hasn't been any problems" and "So use UT1 or TAI for those applications, then". But what do I know.