A Great Leap…Forward?

By John Conway | February 24, 2008 11:04 pm

Pretty soon, on March 9, we’ll all change our clocks one hour forward to change from standard to daylight-savings time. An absolutely pure misnomer, daylight savings time is nevertheless, to my mind, the greatest success story of mass psychological control there ever has been. Just imagine if the government put out some sort of strongly worded encouragement that everyone needs to get up an hour earlier, starting Monday, and should continue to do so for the next eight months, so as to save energy and have a little more time in the evening when it’s light out. I imagine not many people would comply.

But, what they do instead is to say, “okay, starting early Sunday morning, it will suddenly be an hour later on your clock for the next eight months!” And, magically, just about everyone complies…it’s breathtaking, actually.

But what time is it really? This week, on February 29 we have a Leap Day, a once-every-four-years event. Actually, it’s not once every four years; we skip it every hundred years, except we don’t skip it every four hundred years. That is, 2000 was a leap year, but 1900, 1800, 1700 etc. were not. We’ve been doing this since 1582 when Pope Gregory introduced the new calendar to keep Easter from drifting, slowly but surely, away from the spring equinox, that magical moment when the earth’s axis makes an angle of 90 degrees to the line connecting the center of the sun with the center of the earth. On the spring equinox, the length of day and night are equal everywhere on the earth (at the poles the sun remains on the horizon all day). In the Gregorian calendar, the average calendar year is 365.2425 days, because this is the average number of days from one spring equinox to the next.

If you ask the average person on the street, though, just what “one year” means, though, they’ll most likely say “it’s the amount of time it takes the earth to go around the sun”. What they are probably thinking is that the imaginary line mentioned above from the earth to the sun sweeps out a full circle in one year; this is called a sidereal year: the time it takes for the sun to appear in the same place against the backdrop of the fixed stars. They’d be close, but no cigar: the earth’s axis, which is tilted at about 23.5 degrees to the plane of the earth’s orbit, is actually not fixed in its direction in space. The earth rotates on an axis which precesses, similar to that of a spinning top with one point fixed. It takes 26,000 years to go al the way around and come back roughly where it was. And so, in fact, the calendar year (also called the “tropical year”) is about 20 minutes shorter than the sidereal year. (You can easily calculate this yourself: it’s 1/26000 of a year!)

Our Gregorian calendar will keep the spring equinox quite close to March 21 or so, but eventually our familiar winter constellations like Orion will eventually become summer ones, and the North Star will appear to move in ever-widening circles about the celestial north pole.

If you dig further into all this you quickly see that the day, which I am sure you’ll find people to tell you is “24 hours” has a similarly ambiguous definition. The sidereal day, the time it takes the earth to spin once on its axis, is 23 hours, 56 min, 4.1 sec., just less than the solar day of 24 hours. Not surprisingly, after you think about it, this difference is close to 1/365 of a day, since as the earth goes around the sun, one full orbit is in effect a day. (If the earth were not rotating, then there would be one solar day per year.)

But is a day even exactly 24 hours? It turns out that for various reasons, the earth’s rotation speeds up and slows down over long periods. The second was redefined in 1967 to be the time it takes for 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom. This is the basis for our measurement of time in the SI system of units. As a result, we no longer define the second as 1/86400 of a solar day, and we need to add in a leap second every so often to account for the fact that the earth’s rotation is slowing by about 2.3 milliseconds per day per century, and we chose the year 1900 as the reference for the second. This means we are now accumulating one leap second every 430 days or so. We’ve added leap seconds at about that rate since the first one in 1972 (always at midnight on New Year’s Eve).

So now we have International Atomic Time (TAI) with no leap seconds, and Coordinated Universal Time (UTC) which have drifted apart by 33 seconds since 1972. We need both systems, since we want a simple way to calculate accurate time differences without having to take into account leap seconds, but we want noon to stay when the sun is high in the sky. The US Navy is on it, don’t worry.

Except for that one-hour daylight “savings” time…


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