Clocks mark time
(appeared in June 2015)

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Later this month, the world’s clocks will sound one extra tick to get in step with the rotation of the earth, says S.Ananthanarayanan.

Our units for measuring time are derived from the constancy of the earth’s rotation. But if the earth herself slows down or speeds up, the clocks on the earth have to take note, and count one second twice, so that the earth catches up, or skip one second, to catch up with the earth. Although seconds, minutes and hours have their origin in the speed of the earth’s movement, the clocks that we use work on a more accurate timekeeper than the earth. And periodically, when the earth gets nearly a whole second out of step, the clocks need to adjust their own count to be in time with the earth. This happens about once in two years, and such an adjustment is being carried out at midnight on June 30, this year.

Minutes and seconds

A number system based on the number sixty has been found suitable for dealing with time. Just as the decimal system has become popular, the number sixteen was earlier the base for weights and measures and even money – we had 16 ounces to the pound or 16 annas to the Rupee, for example. Locations in computer memory too, are best described by numbers based on 16, the Hexadecimal system. While the base ten, of the decimal system, is considered easier to deal with becausewe have ten digits, the bases, sixteen or twelve, like 12 pence or 12 inches, also have their merits, as the squares, 256 or 144 have more divisors than the number 100. For a simillar reason, that 60 is the smallest number that can be divided by all numbers from 1 to 6, the sexagesimal system, or the number system based on sixty, came into use in treating time.

The number system based on sixty was devised by the Sumerians, near modern Iraq, some 3000 years ago. The Babylonians, who came after the Sumerians, also used the system and in 140 AD, Ptolemy, the Greek astronomer divided the length of the day based on sixtieths. But it was around 1000 AD that Islamic scholars, like Al Biruni divided the day into 24 parts and then divided the hours length of the into sixty minutes and then sixty seconds. The modern second is thus 1/(24x60x60) = 1/86,400 of the mean solar day and in 1874, this was adopted as the unit of time for scientific purposes. But the length of the mean solar day was found to be variable and the base was changed to the length of the day based on the time of revolution of the earth around the sun, first with reference to the constellations and then to the interval between the equinoxes. But even this definition was found inaccurate and in 1967, the second was defined based on the frequency of radiation from the cesium atom, and this has held so far.

The system of the time of the day based on the atomic clock is called the Coordinated Universal Time (known as UTC - a compromise with the French Temps Universel Coordonné), while standards of Mean Solar Time, like Greenwich Mean Time, are known as UT1. As the second based on the atomic clock is quite close to the second based on astronomical time as well as on the average length of the solar day over a long period, UTC does not stray more than a second, over the length of a year, from UT1, , and is now the standard for science, and also for aviation and other civil uses. A practical difference of UTC from othe systems is that it does not observe daylight saving time. However, as the solar day is not exactly 86,400 seconds by the atomic clock, UTC does stray from solar time and needs to be corrected. The year itself, we all know, is not exactly 365 solar days, but some six hours longer. We thus have the device, to adjust the calendar, of adding a day on 29th February every fourth year, as a ‘leap’ year. In the same way, the adjustment of one second which needs to be carried out approximately once in two years to keep UTC in step with Mean Solar Time, is called a ‘leap second’. Keeping track of the progress of UTC and IT1, as well as announcing leap seconds, is managed by the International Earth Rotation and Reference Systems Service (known by an earlier acronym, IERS). The adjustment to be carried out on 30th June this year would be that the UTC clock, at midnight, would mark time for one second, to slow down to the time kept by the rotation of the earth. Thus, where the clock should have moved from 11.59.59 to 12.00.00, it would first move to 11.59.60, and then move to 12.00.00. This is just like the month of February not moving from the 28th to 1st March, but whiling a day away, as 29th Feb.

The 25 corrections since the system of correction started, in 1972 however, have all been cases of delaying UTC by one second and none to save a second. This is to say that the solar year has been a little slower than the year according to the atomic clock. Apart from the way the atomic second is defined, it is also a fact that the rotation of the earth is slowing, by a barely perceptible extent, since centuries. The effects of atmospheric and geological changes have partly compensated, but not in a uniform way. The difference between the two clocks is hence not regular and the time taken for the difference between the clocks to grow to one second has not been the same every time it happens. To have twenty five corrections in forty three years works out to one correction in less than every two years. But the last correction was in 2012 and we can see that the 26th, on June 30, will be well over two years later. In fact, there were no corrections between Jan 1999 and Dec 2005 but there were nine corrections in the eight years from 1972 to 1979.

Leap Minutes

Adding leap seconds, though academically elegant, is not without problems in the real world. Different processes in the world are aligned either to UTC or to UT1 and also different species of local time. Computers hence need to take into account the time system followed and make adjustments. In the case of leap years, all callendars in the world are adjusted at the same time and there is no difficulty. But when leap seconds are announced, although this is done six months in advance, there may be problems if all processes do not effect the change together and also with the working of the Internet, which relies on recording the time that data takes to move, to find paths for connections.

There is hence some controversy about continuing with leap seconds, and alternatives, one being to make adjustments less frequently, are suggested. If leap minutes were used,for instance, adjustments may need to be made only once in a century


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