Issuu

To my loved ones

Werner Gitt

Time and Eternity

Loizeaux Neptune, New Jersey

4 About the author: Prof. Dr Werner Gitt was born in Raineck, East Prussia in 1937. From 1963-1968 he obtained his engineering degree (Dipl.-Ing.) at the Technical University of Hanover. Thereafter he worked as an assistant at the Institute of Control Engineering at the Technical University of Aachen. Following two years of research work he received his doctorate summa cum laude, together with the prestigious Borchers Medal from the Technical University of Aachen, Germany, in 1970. He is now a Director and Professor at the German Federal Institute of Physics and Technology (Physikalisch-Technische Bundesanstalt Braunschweig). He has written numerous scientific papers in the field of information science, numerical mathematics and control engineering, as well as several popular books, some of which have been translated into Bulgarian, Chinese, Czech, French, Hungarian, Italian, Polish, Roumanian, Russian, Spain, and other languages. In 1990 he founded the specialist conference in Information Science which 150 participants attend every year. The aim of this meeting is to combine biblical guidelines with ideas from information science. Since 1984 he has been a regular guest lecturer at the State Independent Theological University of Basle, Switzerland, on the subject ›Bible and Science‹. He has held lectures on related topics at numerous universities at home and abroad, as well as having spoken on the topic ›Faith and Science‹ in a number of different countries (e.g. Australia, Austria, France, Hungary, Kazakhstan, Kirghizia, Namibia, New Zealand, Poland, Portugal, Roumania, Russia, South Africa, and the USA).

First English Edition 2001 © of the German Edition: Werner Gitt, »Zeit und Ewigkeit« 1999 by CLV • Christliche Literatur-Verbreitung e. V. Postfach 11 01 35 • D-33661 Bielefeld, Germany © of the English Edition: 2001 by CLV • Christliche Literatur-Verbreitung e. V. P.O. Box 11 01 35 • D-33661 Bielefeld, Germany Translation: Dr Carl Wieland, Brigitte Stoll Cover: Dieter Otten, Gummersbach Typography: CLV Printed in Germany: by Ebner Ulm ISBN 0-87213-228-5 (Loizeaux) ISBN 3-89397-473-3 (CLV)

Contents Foreword Additional foreword to the English edition

9 12

Part I: Time â€“ a physical quantity

1.1 The International System (SI) of measurement for physical quantities 1.2 The unit of time 1.3 Measuring time with atomic clocks 1.4 Determining position with the aid of precise time measurements a) The fervent quest to determine longitude b) Determining position with the help of GPS 1.5 Shortest and longest time-span 1.6 Time constants and periods a) Time constants and oscillation periods in physics b) Times in astronomy c) Time in biological systems 1.7 Other aspects of physical time

20 20 24 25 26 26 27 28 29

Part II: Time â€“ an anthropological quantity

2.1 Introduction 2.2 Attributes of Time 1. Time cannot be stored 2. Time cannot be lent out 3. Each day has the same amount of time 4. Time cannot be skipped 5. Time earns no interest when invested 6. Time is progressive; the arrow of time has a definite direction

33 35 35 35 35 36 37

13 15 17

Contents

7. Events in our world involve the consumption of time 2.3 Two biblical concepts of time: kairos and chronos 2.3.1 Chronos: the time of man 2.3.2 Kairos: Godâ€™s time 2.4 The five levels of information â€“ a new basis for interpreting time 2.5 The five levels of time 2.5.1 Statistics of Time 2.5.2 Syntax of Time 2.5.3 Semantics of time 2.5.4 Pragmatics of time Some examples by way of encouragement to positive pragmatics The command of God concerning time Be effective in the Kingdom of God in this present time 2.5.5 Apobetics of time Goals or intentions? Biblical exhortation to good apobetics Biblical warnings against wrong apobetics 2.5.6 Summary 2.6 The most important personal decision in time Conversion to Jesus Christ

38 42 43 45 49 53 53 57 64 67 70 74 76 79 79 84 84 86 91 92

Part III: What is eternity?

105

3.1 Ideas of eternity among various peoples 3.2 The sense of eternity 3.3 Eternity according to the Bible 3.3.1 What about hell? 3.3.2 What do we know about heaven? H1: Heaven is the place where we will be perfectly happy H2: Heaven is the place of everlasting celebration

105 108 109 111 115 116 118

Contents

H3: Heaven is a beautiful place H4: Heaven is where our lives will be fulfilled H5: Heaven is a home for us H6: Heaven is a place where we shall reign H7: Heaven is a place where Jesus is H8: Heaven is a place without sin H9: Heaven is a place of welcome and enjoyment H10: In Heaven we receive a new name H11: Heaven is where we become like Jesus H12: Heaven is something special to look forward to

121 123 125 126 127 129 134 138 145 146

Bibliography

149

Translatorsâ€™ note: re Bible versions. Bible verses were often translated directly from the German in an effort to ensure maximum clarity within the authorâ€™s context, while keeping to the meaning of the original Hebrew or Greek. At other times, to achieve this goal, an existing English translation, such as the Authorized Version or the New International Version, was utilized in whole or in part.

Vorwort

Foreword The Problem of Time: People from the most diverse of centuries have pondered the phenomenon of time, without coming to an adequate explanation of it. Augustine (354-430) said, »What is time? If no one asks me, I know; but if any person should require me to tell him, I cannot.« One and a half millennia later, the English philosopher and mathematician Alfred North Whitehead (1861-1947) had nothing but his own frustration to add to Augustine’s bewilderment: »It is impossible to contemplate time… without being overcome by the sense of how limited human intelligence is.« The Australian professor of mathematical physics and the philosophy of science at the University of Adelaide, Paul Davies, wrote in the foreword of his book »About Time« [D1, pp. 9-10]: »Fascination with the riddle of time is as old as human thought. The earliest written records betray confusion and anxiety over the nature of time. …The orthodox account of time frequently leaves us stranded, surrounded by a welter of puzzles and paradoxes.« And it is not just the nature of time which presents a puzzle for thinkers – its origin is just as problematic. Like most – but by no means all – of his contemporaries, Davies proceeds from the Big Bang theory, but finds no answer there either for the origin of time [D1, p. 18]: »Today, the big-bang [has become the orthodox cosmology. It] nevertheless faces a major hurdle in providing a convincing account of how the universe can come to exist from nothing as a result of a physical process. No greater obstacle lies in the path of explanation than the mystery of how

Foreword

time itself can originate naturally. Can science ever encompass the beginning of time within its scope?« Even Einstein’s relativity theory has not brought about the hoped-for breakthrough [D1, p. 34]: »The revolution started by Einstein remains unfinished. We still await a complete understanding of the nature of time.« Why is something as fundamental as time so difficult to comprehend and so hard to explain? The psychologist John Cohen says: »We are here confronted by a deep mystery, in the truest sense of the word – one which on the one hand lies at the heart of human experience, on the other in the nature of things.« The challenge of this book: The above statements clearly show that only a completely new approach to the problem of »time« can help us further. We accept this challenge, in order to arrive at our goal via a new way of thinking. The phenomenon of time is of such supreme significance for our lives, that I believe a renewed analysis is definitely overdue. We will first consider time as a purely physical quantity. Describing time from this aspect is in keeping with the observation of the Japanese philosopher Masanao Toda [D1, p. 274]: »No one, apparently, can claim to know what time is. Nevertheless, there is this brave breed of people called physicists, who used this elusive notion as one of the basic building blocks of their theory, and miraculously, the theory worked.« Only then do we come to the main part of this book, in which we deal with time in a central and novel way as an anthropological [Greek: anthropos = man] quantity. Finally, the third part of this book deals with the issue of what awaits us beyond time: eternity.

Foreword

Advice to readers: This book has been written for a wide, general audience. In my view, parts II and III are the most important. These may be read without necessarily first working through part I, the physics section. Thanks: The contents of this volume were discussing in considerable detail with my wife, after which the manuscript was reviewed by the language professional DĂśrte GĂśtz. Their numerous comments and suggested amendments led to improvements in the bookâ€™s contents, or to making these more readily accessible. I am very grateful to both for their committed co-labours. Werner Gitt

Foreword

Additional foreword to the English edition As the author, I am of course delighted that this book, having been translated into Hungarian and Polish, has now also appeared in English, joining the seven other of my titles available in that language. I want to say a very special ›thank you‹ to my Australian friend Carl Wieland and his sister Brigitte Stoll, who translated this book in its entirety. They achieved more than a stylistically excellent result, as with the translation of a novel; due to Carl’s wide scientific knowledge and their deep Biblical understanding, they were able to add to the book here and there to improve the end result. Dr Wieland is the director of the world-renowed organisation for creation science/research, Answers in Genesis in Brisbane (Australia). He is the editor of their brilliantly presented and colourful English-language magazine Creation (print run > 50,000) which has subscribers in more than 140 countries. Werner Gitt, June 2001

I: Time – a physical quantity 1.1 The International System (SI1) of measurement for physical quantities In the world of science and technology, measuring units such as mile, pint, horsepower, calorie, etc. have long since been relegated to a bygone age. They have been replaced by the easily handled SI system,2 which does away with 1 The international system of units (Système International d’Unites), which carries the universal abbreviation SI in all languages, was introduced in 1960 at the 11th General Conference on Weights and Measures [French: Conférence Générale des Poids et Mesures (CGPM); Committee with representatives from the Metre Convention member states. First conference in 1889. Meeting every 4th year. Approves the SISystem and results from fundamental metrological research]. It ended a confusion of over a century caused by a multiplicity of units and unitary systems. The SI was developed by various international expert committees of measurement, in which the following institutions took part on behalf of the Federal Republic of Germany: the Federal Institute of Physics and Technology (Physikalisch-Technische Bundesanstalt or PTB) and the German Institute for Standardization (Deutsches Institut für Normung, or DIN). In international unitary systems a distinction is made between fundamental and derived units. 2

The effectiveness of the SI system can be demonstrated using a difficult example. The unit of magnetic flux density derives from voltage × time/area: 1 Vs/m2. Expanding the fraction by multiplying top and bottom line by 1 ampere (A), we get 1 VAs/Am2. VA = W (watts, after the Scotsman James Watt (1736–1819) who invented an efficient steam engine), so this becomes 1 Ws/ Am2. Substituting now for 1 Ws = 1 kgm2/s2 (see units of energy, p. 15) we arrive at 1 kgm2/Am2s2 = 1 kg/As2. Thus the magnetic flux density has been expressed using only the fundamental units listed in the main text: 1 kg/(A×s2) = 1 T (= 1 tesla). This is equal to the surface density of a homogenous magnetic field of the strength of 1 weber (Wb), which perpendicularly penetrates all points of a surface of 1 m2. Here the unit is named after the American physicist Nikola Tesla (1856–1943) who in 1881 developed the principle of the rotating field electric motor (three-phase AC

Part I: Time – a physical quantity

complicated conversion factors. All conceivable physical units can be derived from a basic system of seven fundamental quantities which are independent of each other — one of these being time. · · · · · · ·

Length Mass Current strength Temperature Substance amount Light intensity Time

(Unit: (Unit: (Unit: (Unit: (Unit: (Unit: (Unit:

metre, m) kilogram, kg) ampere, A) kelvin, K) mole, mol) candela, cd) second, s)

For each of these fundamental units there is an unambiguous, internationally established physical definition [X1]. All units known to us (and any yet to be formulated) relating to the material world are inevitably derived from some of these fundamental units, interconnected via multiplication and division. Units are often named after an internationally known physicist. It is important to note that the full name of the unit is not capitalised, even if it is named after someone. Abbreviations of units are not usually capitalised unless they are named after someone. And there is never an abbreviation point or a plural ›s‹ after an abbreviated unit. For example, ice melts at 273.15 kelvins or 273.15 K, and a fuse wire may be designed to melt with a current over five amperes (›amps‹) or 5 A. Whenever the resulting unit becomes too unwieldy or unmotor) and in 1887 described the multiphase system for the transmission of electrical power. The field strength unit is named after German physicist Wilhelm Weber (1804–1891).

1.2 The unit of time

sightly, it is given a new name with a corresponding abbreviation. We can see this from some examples of derived units. Velocity (speed in a given direction) is equal to distance/time; from this, it follows that its unit is metre/second = m/s. Because of the relationship (Newton’s Second Law of Motion): Force = mass × acceleration (F = m·a), it follows that the unit of force is 1 kg·m/s2 (acceleration = metres per second per second, or m/s2). This new unit of force is named after the English physicist Isaac Newton (1642–1727), who is regarded as the founder of classical theoretical physics: 1 N (= 1 newton) = 1 kg·m/s2. Energy (mechanical) is calculated as force × distance (in the direction of the force); it follows that its unit is 1 (kg·m/ s2) · m = 1 kg·m2/s2 = 1 J. The unit J (= 1 joule = 1 Nm = 1 Ws) is named after the English physicist James Prescott Joule (1818–1889), who determined the thermal equivalent of mechanical and electrical energy. Returning, then, to time.

1.2 The unit of time The physical unit of time is the second. This was previously defined as 1/86,400th of a mean solar day. However, the mean solar day3 is not constant; currently its du-

The division of time: The choice of a day as a measure of time was a logical connection to a universally known natural phenomenon. However, the division of a day into two lots of 12 hours, and then dividing these again into 60 minutes, each of 60 seconds, was purely arbitrary. It would have been much more convenient to have introduced the tried

Part I: Time – a physical quantity

ration is increasing by 1.8 milliseconds (1 ms = 0.001 s) per century.4 So this definition of a second became inadequate for modern-day requirements. To overcome this dilemma, a new definition of a second was internationally adopted at the 13th General Conference on Weights and Measures in 1967. A second henceforth is: 9,192,631,770 times the duration of one period of oscillation at the characteristic ›vibrational frequency‹ of an atom of cesium-133.5 and tested decimal system here also. There is no natural law which would indicate that, as a unit of time, the second has any inherent advantages, or is likely to be especially useful in everyday practice. Thus the establishment of the duration of a second also rests on a purely arbitrary choice. The clock of the Strasbourg (Straßburg) Cathedral: Among the many clocks constructed over the centuries, one in particular deserves special mention: the Strasbourg Cathedral clock. By decree of the council of Nicea (AD 325), the date of Easter falls on the first Sunday after the first full moon following the beginning of Spring (March 21st). Can a mechanical device indicate such an intricately established date? Built and rebuilt several times over the past 600 years (with the last major rebuild in 1842), the clock of the Strasbourg Cathedral achieves this and much more; this unique and amazing device functions as an astronomical and calendrical computer. Among its achievements; calculating sidereal time, lunar time and solar time, with an error of less than a second a century, and tracking the motion of 5,000 stars. Fully Y2K compliant (including all the complex conventions for tracking leap years) over two lifetimes ago, one of its marvellous conglomeration of gears is designed to turn only once in a century; another once in 2,500 years. 4 According to the Encyclopaedia Britannica, in 1956 the International Conference on Weights and Measures defined a second as 1/ 31,556,925.9747 of the length of the seasonal (tropical) year 1900, and ratified this in 1960. But since 1900 was in the past, there was no way reproduce it. 5

This nuclide of cesium, 133Cs, is the only one that occurs in nature.

1.3 Measuring time with atomic clocks

In fact, the atom does not really vibrate, it is the characteristic frequency of the radiation absorbed when an electron jumps between two hyperfine levels of the cesium atom’s ground state. This duration is established with the help of cesium atomic clocks. So the second has become chopped into more than 9 billion6 parts, each corresponding to a physical process! The number was chosen to match the length of the second to the 1965/ 1906 definition. The measurement of time thus becomes the counting of certain sequentially occurring events. This definition allows the unit of time to be reproduced at any time, and any place, given the appropriate equipment.

1.3 Measuring time with atomic clocks At the Federal Institute of Physics and Technology in Braunschweig (Brunswick), Germany, are found two of the world’s most accurate cesium atomic clocks [B1]. In regard to their degree of accuracy, these clocks, CS1 and CS2, are at the global cutting edge. CS2 (see figure 1) has been operational since 1985, and runs so accurately, that in a theoretical two million years hence (should there still be an earth then, and were this instrument to last that long) it would differ by at most only 1 second from an ideal clock. That corresponds to a relative uncertainty7 of only 6

This book will use the U.S. convention for large numbers, in which one billion = a thousand million (109), and one trillion = a thousand billion, or a million million (1012). 7 Relative uncertainty: This figure is derived by dividing the possible error in time measurement (∆t = 1s) by the time period under consideration (t = 2 million years): ∆t/t = 1s/6.3×1013s = 1.6×10-14. Applied to a day that would be 1.4 nanoseconds.

Part I: Time – a physical quantity

1.6·10-14. Such a value for its functional accuracy does not come from comparing it with another clock — because there is no such ideal clock. It is done via a calculated estimate of the effects of all the participating parameters of the clock CS2. The cesium-133 (133Cs) utilized in atomic clocks is not radioactive; it is stable, and has the remarkable property of melting at the comparatively low temperature of 28 degrees Celsius, and boiling at 690 °C. Simplified, what happens inside an atomic clock is as follows: A beam of free cesium atoms is produced. They are passed through a very strong magnetic field, so that they all find themselves in one of two possible energy states, and are bathed in microwaves in a resonator (based on electromagnetic oscillations). Through this influence, the energy state of the atoms changes, and they switch over to the previously unoccupied energy state when the microwave photon energy h × ν is exactly the same as the energy difference between the two hyperfine levels. During this transition from one to the other state, the atoms either emit (Latin emittere = to send out, to give out) or absorb (Latin absorbere = to swallow, to devour) electromagnetic waves with a very specific frequency, which may be regarded as a natural constant. This thus establishes the quantum mechanical »norm« of the frequency, which forms the basis for the »exact time«. What is then needed is to build an apparatus, i.e. an atomic clock, with which this natural frequency can be measured with great certainty and high precision. For reasons of measuring technology, this is best done when the interaction time between the cesium atoms and the microwave radiation is as long as possible. This in turn comes from using the slowest possible atoms.

1.3 Measuring time with atomic clocks

Figure 1: The cesium atomic clock C2 at the Federal Institute of Physics and Technology, Braunschweig (Brunswick), Germany.

In the primary clock CS2 (and also CS3), the ray tube is horizontal, in CS4 it is vertical. The latest development, the fountain clock [CSF1; CeSium Fountain clock no. 1], utilizes a method for which Steven Chu, Claude Cohen-Tannoudji and William Phillips were awarded the Nobel Prize for Physics in 1997. With the help of laser light, they succeeded in cooling atoms to an extremely low temperature, just a few microkelvins (mK) above absolute zero (-273.15 degrees Celsius), trapping them, like a swarm of bees, as a cloud of a few million atoms. Within such a magneto-optical trap, atoms normally impelled by the ambient temperature into a furious zig-zag pace move at a leisurely speed of only a few millimetres per second. If now the frequency of the laser light is briefly put »out of tune«, these cooled and trapped atoms receive an upwards kick. They leap up at 4 m/s, rising until gravity has »used up« their energy of mo-

Part I: Time – a physical quantity

tion, then they fall back down again. This scenario is reminiscent of a fountain, hence the name »fountain clock«. Just as in a conventional atomic clock, the source atoms are prepared in one or another energy state. They switch their energy state when they pass the microwave field of a resonator during their up-and-down motion. But the time they have in contact with the microwave field is significantly greater: a stone thrown up one metre takes about a second to hit the ground. The atoms in the fountain clock are in contact with the microwave field for about the same amount of time, which is why the measured resonance signal is correspondingly sharper. With this new development, the goal of fixing the duration of a second with even greater precision is now within reach. After construction is completed, the accuracy anticipated is of such a high order that the relative uncertainty would be only 10-15 seconds. Such a clock would be »out« by at most one second in over 10 million years. Time is the physical quantity which can be measured with the highest precision of all. Is such ultra-precision necessary? The following will clarify this in relation to navigation on the earth’s surface.

1.4 De termining position with the aid of precise time measurements a) The fervent to determine longitude For shipping on the open ocean, current position is of crucial significance. If you know the degree of latitude and longitude of a ship at sea, this unambiguously fixes its posi-

1.4 De termining position with the aid of precise …

tion. While latitude can be determined with the help of the stars [G3, pp. 92–97], there is no corresponding method for obtaining longitude. Before the GPS method (see part (b)) became available, position could only be determined by utilizing the distance travelled. This distance s is a product of the velocity v and the travel-time t (s = v·t), so v and t have to be continually measured. Locating one’s position on the ocean thus required accurate time measurement. Not having appropriate clocks (i.e. both seaworthy and sufficiently accurate) at sea will not only mean arriving at the wrong destination, it can be life-threatening. Two significant historical occurrences are worth mentioning in this connection [B2, p. 155]: · In 1691, the English fleet lost several ships, because the aforementioned navigation methods employed by their captains were too inaccurate. One simply no longer knew where one was on the ocean. · In 1707, there was a worse tragedy. A squadron of ships coming from the direction of Gibraltar, under way for twelve days, thought that it was off the shore of Brittany when, on the foggy night of 22nd October, it ran aground on the rocks of the Scilly isles, west of Cornwall. The losses were grave: 2,000 men and four ships. In those days, one tried to sail in the vicinity of a visible coastline where possible, because navigators had no way of determining longitude. In literally hundreds of cases, ships went down because once at sea, there was no way to determine the degree of longitude. Attempts were made to ascertain geographical position using the speed of the ship and the travel time. Had there been really accurate

Part I: Time – a physical quantity

clocks, a ship’s position on the open sea could have been calculated, but as it was, crude estimates had to suffice. The American science reporter Dava Sobel gave her important and gripping book, »Longitude« [S2], the subtitle: »The true story of a lone genius who solved the greatest scientific problem of his time.« In it she wrote [S2, pp. 7-8]: »The active quest for a solution to the problem of longitude persisted over four centuries and across the whole continent of Europe. Most crowned heads of state eventually played a part in the longitude story, notably George III and Louis XIV. Seafaring men such as Captain William Bligh of the Bounty and the great circumnavigator Captain James Cook, who made three long voyages of exploration and experimentation before his violent death in Hawaii, took the more promising methods to sea to test their accuracy and practicability. Renowned astronomers approached the longitude challenge by appealing to the clockwork universe: Galileo Galilei, Jean Dominique Cassini, Christiaan Huygens, Sir Isaac Newton, and Edmond Halley, of comet fame, all entreated the moon and stars for help. Palatial observatories were founded at Paris, London, and Berlin for the express purpose of determining longitude by the heavens. … As time passed and no method proved successful, the search for a solution to the longitude problem assumed legendary proportions, on a par with discovering the Fountain of Youth, the secret of perpetual motion, or the formula for transforming lead into gold. The governments of the great maritime nations — including Spain, the Netherlands, and certain city-states of Italy — periodically roiled the fervor by offering jackpot purses for a workable method.« In 1717 the British Parliament, desperate to overcome this

1.4 De termining position with the aid of precise …

predicament, offered a very large prize. The winner would be whoever could invent and construct a clock usable at sea. The three prizes set out in the »Longitude Act« depended on the level of accuracy with which geographical longitude could be established. - 10,000 pounds sterling for 1 degree of longitude (1o) - 15,000 pounds for 40 minutes of a degree of longitude and - 20,000 pounds for half a degree (30 minutes). In today’s terms, these were several millions of dollars. Considering that half a degree of longitude at the equator is nevertheless still a difference of 56 kilometres, the accuracy demanded appears rather modest. A young man named John Harrison (1693–1776) took up this challenge. He began working on the solution to this problem at the age of 21. · His first clock weighed 35 kg. · The second, finished in 1739, weighed 50 kg. · The third took a few more years, but even this one was not yet satisfactory. · Finally, in 1759, the fourth clock, which met the requirements for accuracy, was finished. Harrison wrote of it, that there was no more splendid mechanical or mathematical instrument in the world. The crucial test at sea came in 1761, during a voyage from Portsmouth to Jamaica. At the stopover port of Madeira the clock had its first test. While the captain fancied himself to be 13o 50’ west of Greenwich, according to the clock it was 15o 19’ — and the clock was right, as the arrival in Porto Santo the next morning confirmed.

Part I: Time – a physical quantity

It was only in the year 1772 — 11 years after that stunningly successful test voyage — that Harrison finally received his well-earned prize. In the meantime, he had become 79 years old, receiving the reward for his life’s work after decades of political intrigues, feuds, academic libels, scientific revolutions and economic upheavals. This lengthy struggle over longitude determination shows just how vitally significant the measurement of time is for the purpose of determining position. Today, from any place on earth, we can determine our position in a few seconds, to within a metre – only because of the highly precise measurement of time with atomic clocks.

b) Determining position with the help of GPS Nowadays, on the basis of very exact measurements of time, it is possible to fix accurately, to the metre, the position of ships on the ocean, or explorers in the desert. This is done via the »Global Positioning System« (GPS). 24 artificial satellites orbit the earth. Four at a time move in unison along one of six orbital paths, beaming their signals to earth. The orbits have been chosen such that at any time, the signals from at least four satellites can be utilized by a GPS receiver from any point worldwide. On board each satellite, there are four atomic clocks. The geographic location of the receiver is calculated from the differences in transit time of the signals from several satellites. These differences are very precisely measurable to within a few nanoseconds. Another example: The space probe Voyager 1, having covered around two billion kilometres in its three year journey through our planetary system, was due to beam pictures of Titan, Saturn’s largest moon, back to Earth. Remarkably, the target destination, as had been calculated

1.5 Shortest and longest time-span

in advance, was missed by only 19 km. A time error of only a thousandth of a second would have resulted in the probe straying off course by hundreds of kilometres.

1.5 Shortest and longest time-span The shortest time-span that physicists have ever been able to measure is the life-time of certain rare elementary particles, which last for only the trillionth part of a billionth of a second. Half of the atomic nuclei of the helium isotope of mass 5 (5He) — each one five times as heavy as the nucleus of a hydrogen atom — decay in the unimaginably short time of 2·10-21 s. This number has a zero in front of the decimal point, and then only after another 20 zeros is there the number two: 0.000 000 000 000 000 000 002 seconds. Or, alternatively: 2·10-12 · 10-9 seconds: expressed in words, that would be two trillionths of a billionth of a second! The longest time-span measurable is the time which has elapsed since the creation of this universe. The Heidelberg astrophysicist and director of the Königsstuhl observatory, Prof. Heinrich Vogt (1890 – 1968) said: »The entire cosmos — space and the matter contained therein — is bounded by time. Time itself began with the origin of the cosmos. Whatever there was before the ›beginning of time‹ is out of the reach of scientific research. At that point, the space-time world accessible to science merges into a spaceless, timeless realm, one which the intellect of man is unable to grasp, and which remains for him an eternally unfathomable, divine mystery.«

Part I: Time – a physical quantity

1.6 Time constants and periods a) Time constants and oscillation periods in physics. In physics, various reproducible processes are of differing duration. The oscillation period T is referred to in the case of periodic events, or the time constant T for nonperiodic ones. (In a first order reaction, like nuclear decay, the amount of material N(t) remaining at time t with an initial amount N0 is given by N(t) = N0·e–t/T. The halflife (τ) is related to the time constant T by τ = T·ln2). Let’s look at some physical constants: The half-life of helium-5 (5He): τ = 2·1021 s The half-life of uranium-235 (235U): τ = 700 million years. (Note: A half-life has nothing to do with age!) Oscillation period of a pendulum of length L = 20 m: T = 2 · π · SQRT(L/g) = 8.97 s where Earth’s gravitational acceleration g = 9.81 m/s2 T ≅ 9 seconds Oscillation period of a pendulum of length L = 1 m: T = 2.006 s ≅ 2 seconds The oscillation period of a 440 Hz tone (= the musical note A) has a period: T = 1/f = 0.00227 s ≅ 2 ¼ thousandths of a second = 2 ¼ ms ›Oscillation period‹ T of a 133Cs atom (actually the oscillation period of the electromagnetic radiation corresponding to one particular electronic transition):