Quid sit Tempus (what is time) will I find the answer in Lintong (临潼)? René Oosterlinck

Quid sit Tempus (what is time) will I find the answer in Lintong (临潼)?

Some 20 years ago I wrote a book “Sur le chemin de Compostelle : Quid sit tempus ?”. When walking from Tours to Santiago de Compostela in 57 days I realized that although time flows continuously at a steady pace I perceived it differently and realized its subjectivity.  This was not really new to me but this time what made the difference is that I experienced it during some fifty days.

When planning my journey to Santiago de Compostela I decided to do it alone which I thought would give me opportunities to reflect on some philosophical questions which in fact were at the origin of my “pilgrimage”.

I remembered many Latin expressions concerning time which were self-explanatory such as “tempus fugit” but there was one which was not a statement but a question: “Quid sit Tempus”.  Walking some 30 to 40 km almost every day was not easy physically and pain results sometimes in obsessions you don’t want to think about it but your brain decides differently! Such an obsession was the question “Quid sit Tempus” Almost every day I tried to find a satisfactory answer which at the end I found but now many years afterwards I realise that I only considered the flow of time but not so much time as a physical quantity.

Some ten years later I became responsible for the European Satellite Navigation Programme “Galileo” and if there is one thing important in Satellite Navigation it is time. Now I was not confronted anymore with the flow of time but time as a physical quantity and in particular the accuracy of time. Satellite Navigation requires clocks to work at a precision of minimum 10^-12  seconds!  Most clocks on-board of the Galileo Satellites have even a better accuracy.

During my “learning period” reference was often made to the Coordinated Universal Time (UTC) but I found it very difficult to grasp the meaning of it. I tried to better understand this issue but some of my colleagues specialised in Atomic Clocks told me that it was not really important and that I shouldn’t bother too much about the real meaning of UTC since GPS and Galileo have each their own time system. As a site remark if logic would have prevailed the abbreviation for the Coordinated Universal Time should have been CUT but since the Bureau international des poids et mesures is located near Paris and has historical responsibilities in physical constants a compromise had to be found; the French could not accept that the name and abbreviation would be English!

Since Galileo has its own time I forgot the UTC issue but now that I was giving a lecture at the National Time Service Centre of the Chinese Academy of Sciences located in Lintong ( near Xi’an) I was again confronted by the UTC. When visiting the centre that is responsible for establishing time and disseminating it over China one of the experts told me that China also contributes by around 10% to the UTC.  Interesting, I said politely, but it didn’t dare to ask: what does it mean?

That evening in my Hotel I went back to: Quid sit Tempus?

Quid sit tempus is a question Saint Augustine asks himself in one of his most famous books “Confessions” (better known as: The Confessions of Saint Augustine).

Saint Augustine (354 – 430) is considered as the first Christian theologian and philosopher. He was bishop of Hippo Regius (now Annaba, Algeria)   located in Numidia (Roman province of North Africa).

The phrase, in Latin, in which he refers to time, reads as follows Book 11, chapter 25:

“ Et confiteor tibi, domine, ignorare me adhuc, quid sit tempus”

Which can be translated in English as:  “And I confess to thee, O Lord, that I am still ignorant as to what time is“.

That evening I also had to confess that I was ignorant of what time in the context of the UTC means!

The next day I was invited to visit a Museum on Time on the premises of the National Time Service Center – Chinese Academy of Sciences. The Museum is still under construction but is almost finished and I was very lucky that I could visit it before it is officially opened. I was accompanied by 张小贞,邓静静,张兴刚,吕宏春,黄夏妹 and 张柯.

I was really impressed by the Museum it is without hesitation the best one I have ever seen.

When entering the Museum we see on a wall, shown on the picture with zhāng kē, a timeline of the cosmic time i.e. what happened since the birth of the Universe until today. Since we are talking about billions of years it is good to illustrate what exact a billion means. Very often people have no idea what a billion is they can imagine a million but for many a billion is just a little bit more.

When I lecture Space Law, an optional course in the fifth year, at the University of Gent (Belgium) I always illustrate a billion by saying let’s assume that our solar system exists since 5 billion of years and that we represent this by a straight line of 5 meters. In such a case one millimetre represents one million!!

At the museum they have taken another very good pedagogic approach whereby the time since the creation of the Universe (Big Bang) until now is represented by one year divided by the twelve months.

There is still debate on the “exact” dates, whatever that might be, of some of the Cosmic events that took place such as the creation of the first galaxies etc but the purpose of the exhibition is not to enter in debates amongst specialist but just to illustrate the flow of time since it all started including time itself!

The Big Bang (time zero on the time line) took place according to the latest estimations some 13.7 billion years ago meaning that on the above time line one month corresponds to 1.14 billion of years!

The first galaxies as shown were created relatively soon after the Big Bang some 10 billion year ago i.e. in May. Then came the formation of our Solar System some 5 billion years ago shown in September, Life occurred on our planet around 3.5 billion years ago i.e. in October.  Then came the first sexual reproduction or sometimes called origin of gender end November.

The month of December is broken up in its 31 days starting some 1.1 billion years ago i.e. each day corresponds to 37.5 million years.

The oldest known hominid appears some 7 million years ago and the Homo Erectus around 2.5 million years whereas the Homo Sapiens between 1 and 1.5 million years. In other words Homos Sapiens appears at the 31 December. Structured civilisations such as in China, Egypt and Greece appeared only some seconds before the end of the year!

In conclusion in the context of Cosmic Time civilisation just happened now!

The next section deals with the evolution of time measurement devices over the years in China. Three different instruments are highlighted starting with the water clock followed by candle clocks and finally hourglasses. In Europe we know very well the existence of candle clocks and hourglasses but not much is known about water clocks, this was for me an occasion to learn more about this type of clocks.

The development of measuring time in China is illustrated by the work of three eminent scientists: Zhang Heng (張衡; AD 78–139), Su Song (苏颂; (1020 –1101)  and Guo Shoujing (郭守敬, 1231–1316).

The most elementary water clock or Clepsydra is an outflow Clepsydra and is composed of a water reservoir from which water escapes at a constant rate. The level of the water in the reservoir is an indication of the elapsed time. A first improvement took place around 200 BC; instead of using outflow it was replaced by inflow it comprised an indicator rod on a floater. One of the problems with such water clocks is the falling pressure in the reservoir slowing the inflow and thus resulting in an error of time measurement.

Zhang Heng addressed this problem by adding an extra compensating tank between the reservoir and the inflow vessel.

The Qian Zhang Clepsydra

The Qian Zhang water clock (27 AD) of Western Han is the biggest one in volume in the history of China. Found during excavations that took place in 1976

Xingping copper clepsydra

The Xingping copper Clepsydra was found during excavation activities in Shaanxi province. The kettle reservoir is 23.8 cm high and has a diameter of 10.6 cm.

Steelyard Clepsydra

Over the years the demand for more efficient clock increased steadily. The steelyard clepsydra (秤漏 chènglòu) is a more sophisticated type of water clock. Water flows from one bucket into another; once bucket is full his weight will be such that it changes the ridge mark on a steelyard. Each ridge corresponds to a predefined time. The bucket is then emptied and filled up again.  In order to stabile
the system a counter-weight keeps the steelyard in place. The steelyard clepsydra was so accurate that it replaced other forms of clepsydra and was used in the Northern Song Dynasty (960-1127).

Next is Su Song’s clock of which a very nice replica is shown.

From measurement to applications

Astronomical Calendars

Measuring time is not a goal in itself it has a purpose of which the calendar is an example. There are several types of calendars but they have all in common the combination of time and Cosmos. It is therefore not surprising that an astronomer is honored here i.e. Guo Shoujing ((郭守敬).

Three different calendars are quoted:

Solar calendar

A solar calendar is a calendar whose dates indicate the position of Earth on its revolution around the Sun

Lunar calendar

The Lunar calendar is a calendar that is based on cycles of the lunar phases. There however slightly more than twelve lunations meaning that a solar year to not correspond exactly to a lunar year.

Solar Lunar calendar

A Solar Lunar calendar is a calendar that combines the solar and lunar calendar it is therefore often called the lunisolar calendar. Such calendar indicates both the moon phase and the time of the solar year.

The Chinese calendar is lunisolar. It is based on exact astronomical observations of the sun’s longitude and the moon’s phases. The months begin on the day with the dark (new) moon. The years begin with the dark moon near the midpoint between winter solstice and spring equinox.

Next section is on the name of years

Heavenly stems and Earthly branches 60 year cycle (干支; gānzhī)

In China for historical reasons years may be identified by their numerical value or by their name. The names are given according to a “Sexagenarian Circle” whereby names of the years are repeated every 60 years.

It is interesting to see that the names of the years are repeated every 60 years as if it uses a sexagesimal system. We have inherited the use of the sexagesimal base (base 60) from the Sumerians. It was in use most probably before 2000 BC. The Babylonians used it for their astronomical observations and calculations.

It is unknown why a sexagesimal system was introduced some think that it was chosen because it was very easy to express fractions since 60 is the smallest number divisible by the first six counting numbers.

In China the name of years are given by assigning to each year two components: one name from a cycle of 10 Heavenly Stems and one name from a cycle of 12 Earthly Branches.

Each of the above two components is used sequentially.

The 1st year of a 60 year cycle would be named jia – zi; The 2nd year of a 60 year cycle would be named yi – chou; The 3rd year of a 60 year cycle would be named bing – yin; The 10th year of a year cycle would be named gui – you ; The 11th year of a 60 year cycle The would be named jia-xu (restarting Heavenly  Stem).

The 12th year of a 60 year cycle would be named yi-hai; The 13th year of a 60 year cycle would be
named bing-zi (restarting Earthly Branch); The 60th year of a 60 year cycle would be named gui-hai.

I found this very interesting from a historical pint of view but I was really surprised when one of those with me showed the name of the year on his Smart Phone!

Zhang Ke drew my attention to the decision taken on 30 November 2016 by the UN Educational, Scientific, and Cultural Organization (UNESCO) to inscribe China’s “The Twenty-Four Solar Terms” on the “Representative List of the Intangible Cultural Heritage of Humanity”.  I was not aware of this decision when exactly the same day i.e. 30 November 2016 I visited the Drum Tower in Beijing and to my surprise found on the balcony wall of the tower 24 copper plates describing each a special weather event. I now realise that these 24 plates contain respectively the 24 Solar Terms.

Zhang Heng (張衡), Su Song (苏颂)  and Guo Shoujing (郭守敬)  

I now wish to pay tribute to the three famous scientists mentioned in this first part of the Museum; it is thank to such men that science is what it is today.

Zhang Heng (張衡; AD 78–139)

I knew Zhang Heng as a poet but not as a scientist!

Zhang Heng was a typical example of a polymath (from Greek: “having learned much”) i.e. a person whose expertise covers many different subject areas. In his case it said that he was an astronomer, mathematician, inventor, geographer, artist, poet, statesman, and literary scholar of the Eastern Han Dynasty in ancient China.

According to Joseph Needham (1900 – 1995) a British scientist and sinologist who has spent most of his life in studying history of Chinese sciences; “Zhang Heng was able to make three wheels rotate as if they were one. He is best known for his invention of the world’s first water-powered armillary sphere to represent astronomical observation, and the world’s first seismometer device, which discerned the cardinal direction of earthquakes from incredibly far distances.”

Astonishing is the place that poets and poems play in Chinese Culture Zhang Heng is a typical example. As I said I knew him through one of his poems: “The four Sorrows” which is one of the first if not the first poem having 7 words per line.

I thought it would be useful to give the Chinese version of the “first sorrow” since it is very difficult to find it on western internet pages. Most of the time only English translation of this first sorrow is found on internet but nothing about the three others except on www.silkqin.com/index.html where the full text is given in Chinese. I have added an English translation made by and one in Dutch , my mother tongue.

Four sorrows

In Taishan stays my dear sweetheart,            Mijn liefste is in Taishan

But Liangfu keeps us long apart;                      Graag wil ik erheen maar Liangfu scheidt                                                                                         ons

Looking east, I find tears start.                        Oostwaarts blikkend dan rollen mijn tranen                                                                                    op mijn pen

She gives me a sword to my delight;               Mijn liefste stuurde mij een gouden dolk

A jade I give her as requite.                               Een jade schenk ik haar terug

I’m at a loss as she is out of sight;                Ik ben verloren, ‘t is te ver om daarheen te                                                                                       gaan.

Why should I trouble myself all night?       Waarom zou ik mij eraan storen ?

Su Song (苏颂; (1020 –1101) 

Su Song was also a polymath his biography mentions that he was a scientist, mathematician, statesman, astronomer, cartographer, horologist, medical doctor, pharmacologist, mineralogist, zoologist, botanist, mechanical and architectural engineer and … a poet. Unfortunately I couldn’t find any poem written by him.

Su Song used in his clock of which a replica is shown in the museum a escapement mechanism that was already invented in 725 AD but new was the use of an endless power-transmitting chain drive which was called “celestial ladder” (天梯 tiān tī).

Su Song also wrote a treatise on clocks (新儀象法要 xīn yí xiàng fǎ yào), which was printed in 1094 and has survived. In his book Su Song credited Zhang Heng (78–139 AD as one of his predecessors.

In addition he compiled a celestial atlas and terrestrial maps. He wrote treatise on pharmacology.

Guo Shoujing (郭守敬, 1231–1316).

Guo Shoujing was an astronomer, engineer and mathematician. His instruments were of very high quality and impressed Matteo Ricci and Johann Adam Schall von Bell some 300 years later when they came to Beijing. Johann Adam Schall called him the “the Tycho Brahe of China.”

He used for his astronomical calculations plane and spherical trigonometry. His work was based on a book published some 250 years earlier on trigonometry written by Shen Kuo ( 沈括; 1031–1095).

Guo Shoujing’s work on trigonometry will remain for a long time the reference work on trigonometry; no other important book on this subject would be printed in China until the collaborative efforts of Xu Guangqi and his Italian Jesuit associate Matteo Ricci in 1607, during the late Ming Dynasty.

Pendulum clocks

Next is shown a major invention with respect to time measurement i.e. the invention of the pendulum clock. This type of clock was invented in 1656 Christiaan Huygens (1629 – 1695). Huygens was a prominent Dutch mathematician, astronomer, physicist and horologist. Huygens was inspired by the investigations of pendulums made by Galileo Galilei around 1602. With the introduction of the pendulum clock the accuracy in time keeping increased substantially up to 15 seconds per day !

In this sections there are three small pedagogic pendulums shown which you can with your hand swing the pendulum mass. It illustrates very well that the period T is independent from the mass and varies with the square root of its effective length.

From time measurement to navigation through Longitude

During the XVII^th  century navigation on the high seas has grown almost exponentially! But many ships sailing East did not return due to bad weather conditions, diseases and lack of precise maps and methods for determine the position of ships on the high seas.

For determining a position on the high seas both latitude and longitude of the ship are required.

Determining latitude was relatively easy by using the altitude of the sun at noon (i.e. at its highest point) or from many stars at night.  Longitude was however impossible to establish when on the high seas.

What is longitude? Since the Earth rotates at a steady rate of 360° per day, or 15° per hour (in mean solar time), there is a direct relationship between time and longitude. One could say that Time equals longitude!

With the advent of precise clocks the idea was to calculate longitude by time! Imagine that a navigator before sailing on the high seas synchronizes his clock at a reference point with a known longitude. If at a certain moment sailing on the high seas he wishes to know his position and in particular his longitude he will compare the apparent time at his location with the reference time i.e. his clock on-board of the ship. The difference between the reference time and the apparent local time enables him to establish his longitude.

Huygens pendulum was inadequate for time measurements because of the pitching and rolling of ships.

Henry Sully (1680–1729) invented a marine clock in 1716 to determine longitude accurately, but the clock was too sophisticated and performed only well in calm weather, but not on the high seas.

John Harrison (1693 – 1776) was the first to build a marine chronometer that could be used on-board of ships.

Several clocks are displayed in the Museum.

Satellite Navigation Systems

The next step was to disseminate time via electro-magnetic waves.

Next was “GPS” the first satellite navigation system. Satellite navigation is based on very accurate time measurements i.e. clocks. Since the electro-magnetic waves travel at the speed of light an error in time of 1 sec would mean an error of position of 300.000 km! Even an error of 10^-9(Nano second) would still give an error of 30 cm.

Clocks with such accuracy are often called “atomic clocks”; typical examples are the Rubidium Clock, the Passive Hydrogen Maser, Cesium clocks etc. In the museum a ground atomic clock is exhibited.

An interactive panel shows the current different Global Navigation Satellite Systems.

The last panel mentions UTC!

Coordinated Universal Time (UTC)

Before discussing the UTC it is important to know what is meant by International Atomic Time (TAI).

International Atomic Time (TAI) is one of the main components of Coordinated Universal Time (UTC), the time scale used to determine local times around the world. It tells us at which speed our clocks should tick.

During many years the second was based on the period of the Earth’s revolution around the Sun. This definition was satisfactory for many years but with science moving forward this definition was not precise enough anymore. in 1967 the Thirteenth General Conference on Weights and Measures defined the SI second of atomic time as: the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.

This definition refers to a cesium atom at rest at a temperature of 0 K.

Now that the second is defined there was also a need to have an international recognized time which will be the International Atomic Time.

The International Atomic Time (TAI, from the French name Temps Atomique International) is a high-precision atomic coordinate time standard based on the notional passage of proper time on Earth’s geoid.

The problem of clocks is that they are subject to their environment such as altitude, gravitational field etc . In the 1970s, it became clear that  clocks were ticking at different rates in particular due to gravitational time dilation.

In order to achieve the highest possible level of accuracy, it was agreed that the International Bureau of Weights and Measures would combine the output of about 400 atomic clocks in 69 national laboratories worldwide to determine TAI. The long-term stability of TAI is assured by a judicious way of weighting the participating clocks. The scale unit of TAI is kept as close as possible to the SI second by using data from those national laboratories which maintain the best primary cesium standards.

The next question from which moment the TAI will be running?

It was decided that as from 1 January 1977 00:00:00, corrections would be applied to the output of all participating clocks, so that TAI would correspond to proper time at mean sea level (the geoid). The TAI is a continuous running time without any leap seconds meaning that over time there will be a difference between the TAI and the time based on the Earth rotation around the sun.

For that reason another time should be intoduced that reflects the real time based on the Earth rotation around the Sun that time is the Universal Time UT1! The Universal Time (UT1), also known as astronomical time or solar time, refers to the Earth’s rotation.  But UT1 is changing at micro second level constantly compared to the TAI and was therefore considered not suitable as reference time at level of a second. There was thus a need to introduce another time reference which became the International Coordinated Time UTC; UTC would be based on the TAI with corrections at the level of a second based on the UT1.

At the start of the TAI the TAI = UTC = UT1.  Then a first correction was made by introducing a leap second i.e. UTC = TAI + leap second. The decision to introduce a leap second is based on the difference (DUT) between Universal Time (UT1) and the UTC .

DUT = UT1 – UTC ; The UTC is maintained via leap seconds, such that DUT remains within the range −0.9 s < DUT < +0.9 s. Whenever the differnce becomes larger a leap second is introduced!

Leap seconds have been added over the years and since 30 June 2015 the TAI is exactly 36 seconds ahead of UTC.

The situation can be summarized as follows: The TAI and UTC are time keeping systems with accuracy at second level. The only difference between the TAI and the UTC are the leap seconds.

Conclusion

Thanks to discussions with those who accompanied me during the visit of the Museum and in particular Zhang Ke I have now understood the meaning of UTC.  I made here in Lintong a step forward to answer the  question “Quid Sit Tempus” but I know that my quest will go on!