The Long History of One Second (Part I)

    For Timing

Let's start with question one:
The movie starring Tom Hanks which received 11 nominations and 5 wins (including Best Director) at the 1999 Academy Awards was titled Saving Private Ryan. The climax of the film's first half focused on D-Day, or the Allied invasion of Normandy during World War II. This same invasion was also depicted in a 1962 movie; what was that movie's name?

The Changing Length of a Day

This question is worded in somewhat confusing fashion, as is commonly seen in television quiz shows and the like. By the way, the correct answer to the question is The Longest Day. Some of you may recall the heroic yet heartbreaking march from this film, which focuses on the importance of this ground battle in relation to the direction of the war and of history itself.
As these titles demonstrate, people perceive and interpret time in subjective ways. However, in objective terms, a day's length actually increases and decreases throughout the year. Let's move on to question two, which pertains to this topic:

The length of one day, as measured precisely based on earth's position relative to the sun, changes from season to season. By what degree does each day's length fluctuate? Choose one of the following answers:
(1) By milliseconds (2) By seconds (3) By minutes (4) By hours

Many readers likely chose answer 4 based on the idea that "one day" refers to the number of daylight hours in a day, but this is incorrect. Alternatively—and for good reason—some of our particularly knowledgeable readers may have chosen answer 1.
Returning to the subject at hand for now, a day's length is defined as the time between the sun's crossing of the southernmost point on its meridian transit for one day, and that same crossing of the southernmost point on the next day, which is referred to as "meridian transit time." The answer to the above question can be confirmed by looking at the accompanying graph. Meridian transit time fluctuates by approximately ±30 seconds throughout a single year, but the maximum range of this fluctuation does not reach a full minute, which tells us that answer 3 cannot be correct. Answer 2, then, is the correct one: a day's length varies by seconds. However, even just a few seconds here and there seems like quite a large change for a single day's length, doesn't it?

Disparities Caused by the Earth's Rotation and Orbital Revolution

Let's delve a bit deeper into this topic. The graph shows two major spikes over a year's time, but their heights differ. Upon closer examination, we can determinate that this is caused by one annual spike and two biannual spikes, which overlap during one of the biannual spikes.
The annual spike is due, of course, to the revolution of the earth around the sun, which proceeds in an orbit that is slightly elliptical rather than perfectly circular in shape and thus results in a change of distance from the sun, approximatly 5 million kilometers at most (the earth is at an average total distance of 150 million kilometers from the sun). Earth's aphelion, or its most distance point from the sun, occurs in early July, and at that time orbital speed decreases. In early January, earth reaches its perihelion, or its closest point to the sun, at which time its orbital speed increases. This explains the first reason for each day's variation in length.

However, simply reading a written explanation of this phenomenon may not make it easy to visualize. Let's look at it from another angle—specifically, from an airborne perspective, as if we were hovering above the North Pole. From this vantage point, we can observe the earth spinning counterclockwise below us, like a spinning top toy, as well as the gradual counterclockwise curve of its orbit around the sun.
Keep in mind that the length of one day is not equal to the amount of time it takes the earth to rotate 360 degrees, because earth also advances one day's worth along its orbital path during each rotation of the planet, which causes the facing of the sun in the sky as viewed from earth to rotate leftward and away. When the sun once again reaches its southernmost position, a new day is marked as having started—with, of course, the above rotational angle factors taken into consideration.
The following simple equation can be used to explain the changing length of a day:

1 day (meridian transit time) = 1 rotation of the earth + α (required rotational angle relevant to one day's worth of orbital progression)

Even if the planet's rotation is constant, the orbital speed increases and decreases at different times of the year, which changes the α variable in the above equation and thus results in differing day lengths. In the graph we looked at earlier, the largest spike is during winter, when the earth is at its closest point to the sun and its orbital speed the fastest.

The cause of the two biannual spikes, on the other hand, is axial tilt of the planet. Relative to its revolution around the sun, earth's axis of rotation has a set and unchanging degree of tilt. However, when viewed from the perspective of the sun, earth's axis goes through two cycles of tilt and return: the axis is vertically oriented at the winter solstice, tilted to its maximum degree at the spring equinox, vertical again at the summer solstice, and tilted to its maximum degree again at the autumnal equinox. In geometric terms, the α variable in the above equation reaches its highest values at the winter and summer solstices, and its lowest values at the spring and autumnal equinoxes, thus creating the biannual variations in the graph.

Going back to D-Day: This invasion took place on June 6, 1944. This was not the longest day of the year, but it was still one of the longer ones nevertheless (viewed in objective terms, of course).

The tilt of the earth relative to its orbital plane with the sun varies throughout the year from 23.4 degrees to –23.4 degrees,
which in absolute terms represents a biannual cycle and thus creates the biannual variations in variable α.
Created based on Google Earth images (Landsat, Copernicus)

Defining One Second Without Relying on Earth's Movements

The length of one second, which is our standard division of time, is based on a duodecimal division of the length of a day. Therefore, the fact that a year varies in either direction by a degree of up to 30 seconds in either direction is no trivial detail. That's why the concept of a "mean solar day," which is an average of all solar days for the year, has been adopted.
A mean solar day doesn't refer to the average value calculated for a specified period, but instead to the length of a day based on a theoretical earth which travels in a perfectly round orbit around the sun and maintains a vertical axial orientation throughout relative to the orbital plane. Looking once again at the graph above, the mean solar day is the horizontal line that extends across from the zero value. In 1799, the French revolutionary government publicized its metric system, which defined 1 second as 1/86,400th of a mean solar day, and this definition was used for many years since.

Source: W.A. Marrison. "The Evolution of the Quartz Crystal Clock." The Bell System Technical Journal, 1948.

As technologies used to measure time advanced, so did the definition of one second. Mechanical clocks and watches, as well as the chronometer which uses a spring-driven mechanism, were invented around the start of 19th century. At that time, improvements were also made to pendulum clocks, which take advantage of gravitational force to keep time. These enabled more precise measurement of variations in a day's length, down to roughly a second's accuracy. Quartz clocks and watches, which use a quartz-regulated oscillator mechanism, were invented in the 20th century and provided a means of measuring daily time with precision down to the millisecond.
Building on this technological progress after World War II, the Comité international des poids et mesures (CIPM), which is known in English as the International Committee for Weights and Measures (ICWM), put forth the fraction 1/31,556,925.9747 in 1956 as a more equal division of the year (earth's orbital cycle) into seconds in pursuit of a time definition based on a more perfect imagining of the earth's orbit with fewer fluctuations. This came roughly 150 years after the establishment of the metric system and its original definition.

but the postwar definition would be updated once again when the atomic clock came along. Each atom (isotope) has its own unique vibration frequency, which is used like an oscillator in an atomic clock. Each transition between an atom's state occurs in sync with a specific electromagnetic frequency, and these are detected and counted to define one second. The concept for this clock existed before World War II, and in the 1950s confirmation was successfully made of stable time-measuring performance in an atomic clock using nonradioactive cesium (Cs). In 1967, 1 second was defined anew as a duration equivalent to 9,192,631,770 cycles of radiation for the transition between two energy levels of the ground state for cesium-133.

This was adopted as a standard unit of time that did not rely at all on measurements of earth's rotations and orbital revolutions. Moreover, this standard enabled accurate measurement of inconsistencies in the earth's movements.

The Long History of One Second (Part II)

Writer introduction

Mr. Mitsunari Kita

Mr. Mitsunari Kita   Science and technology writer

Born in Ishikawa Prefecture in 1964. Based on his experience in covering industrial technology, cutting-edge technology, and space development, he is passionate about unraveling and conveying difficult topics in an interesting way to people of all ages, from children to senior citizens. From 2009 to 2014, he was a member of the editorial board of "JAXA's," the official magazine of the Japan Aerospace Exploration Agency. Author and co-author of the following books: 『あなたにもミエル化? ~世間のなりたちを工学の視点から~』(幻冬舎mc)、『私たちの「はやぶさ」その時管制室で、彼らは何を思い、どう動いたか』(毎日新聞社)、『東京大学第二工学部70周年記念誌 工学の曙を支えた技術者達』(東京大学生産技術研究所) etc.,

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Column by Mr. Mitsunari Kita  (Science and technology writer)