From the calendar to the second atom
From the calendar to the second atom
by David Monrós
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The first human beings only knew that night follows day, that hot and cold seasons alternate and that the Moon appears or disappears. It took them a long time to discover that there is a periodicity and regularity to these natural phenomena, even though they have a profound influence on the development of daily life.
As our mind evolved, so did our way of thinking, of anticipating the events we knew were coming. At first it was cyclical, because we discovered the natural patterns of the weather and the movements of the stars in the sky, but as we developed increasingly sophisticated tools and began to master the secrets of nature for our own benefit, we learned to think in future time.
Our way of measuring time and understanding it in a linear and non-cyclical way, meant a gradual change in the appearance of modern man, which made the way of understanding life in many ancient civilizations collapse and was fundamental for the development of the West and what we know as modernity.
Our mind has the particularity of recognizing regularities in chaos and acting accordingly. It does not respond to a classic survival pattern, in fact, it is the only animal species on earth capable of performing premeditated acts, ordering ideas to reach conclusions thanks, also, to an abstract perception of space and time.
This article takes a brief look at the history of time as a magnitude, the problems that have arisen in measuring it and how we are solving them in the era of electronic positioning systems, where differences in the computation of the value of a second are fundamental in determining our instant geographic location.
DEFINITIONS:
Lunar calendar: The lunar calendar is the way to calculate the years according to the moon. In the lunar calendar, each lunation corresponds to a lunar month, that is, each period between two times when the moon is in exactly the same phase (either waxing or waning) is called a "lunar month. Each lunar month corresponds to 29.53 solar days.
The "lunar month" has always been used by human beings to calculate certain regularities in Nature, such as the sexual cycle of women or the tides. The beginning of the lunar month is an arbitrary point that varies according to culture: for example, the Chinese calendar considers the new moon (the first day on which the moon is not seen in the sky) as the beginning of the month, while other lunar calendars take the first day of the month as the first waxing moon.
Julian Calendar: The new calendar was introduced in 46 BC with the name "Julius" and much later "Julian", in honor of Julius Caesar. In that year alone, 445 days were counted, instead of the normal 365, to correct the mismatches of the previous calendar, and it was called "the last year of the confusion". To this end, two Merkedinus months were added, between November and December, one of 33 days and another of 34, in addition to the month intercalated in February.
The Julian calendar considered that the tropical year was made up of 365.25 days, while the correct figure is 365.242189, i.e. 365 days, 5 hours, 48 minutes and 46 seconds. Those more than 11 minutes added to each year, mean one additional day every 128 years.
Gregorian Calendar: The Gregorian calendar is a calendar that originated in Europe and is now used officially almost everywhere in the world. It is named after its promoter, Pope Gregory XIII, who promulgated its use through the Bull Inter Gravissimas. From 1582 onwards, it gradually replaced the Julian calendar in different countries, which had been used since Julius Caesar established it in 46 BC. The Julian calendar was certainly the Egyptian calendar, the first known solar calendar that established the length of the year at 365.25 days.
The Gregorian reform was born from the need to implement one of the agreements of the Council of Trent: to adjust the calendar to eliminate the gap produced since the first Council of Nicea, held in the year 325, which had fixed the astral moment in which Easter should be celebrated and, in relation to it, the other mobile religious festivals. What mattered, then, was the regularity of the liturgical calendar, for which it was necessary to make certain corrections to the civil one. Basically, it was a matter of adapting the civil calendar to the tropical year.
A tropical year is the time required to increase the mean longitude of the Sun by 360 degrees above the ecliptic, i.e. to complete one revolution. Its duration is 365.242189 days of mean solar time (365 days 5 h 48 m 46 s).
A "day" is the period of time that the Earth takes from the time the Sun is at its highest point on the horizon until it is at its highest point again. It is a way of measuring time although the development of astronomy has shown that, depending on the reference used to measure a turn, it is either solar time or sidereal time. The first takes as its reference the Sun and the second takes as its reference the stars.
The mean solar day is an average of the true solar day, and corresponds to calendar time. It is equivalent to 86 400 seconds, a unit currently defined by very precise atomic properties, which allows the differences from the true solar day to be measured (the time it takes for the Earth to reach the highest point on the horizon until it reaches that point again).
The mean solar time is the time measured over the reference of the average solar day. It consists of the time between the consecutive passage of the average sun through the upper meridian of the place, being an average of the true solar day, and corresponds to the civil time. It is fundamentally a local time, since it depends on the observation of the consecutive passage of the average Sun by the meridian of each place. This phenomenon shows that it depends fundamentally on the longitude of the place of observation (all the places with the same longitude, independently of the latitude in which they are located, have the same average solar time).
EqT: Equation of time. The equation of time is the difference between mean solar time (usually measured by a clock or stopwatch) and apparent solar time (the time measured by a sundial). This difference varies throughout the year and reaches a greater difference in early November, when mean solar time is more than 16 minutes behind apparent solar time (specifically 16 minutes 33 seconds around November 3), and in mid-February, when mean solar time is more than 14 minutes ahead of apparent solar time.
GMT: Greenwich Mean Time, the time standard that originally referred to average solar time at the Royal Greenwich Observatory, the site chosen in 1884 by the International Meridian Conference as the first meridian.
UT: Universal Time. UT was introduced in 1928, replacing GMT. The main reason for this was that GMT was based on measuring the position of the Sun, and due to the different inherent motions of the Earth, several problems associated with accurately measuring its position arise.
On the other hand, the UT was based on the measurement of the position of astronomical references other than the Sun, which leads to greater precision but is still a non-uniform time scale, since it is basically based on the measurement of the planet's period of rotation and this has anomalies for various reasons.
Currently the UT has several definitions with differences not exceeding 0.03 s.
UTC: Coordinated Universal Time (UTC is a compromise between the English version, Coordinated Universal Time, and the French version, Temps Universel Coordonné), is the current time standard based on non-astronomical references.
For UTC, the different atomic clocks scattered around the planet are periodically consulted and an average of the different results is made in order to subsequently adjust the world reference time with respect to Universal Time (UT).
UTC time is defined in many ways on the Internet, most of them are simplifications in order not to lengthen the explanation but, as it can be deduced, UTC is a system that harmonizes several systems summarized in two aspects: on the one hand TAI time and on the other hand UT time itself.
NOTE:
In abbreviated form, the nomenclature of this article is: Year-Month-Day and Hour:Minute h in 24-hour format.
The first step towards the constitution of a calendar was taken when human beings understood that the Moon appears, grows and wanes in a periodic and regular way. They thus adjusted their measure of time to the lunar rhythm, and the month appeared, based on the variations of the Moon's shape.
For thousands of years, the Moon governed time. Astronomers observed that its cycle repeated itself every twenty-nine and a half days, and thus fixed the length of the months. Then, seeing that the rhythm of nature repeats itself and that plants grow, flower, mature, and die periodically, they determined to extend their measure of time by joining twelve lunar months into one year.
The ancient Greeks and Romans still used the lunar year to calculate time. Twelve lunar months totaled 354 days, 11 fewer than today. There were still many centuries to go before people would find out the exact length of a year as we calculate it today, that is, the time it takes the Earth to go around the Sun. Therefore, it was necessary to add 45 additional days every four years to prevent the cycle of the seasons from being out of step with that of the months.
In the Roman Empire, the people in charge of making the division of time took advantage of these periods of adjustment according to their interests, until there was total confusion, as each province was governed by the convenience of its rulers. This was the case until 46 B.C., when Julius Caesar ordered that year to reach no less than 445 days to recover all the accumulated differences and errors, and from then on, a calendar was imposed that was in force in Europe until 1582.
The Julian calendar, named after Julius Caesar, had 365 days to which one day was added every four years. This day was interspersed at the end of February, the last month of the year at that time, between the sixth and fifth day before the calends of March, so it was called the bisexual day before the calends.
In 1582, astronomers decided to correct the Julian calendar, since it also did not exactly correspond to the time that the Earth takes to go around the Sun. In the sixteen centuries that this measurement of time had been used, an error had accumulated that added up to ten days.
Pope Gregory XIII applied the last correction to give the definitive form to the calendar we use today: on October 4, 1582, he followed the 15th of October, instead of the 5th, so that he advanced the year in the ten days of delay accumulated since the promulgation of the Julian calendar.
In astronomical terms, the Julian calendar is approximately one day ahead of the tropical year every 128 years, which is equivalent to 11 minutes 14 seconds of excess per year. For the Gregorian calendar, the figure is one day every 3,324 years.
The Gregorian reform consisted in eliminating the leap days at the end of each century. To this end, it stipulated that the years 1700, 1800 and 1900 should be 365 days, despite the fact that 366 days correspond to them. Only the year 1600, 2000, 2400 and all multiples of four hundred will be leap days.
However, there is still a difference of about 26 seconds a year which will mean that in about three thousand years time a new correction of one day will have to be made, but this is no longer covered by the Gregorian calendar.
As already mentioned, if we look at the calendar in numerical terms we see that the duration of a tropical year is 365 days, 5 hours, 48 minutes and 46 seconds. If we had made the seconds, minutes and hours a little longer, the year could have exactly 365 days, but these units are based on the day, which is the time it takes the Earth to go around itself.
The problem arises when we realize that, in a complete revolution of the Earth around the Sun, there is no room for a whole number of turns on itself. In general, the periods of movement of the celestial bodies are never divisible from each other without leaving a remainder. Thus, this remnant of time which exceeds 365 days up to the completion of a year, must be accepted and corrected by adding an extra day at certain intervals.
The Gregorian reform has an error of one day every 3 300 years, 24 times greater than a solution proposed by Mr. E. Hope-Jones in the Horological Journal in April 1942.
Mr Hope-Jones, after explaining how the Gregorian calendar works, which as has already been mentioned is not a simple thing, offered a much more exact and simple solution: starting again from the Julian calendar, in which every three years of 365 days he interposes one of 366, which generates an error of 44 minutes and 56 seconds every four years, he proposed that every 128 years, a year that would correspond to be a leap year, should not be a leap year.
Hope-Jones proves it with the following operations: every 128 years we would have 97 years of 365 days and 31 of 366 days, which gives us a total of (97 x 365) + (31 x 366) = 46 751 days. The actual length of the year is 365.2422 days which multiplied by 128 gives us 46 751.0016. In other words, the error is 0.0016 days every 128 years, that is, one day every 80 000 years, which is not bad if we compare it with the current Gregorian reform.
At the same time, if not before, as the seasons were divided up, the day also began to be divided up, the unit of time for drawing up the calendar and, in turn, the time spent on human activities with the light of the sun. Although the division of the day into 24 hours, as well as the year of 365 days, was certainly established by the ancient Egyptians, the perception of time in Greek society in the 5th century BC is evident from the reading of several Greek and Roman writers of the time who describe, and give references to, instruments identified as the first sundials.
The Greeks' time system was temporary, that is, time was understood as one twelfth of the daytime arc traveled by the Sun, but as such an arc varies throughout the year, time also varies. The Romans, in turn, inherited this day-division system from the Greeks, which eventually led to the introduction of a calendar based on solar time rather than problematic lunar time.
With the exception of the Middle Ages, the technique for measuring the hours evolved thanks to the rise of Arabian astronomy until the Renaissance, when the first mechanical clocks began to be built that did not depend on a direct astral reference such as that of the Sun. Therefore, and more importantly, the use of measurement based on apparent solar time gradually changed to that based on mean solar time, the latter being directly related to the Earth's longitude.
Since the Earth rotates at a constant speed of 360° per day and the new mechanisms for measuring it divide it into 24 hours of 60 minutes and 60 seconds for each minute, there is a direct relationship between time and the geographical coordinate of Longitude, the angular distance of a parallel from a reference meridian, at a rate of 4 minutes per degree.
This circumstance converges in the 1884 International Meridian Conference, where, as a result of the need to create a synchronized universal system for time and position, it is agreed to determine a meridian (of the many used up to that day) as Common Zero Longitude, which makes it possible to establish whether we are to the East or the West and to create a reference time standard throughout the world, the Greenwich Meridian and GMT (now UTC).
In addition, the creation of 24 time zones was proposed (1 hour of time is 15º of arc of a parallel of Length). Since the Earth rotates from West to East, when passing from one time zone to another in an Eastern direction, one hour must be added. On the other hand, when passing from East to West, one hour must be subtracted. This system made it possible to determine the international date change line (the anti-Greenwich meridian) and to enable the various countries, as they adopted this convention, to establish their respective time zones according to their needs (the official or legal time).
GMT is based on the average position of the Sun and was first defined from Greenwich Mean Time, but on January 1, 1925, the convention was adopted that the day should begin at midnight, with 12 hours delay on that day, and since then GMT has been defined from Greenwich Mean Time.
At the same time, the determination of the measurement of time was perfected by improving the machines and techniques to do so. Universal Time was introduced in 1928, replacing GMT, because different inherent motions of the Earth were detected that caused various problems associated with the accurate measurement of its position relative to the Sun.
At that time, the time scale was linked to the period of rotation of the Earth, which was supposed to be uniform, and where the second was defined as 1/86 400 of the mean solar day. Universal Time is based on the measurement of the position of astronomical references other than the Sun, which entails greater precision, but it was still a non-uniform time scale, since it is basically based on the measurement of the rotation period of the planet and this presents anomalies.
The rotation of the Earth is not uniform due to multiple causes (tidal forces, earthquakes, gravitational interactions with the Sun and Moon, etc.). To solve this problem, the Ephemeris Time was defined, which is based on the orbital movement of the Earth around the Sun rather than on the rotation of the Earth on its axis. On the other hand, with the invention of the atomic clock in 1948, it became possible to measure time more precisely and independently of the movements of the Earth, through the counting of the transitions of the caesium 133 atom, with which physicists assumed the work of measuring time that astronomers did.
In summary, the unit of the second is the result of the length of a day, an average of the Earth's rotation which, at first, was with respect to the Sun, GMT time; later with respect to the stars, UT time and, at present, with respect to a radioactive element, UTC-weighted atomic time.
However, a number of problems arise in various aspects of non-civilian life. Mean solar time is as much as 16 minutes behind apparent solar time as it approaches November 3, and by mid-February, mean solar time is more than 14 minutes ahead of apparent time.
The mean solar time (the one shown by a clock or chronometer) and the apparent solar time (the one shown by a sundial and which we can tabulate by observing the sun from a certain place, such as Greenwich) are only equal in four instants of the year, which in our time are April 15, June 14, September 1 and December 25 (and which, moreover, are close to the dates of the equinoxes and solstices).
The origin of this circumstance is derived from the different speed of the earth's movement around the Sun. The Earth's orbit, which is called ecliptic because it is where eclipses occur, is not circular but elliptic, with the Sun occupying one of the foci of the ellipse. According to the laws formulated by Johannes Kepler on translation movements, equal times sweep equal spaces, the Earth slows down its translation speed when it is further away from the Sun because the attraction of the Sun is lower and it speeds up when it gets closer.
Thus, the earth's translation movement is a uniformly varied movement that makes it difficult to find a practical system for measuring daily time in line with the position of the Sun at noon. That is why we have established a regular average time of 24 hours a day instead of constantly adjusting the chronometer or clock for different moments of translation as the Greeks did with the sundial and its temporal measurement of time.
Therefore, when we calculate the time difference with noon of the Greenwich meridian, the passage of the true Sun through the upper meridian of the place, we will have to apply a correction to this phenomenon by means of an equation, that of time, which is a direct consequence of the way we have established to measure time.
On the other hand, in view of all this scientific progress in measuring time accurately, we see that the Earth has slow surprises in store for us, since the day, as such, is becoming longer because the speed of rotation of the Earth is becoming slower as well as variable, so that such accurate precision must be constantly reviewed and adjusted to what really gives rise to the need to measure time, that is, our life on Earth.
In the International System of Units the second, which is measured by atomic time standards, has been defined so that its duration coincides with the nominal second of 1/86 400 of an average solar day between 1750 and 1890. Since that date, the length of the solar day has been slowly increasing. Therefore, the time calculated by the Earth's rotation has been accumulating a gap with respect to current atomic time standards.
The time lag between UT1 and UTC is what currently motivates the use of the second intercalary (represented by the vertical lines).
Civilization in general needs a stable and smoothly functioning time system. But humanity is also linked to the natural cycle of the day, i.e. the movement of the Sun, even if it is variable.
Part of the solution to the problems of measuring time accurately has been to redefine the basic unit of time, the second. One second is no longer exactly 1/86 400 of an mean solar day. Since 1967, the second has been defined as how long it takes for caesium-133 atoms to emit 9 192 631 770 cycles of some microwave radiation in an atomic clock.
Since the second is no longer defined astronomically, the Earth can rotate at will without disrupting the clocks of the world. But there is a price to pay. A day no longer has 24 hours. Today there are about 24.0000003 hours in a normal day.
To keep our watches synchronized with the Earth's rotation, an interleaving second is inserted into Universal Time when deemed necessary, approximately once a year on average. An interleaving second can be added at the end of June 30 or December 31 UT, giving the last minute of the chosen day 61 seconds.
The result is Coordinated Universal Time or UTC, the system by which all clocks in the world are configured. UTC is the basis for all radio transmissions with a time signal among many other services. It is sometimes called world time, Z or Zulu time and also Greenwich Mean Time (GMT). But the predictions of the almanacs given in UT (in the nautical GMT/UT), are actually found in the UT1 system, the main form of universal time based, at first, on astronomical observations and which is always within 0.9 seconds of UTC.
Modern times:
TAI Temps Atomique International
Weighted average of time maintained by approximately 200 atomic clocks in more than 50 national laboratories worldwide.
TAI-UT1 was approximately 0 on January 1, 1958.
UTC Coordinated Universal Time - Temps Universel Coordonné
Introduced in 1972, it differs from TAI by a whole number of seconds. When necessary, leap seconds are introduced to keep the difference between TCU and TU less than 0.9 s.
Previously determined by astronomical observations, but today GPS satellites are used instead. This time scale is slightly irregular. There are different definitions of UT, but the difference between them is always less than about 0.03 s.
UT0: UT uncorrected, derived from observations of the meridian circle or by more modern methods using GPS satellites.
UT1: UT0 corrected for polar drift. Usually used as a synonym for UT.
UT2: Today obsolete, it is UT1 corrected for seasonal variations in the Earth's rotation speed, adding up:
+ 0,022 * sin (2 * pi * t) - 0,017 * cos (2 * pi * t) - 0,007 * sin (4 * pi * t) + 0,006 * cos (4 * pi * t) seconds to UT1, where t is the fraction of the year (zero at 1 January).
Used between 1960 and 1983, it was replaced by TDT and TDB in 1984. For most purposes, ET until 1981-12-31 and TDT from 1984-01-01, can be considered as a continuous time scale.
TDT Terrestrial Dynamical Time
Used between 1984 and 2000 as an ephemeris time scale from the Earth's surface. TDT = TAI + 32.184 s. Replaced ET in 1994, and was in turn replaced by TT in 2001.
TDB Barycentric Dynamical Time
Used as an ephemeris time scale referring to the barycenter of the solar system. It differs from TDT by a few milliseconds at most.
TDB = TT + 0,001658s * sin (g) + 0,000014s * sin (2 * g)
g = 357.53_d + 0.985 600 28_d * (JD - 245 1545.0)
With higher order terms despised and g = average Earth anomaly.
Originally used instead of TDT or TDB when the difference between them did not matter. It was defined in 1991 as consistent with the second SI and the General Theory of Relativity. It replaced TDT in the ephemeris since 2001. TT is a theoretical ideal, which does not depend on any practical realization. Currently, TT = TAI + 32.184 s is used, but the use of pulsar groups is being studied instead, which could also identify defects in TAI.
TCG Geocentric Coordinate Time
Defined in 1991 together with TT.
TCB Barycentric Coordinate Time
Defined in 1991 together with TT.
ET - UT before 1984
TDT - UT in the period 1984 - 2000
TT - UT from 2001 onwards
delta-UT = UT - UTC
Predicted value of delta-UT, rounded to 0.1 s, given in some radio time signals.
GPS time = TAI - 19 seconds.
The GPS time coincided with UTC from 1980-01-01 to 1981-07-01. No interleaving seconds are inserted into the GPS time, therefore the GPS time is 13 seconds ahead of UTC on 2000-01-01. The GPS time is 00:00 h (midnight) UTC on 1980-01-06.
Greenwich Mean Time is now used in the UTC sense.
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