## 3.1.2. Physical Clocks

3.1.2. Physical Clocks

Although Lamport's algorithm gives an unambiguous event ordering, the time values assigned to events are not necessarily close to the actual times at which they occur. In some systems (e.g., real-time systems), the actual clock time is important. For these systems external physical clocks are required. For reasons of efficiency and redundancy, multiple physical clocks are generally considered desirable, which yields two problems: (1) How do we synchronize them with real-world clocks, and (2) How do we synchronize the clocks with each other?

Before answering these questions, let us digress slightly to see how time is actually measured. It is not nearly as simple as one might think, especially when high accuracy is required. Since the invention of mechanical clocks in the 17th century, time has been measured astronomically. Every day, the sun appears to rise on the eastern horizon, climbs to a maximum height in the sky, and sinks in the west. The event of the sun's reaching its highest apparent point in the sky is called the transit of the sun. This event occurs at about noon each day. The interval between two consecutive transits of the sun is called the solar day. Since there are 24 hours in a day, each containing 3600 seconds, the solar second is defined as exactly 1/86400th of a solar day. the geometry of the mean solar day calculation is shown in Fig. 3-3.

Fig. 3-3. Computation of the mean solar day.

In the 1940s, it was established that the period of the earth's rotation is not constant. The earth is slowing down due to tidal friction and atmospheric drag. Based on studies of growth patterns in ancient coral, geologists now believe that 300 million years ago there were about 400 days per year. The length of the year, that is, the time for one trip around the sun, is not thought to have changed; the day has simply become longer. In addition to this long-term trend, short-term variations in the length of the day also occur, probably caused by turbulence deep in the earth's core of molten iron. These revelations led astronomers to compute the length of the day by measuring a large number of days and taking the average before dividing by 86,400. The resulting quantity was called the mean solar second.

With the invention of the atomic clock in 1948, it became possible to measure time much more accurately, and independent of the wiggling and wobbling of the earth, by counting transitions of the cesium 133 atom. The physicists took over the job of timekeeping from the astronomers, and defined the second to be the time it takes the cesium 133 atom to make exactly 9,192,631,770 transitions. The choice of 9,192,631,770 was made to make the atomic second equal to the mean solar second in the year of its introduction. Currently, about 50 laboratories around the world have cesium 133 clocks. Periodically, each laboratory tells the Bureau International de l'Heure (BIH) in Paris how many times its clock has ticked. The BIH averages these to produce International Atomic Time, which is abbreviated TAI. Thus TAI is just the mean number of ticks of the cesium 133 clocks since midnight on Jan. 1, 1958 (the beginning of time) divided by 9,192,631,770.

Although TAI is highly stable and available to anyone who wants to go to the trouble of buying a cesium clock, there is a serious problem with it; 86,400 TAI seconds is now about 3 msec less than a mean solar day (because the mean solar day is getting longer all the time). Using TAI for keeping time would mean that over the course of the years, noon would get earlier and earlier, until it would eventually occur in the wee hours of the morning. People might notice this and we could have the same kind of situation as occurred in 1582 when Pope Gregory XIII decreed that 10 days be omitted from the calendar. This event caused riots in the streets because landlords demanded a full month's rent and bankers a full month's interest, while employers refused to pay workers for the 10 days they did not work, to mention only a few of the conflicts. The Protestant countries, as a matter of principle, refused to have anything to do with papal decrees and did not accept the Gregorian calendar for 170 years.

Fig. 3-4. TAI seconds arc of constant length, unlike solar seconds. Leap seconds are introduced when necessary to keep in phase with the sun.

BIH solves the problem by introducing leap seconds whenever the discrepancy between TAI and solar time grows to 800 msec. The use of leap seconds is illustrated in Fig. 3-4. This correction gives rise to a time system based on constant TAI seconds but which stays in phase with the apparent motion of the sun. It is called Universal Coordinated Time, but is abbreviated as UTC. UTC is the basis of all modern civil timekeeping. It has essentially replaced the old standard, Greenwich Mean Time, which is astronomical time.

Most electric power companies base the timing of their 60-Hz or 50-Hz clocks on UTC, so when BIH announces a leap second, the power companies raise their frequency to 61 Hz or 51 Hz for 60 or 50 sec, to advance all the clocks in their distribution area. Since 1 sec is a noticeable interval for a computer, an operating system that needs to keep accurate time over a period of years must have special software to account for leap seconds as they are announced (unless they use the power line for time, which is usually too crude). The total number of leap seconds introduced into UTC so far is about 30.

To provide UTC to people who need precise time, the National Institute of Standard Time (NIST) operates a shortwave radio station with call letters WWV from Fort Collins, Colorado. WWV broadcasts a short pulse at the start of each UTC second. The accuracy of WWV itself is about ±1 msec, but due to random atmospheric fluctuations that can affect the length of the signal path, in practice the accuracy is no better than ±10 msec. In England, the station MSF, operating from Rugby, Warwickshire, provides a similar service, as do stations in several other countries.

Several earth satellites also offer a UTC service. The Geostationary Environment Operational Satellite can provide UTC accurately to 0.5 msec, and some other satellites do even better.

Using either shortwave radio or satellite services requires an accurate knowledge of the relative position of the sender and receiver, in order to compensate for the signal propagation delay. Radio receivers for WWV, GEOS, and the other UTC sources are commercially available. The cost varies from a few thousand dollars each to tens of thousands of dollars each, being more for the better sources. UTC can also be obtained more cheaply, but less accurately, by telephone from NIST in Fort Collins, but here too, a correction must be made for the signal path and modem speed. This correction introduces some uncertainty, making it difficult to obtain the time with extremely high accuracy.

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