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Plots of the time dilemma

What nature does, and what time providers must handle

The plot below shows the variability of the rotation of the earth and the challenge that it poses to time keepers who are tasked with keeping clocks set to agree with the ongoing count of days in a calendar. Note that the earth sometimes spins slower, and sometimes spins faster. The variations are basically due to weather in the atmosphere, oceans, and core of the earth. This is why there cannot be a leap second schedule, for issuing a schedule of leap seconds would be like making a schedule of the weather.

length of day
PDF file SVG file Many more details about the above plot

The insertion of leap seconds is required by international agreements that define the meaning of the word "day".
The number of leap seconds which must be inserted into UTC is proportional to the shaded area under the curve.

What humans do, and what time consumers must accept

People like to agree on the answer to the question

What time is it?
In the 1800s the UK Admiralty recognized that most ships were navigating using chronometers so they switched the nautical almanac to the mean solar time of Greenwich. Then the railroads demanded the use of watches set to standard time to simplify scheduling and avoid crashes. The advent of the trans-Atlantic telegraph cables required the whole world to find a way to agree on the time, and the 1884 International Meridian Conference produced that agreement.

In order to set all clocks to the same time at a nanosecond level there must be some agency in charge of deciding what time it is, and there must be mechanisms for distributing that time from the time producers to the time consumers. Radio broadcasts of time signals have long been the most common mechanism, and consumers do not have much choice about how they get their time.

The plot below shows the kinds of time which have been used internally by physicists and astronomers along with the kinds of time which have been available to the general public.

The multitude of horizontal lines makes it evident that people engaged in technical purposes (such as navigation) have repeatedly chosen to abandon the notion of counting days in favor of counting atomic seconds, but the termination of LORAN-C shows that all the atomic time scales are products of human decisions that can be changed or abandoned at any time. Only a time scale based on the rotation of the earth is guaranteed to persist indefinitely. In all calendar systems the ongoing counts of days have been based on the rotation of the earth, not on cesium atoms.

How the leap second came into being

The descending slide and staircase show the two goals which have been the underlying principles for radio broadcast time signals since 1960:

Those two goals are incommensurate. This was plainly explained by the
IAU in 1964, but the powers that be deemed that radio broadcast time signals must satisfy those two goals. Therefore in 1972 the CCIR (now ITU-R) changed radio broadcast time signals such that there has been no relationship between the duration of the day and the duration of the second, and that one day is not the same as 86400 seconds. Without foresight for the confusion that would result, those simple and ancient notions of the way that calendars and clocks work were abrogated for the sake of radio broadcast time signals that satisfied the two goals. In the radio broadcasts now known as UTC the notions of time and date are two separate concepts where the two goals are maintained by the insertion of leap seconds.

With leap seconds in UTC one calendar day counts one turn of the earth on its axis with respect to the sun. Without leap seconds one calendar day would count 794 243 384 928 000 hyperfine oscillations of cesium-133. The fifteen year long process during which the ITU-R has not reached a decision indicates that many are not prepared to redefine the day from the sun to the cesium.

differences between time scales
PDF file SVG file Many more details about the above plot

What humans used to do, and why reconstructing the past is a mess

Prior to the era of coordination every agency responsible for broadcasts of time signals reset its clock as needed in order to keep the broadcasts in agreement with earth rotation. From the beginning it had been inconceivable that the radio broadcasts could be allowed to differ significantly from earth rotation. The following plot shows the behavior of time signals broadcast by the US NBS which made 29 leaps during 3 years. In constrast with the plot above where flat means uniform, the following plot shows UT2 as flat, and atomic time as slanted curves with leaps.

broadcasts before UTC
source: NBS Misc. Pub 236 (1960/1961)

The US and UK agreed to coordinate their broadcasts of time signals in 1959 August, and coordination began early in 1960. Prior to that date these sorts of steps or leaps were inserted regularly into all time scales, and each national agency responsible for broadcasts of time signals added steps of different sizes at different times. Prior to atomic chronometers there was no easy way to make a record of the steps or a plot like this because there was no chronometer more stable than the earth.

a chronometer precise to one second in 300 million years

means a purely atomic calendar off by 3 billion days in 300 million years

The precision of atomic chronometers is often described by pointing out that the NIST-F2 cesium fountain chronometer "would neither gain nor lose one second in about 300 million years". This means that if NIST were to build two of these chronometers, and if they were to operate them for 300 million years, then the two chronometers would agree to within one second.

300 million years is about 100 billion days. If NIST-F2 were used as the basis of UTC, and if the ITU-R were to abandon leap seconds in UTC, then in 300 million years a calendar based on that UTC without leap seconds will have counted about 3 billion more days than the inhabitants of the earth will have witnessed by watching the sun rise and set as the earth rotates. The cesium atomic chronometer is extremely precise, but a calendar based on it is very different than what humanity has always used.

Steve Allen <sla@ucolick.org>
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