Time

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For the news magazine, see Time (magazine). For other uses, see Time (disambiguation).
A pocket watch, a device used to tell time
A pocket watch, a device used to tell time
Look up time in Wiktionary, the free dictionary.

There are two distinct views on the meaning of time. One view is that time is part of the fundamental structure of the universe, a dimension in which events occur in sequence, and time itself is something that can be measured. This is the realist's view, to which Sir Isaac Newton subscribed.[1]

A contrasting view is that time is part of the fundamental intellectual structure (together with space and number) within which we sequence events, quantify the duration of events and the intervals between them, and compare the motions of objects. In this view, time does not refer to any kind of entity that "flows", that objects "move through", or that is a "container" for events. This view is in the tradition of Gottfried Leibniz[2] and Immanuel Kant,[3][4] in which time, rather than being an objective thing to be measured, is part of the mental measuring system. The question, perhaps overly simplified and allowing for no middle ground, is thus: is time a "real thing" that is "all around us", or is it nothing more than a way of speaking about and measuring events?

In science, time (and space) are considered fundamental, (i.e. not definable via other quantities because other quantities are defined via time and space) thus they can only be "defined" via measurement - using operational definitions that specify the units of measurement that quantify time. Regularly recurring events and objects with apparent periodic motion have long served as standards for units of time. Examples are the apparent motion of the sun across the sky, the phases of the moon, the swing of a pendulum, and, currently, oscillations of Cesium atoms.

Time has long been a major subject of science, philosophy, and art. The measurement of time has occupied scientists and technologists, and was a prime motivation in astronomy. Time is also of significant social importance, having economic value ("time is money") as well as personal value, due to an awareness of the limited time in each day and in human lifespans.

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[edit] Measurement

Time is currently one of the few fundamental quantities. These are quantities which cannot be defined via other quantities because there is nothing more fundamental than what is presently known. Thus, similar to definitions of other fundamental quantities (like space and mass), only the units of time measurement are defined in science, not time itself.

The origins of our current measurement system go back to the Sumerian civilization of approximately 2000 BCE. This is known as the Sumerian Sexagesimal System based on the number 60. 60 seconds in a minute, 60 minutes in an hour - and possibly a calendar with 360 (60x6) days in a year (with a few more days added on). Twelve also features prominently, with roughly 12 hours of day and 12 of night, and 12 months in a year.

[edit] Measurement devices

Horizontal sundial in Taganrog (1833).
Horizontal sundial in Taganrog (1833).

A large variety of devices have been invented to measure time. The study of these devices is called horology.

An Egyptian device dating to c.1500 BCE, similar in shape to a bent T-square, measured the passage of time from the shadow cast by its crossbar on a non-linear rule. The T was oriented eastward in the mornings. At noon, the device was turned around so that it could cast its shadow in the evening direction.[5]

A sundial uses a gnomon to cast a shadow on a set of markings which were calibrated to the hour. The position of the shadow marked the hour in local time. Pliny the Elder records that the first sundial in Rome was looted from Catania, Sicily (264 BCE), which gave the incorrect time for a century, until the markings appropriate for the latitude of Rome were used (164 BCE).[6] Noontime was an event which could be marked by the time of the shortest shadow on a sundial. This was used in Rome to judge when a court of law was open; lawyers had to be at the court by that time.

The most accurate timekeeping devices of the ancient world were the waterclock or clepsydra, first found in Egypt. A waterclock was found in the tomb of pharaoh Amenhotep I (1525 - 1504 BCE). Waterclocks were used in Alexandria, and then worldwide, for example in Greece, from c.400 BCE. They could be used to measure the hours even at night, but required manual timekeeping to replenish the flow of water. Plato is said to have invented a water-based alarm clock. It depended on the nightly overflow of a vessel containing lead balls, which would float in a columnar vat. The vat would hold an increasing supply of water supplied by a cistern. Eventually the vessel would float high enough to tip over. The lead balls would then cascade onto a copper platter. The resultant clangor would then awaken his students at the Academy (378 BCE).[7] The Greeks and Chaldeans regularly maintained timekeeping records as an essential part of their astronomical observations. In particular, Arab engineers improved on the use of waterclocks up to the Middle Ages.[8]

The hourglass uses the flow of sand to measure the flow of time. They were used in navigation. Ferdinand Magellan used 18 glasses on each ship for his circumnavigation of the globe (1522).[9] The English word clock actually comes from French, Latin, and German words that mean bell. The passage of the hours at sea were marked by bells, and denoted the time (see ship's bells). The hours were marked by bells in the abbeys as well as at sea.

Incense sticks and candles were, and are, commonly used to measure time in temples and churches across the globe. Waterclocks, and later, mechanical clocks, were used to mark the events of the abbeys and monasteries of the Middle Ages. Richard of Wallingford (1292–1336), abbot of St. Alban's abbey, famously built a mechanical clock as an astronomical orrery about 1330.[10][11]

The most common devices in day-to-day life are the clock, for periods less than a day, and the calendar, for periods longer than a day. Clocks can range from watches, to more exotic varieties such as the Clock of the Long Now. They can be driven by a variety of means, including gravity, springs, and various forms of electrical power, and regulated by a variety of means such as a pendulum. There are also a variety of different calendars, for example the Lunar calendar and the Solar calendar, although the Gregorian calendar is the most commonly used.

A chronometer is a timekeeper precise enough to be used as a portable time standard, needed to determine longitude by means of celestial navigation. Nowadays over 1,000,000 "Officially Certified Chronometer" certificates, mostly for mechanical wrist-chronometers (wristwatches) with sprung balance oscillators, are being delivered each year, after passing the COSC's most severe tests and being singly identified by an officially recorded individual serial number. According to COSC, a chronometer is a high-precision watch capable of displaying the seconds and housing a movement that has been tested over several days, in different positions, and at different temperatures, by an official, neutral body (COSC). Each movement is individually tested for several consecutive days, in five positions and at three temperatures. Any watch with the denomination "chronometer" is provided with a certified movement.

The most accurate type of timekeeping device is currently the atomic clock, which are used to calibrate other clock and timekeeping instruments.

Today, the GPS global positioning systems in coordination with the NTP network time protocol can be used to synchronize timekeeping systems across the globe.

[edit] Standards

Common units of time
Unit Size Notes
Nanosecond 1/1,000,000,000 second
Microsecond 10−6 second
Millisecond 1/1,000 second
Second SI base unit
Minute 60 seconds
Hour 60 minutes
Day 24 hours
Week 7 days
Fortnight 14 days; 2 weeks
Month 28 to 31 days
Quarter 3 months
Year 12 months
Year 52 weeks approximate
Common Year 365 days
Leap year 366 days
Tropical year 365.24219 days Average
Gregorian year 365.2425 days Average
Olympiad 4 years
Lustrum 5 years
Decade 10 years
Score 20 years
Generation 25 years approximate
Century 100 years
Millennium 1,000 years
See also: Time standard and Orders of magnitude (time)

The SI base unit for time is the SI second. From the second, larger units such as the minute, hour and day are defined, though they are "non-SI" units because they do not use the decimal system, and also because of the occasional need for a leap-second. They are, however, officially accepted for use with the International System. There are no fixed ratios between seconds and months or years as months and years have significant variations in length.[12]

The official SI definition of the second is as follows:[12][13]

The second is 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.

Previous to 1967, the second was defined as:

the fraction 1/31,556,925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time.

This definition of time (coupled with current definition of space) makes our space and time to be Minkowski space-time and makes special relativity theory absolutely correct by definition.

[edit] World time

The measurement of time is so critical to the functioning of modern societies that it is coordinated at an international level. The basis for scientific time is a continuous count of seconds based on atomic clocks around the world, known as the International Atomic Time (TAI). This is the yardstick for other time scales, including Coordinated Universal Time (UTC), which is the basis for civil time.

Earth is split up into a number of time zones. Most time zones are exactly one hour apart, and by convention compute their local time as an offset from Greenwich Mean Time.

[edit] Chronology

Another form of time measurement consists of studying the past. Events in the past can be ordered in a sequence (creating a chronology), and be put into chronological groups (periodization). One of the most important systems of periodization is geologic time, which is a system of periodizing the events that shaped the Earth and its life. Chronology, periodization, and interpretation of the past are together known as the study of history.

[edit] Interpretations

See also: Philosophy of space and time

Many ancient philosophers wrote lengthy essays on time, believing it to be the essence around which life was based. A famous analogy compared the time of life to the passing of sand through an hourglass. The sand at the top is the future, and, one tiny grain at a time, the future flows through the present into the past. The past ever expanding, the future ever decreasing, but the future grains being moulded into the past through the present. This was widely discussed in around the 3rd century CE.[citation needed]

The earliest recorded philosophy of time was expounded by Ptahhotep, who lived c.2650–2600 BC said: "Do not lessen the time of following desire, for the wasting of time is an abomination to the spirit."

In the Old Testament book Ecclesiastes, traditionally thought to have been written by King Solomon (970–928 BC), time (as the Hebrew word עת ’êth is often translated, as well as as "season") was regarded as a medium for the passage of predestined events. (Another word, זמן zman, was current as meaning time fit for an event, and is used as the modern Hebrew equivalent to the English word "time".)

There is an appointed time (zman) for everything. And there is a time (’êth) for every event under heaven–

A time (’êth) to give birth, and a time to die; A time to plant, and a time to uproot what is planted.

A time to kill, and a time to heal; A time to tear down, and a time to build up.

A time to weep, and a time to laugh; A time to mourn, and a time to dance.

A time to throw stones, and a time to gather stones; A time to embrace, and a time to shun embracing.

A time to search, and a time to give up as lost; A time to keep, and a time to throw away.

A time to tear apart, and a time to sew together; A time to be silent, and a time to speak.

A time to love, and a time to hate; A time for war, and a time for peace.

– Ecclesiastes 3:1–8

Around 500 BC Heraclitus, a fatalist, held that the passage of time and the future both lay beyond the possibility of human influence: "Everything flows and nothing abides; everything gives way and nothing stays fixed. You cannot step twice into the same river, for other waters and yet others, go flowing on. Time is a child, moving counters in a game; the royal power is a child's."

[edit] Time in philosophy

Newton believed time and space form a container for events, which is as real as the objects it contains.

Absolute, true, and mathematical time, in and of itself and of its own nature, without reference to anything external, flows uniformly and by another name is called duration. Relative, apparent, and common time is any sensible and external measure (precise or imprecise) of duration by means of motion; such a measure—for example, an hour, a day, a month, a year—is commonly used instead of true time.

– Principia[14]

In contrast to Newton's belief in absolute space, and closely related to Kantian time, Leibniz believed that time and space are a conceptual apparatus describing the interrelations between events. The differences between Leibniz's and Newton's interpretations came to a head in the famous Leibniz-Clarke Correspondence. Leibniz thought of time as a fundamental part of an abstract conceptual framework, together with space and number, within which we sequence events, quantify their duration, and compare the motions of objects. In this view, time does not refer to any kind of entity that "flows," that objects "move through," or that is a "container" for events.

Immanuel Kant, in the Critique of Pure Reason, described time as an a priori intuition that allows us (together with the other a priori intuition, space) to comprehend sense experience. With Kant, neither space nor time are conceived as substances, but rather both are elements of a systematic mental framework necessarily structuring the experiences of any rational agent, or observing subject. Spatial measurements are used to quantify how far apart objects are, and temporal measurements are used to quantify how far apart events occur. Similarly, Schopenhauer stated in the preface to his On the Will in Nature that "Time is the condition of the possibility of succession."

In Existentialism, time is considered fundamental to the question of being, in particular by the philosopher Martin Heidegger. See Ontology.

Einstein showed that if time and space is measured using electromagnetic phenomena (like light bouncing between mirrors) then due to the constancy of the speed of light, time and space become mathematically entangled together in a certain way (called Minkowski space) which in turn results in Lorentz transformation and in entanglement of all other important derivative physical quantities (like energy, momentum, mass, force, etc) in a certain 4-vectorial way (see special relativity for more details).

[edit] Time as "unreal"

In 5th century BC Greece, Antiphon the Sophist, in a fragment preserved from his chief work On Truth held that: "Time is not a reality (hupostasis), but a concept (noêma) or a measure (metron)." Parmenides went further, maintaining that time, motion, and change were illusions, leading to Zeno's paradoxes (Zeno was a follower of Parmenides).

Ralph Waldo Emerson considers time as presentness, where past and future are but our present projections (of our memory, hope, etc.). For Emerson, time needs a qualitative measurement rather than a quantitative one.[citation needed]

Writers such as J. M. E. McTaggart in his 1908 The Unreality of Time have argued that time is an illusion (see also The flow of time).

Contemporary thinker and buddhist teacher Tarthang Tulku writes that there is no moving time.[15]

Another contemporary philosopher, Dr. Edward S. Casey, suggests that time may be wholly the work of our imagination and memory.[16]

Interesting that indeed nothing physical in our Universe depends on time (nor on space) per se. This in turn mathematically results in all known conservation laws - see Emmy Noether theorem for the proof of this. So, it is quite possibly that time (and space) are not "physical" quantities but rather intermediate mathematical abstracts invented by us to relate various observable phenomena together.

[edit] Linear time

In general, the Judaeo-Christian concept, based on the Bible, is that time is linear, with a beginning, the act of creation by God. The Christian view assumes also an end, the eschaton, expected to happen when Christ returns to earth in the Second Coming to judge the living and the dead. This will be the consummation of the world and time. St Augustine's City of God was the first developed application of this concept to world history. The Christian view is that God and the supernatural world are outside time and exist in eternity. This view relies on interpretation however, for some Jewish and Christian sects believe time may in fact be cyclical.[citation needed] It is also possible to see time as having more than one dimension. In this view, over time the universe branches into multiple alternative universes where different events have occurred. This view has not been scientifically verified.

[edit] Cyclical time

Main articles: Time Cycles and Wheel of time

The dharmic religions such as Hinduism and Buddhism, have a concept of a wheel of time, that regards time as cyclical and quantic consisting of repeating ages that happen to every being of the Universe between birth and extinction. In recent years this cyclical vision of time has been embraced by theorists of quantic space-time and systems theory. This view has also not been scientifically verified.

[edit] Time in the Physical Sciences

From the age of Newton up until Einstein's profound reinterpretation of the physical concepts associated with time and space, time was considered to be "absolute" and to flow "equably" (to use the words of Newton) for all observers.[17] The science of classical mechanics is based on this Newtonian idea of time.

Einstein, in his special theory of relativity,[18] postulated the constancy and finiteness of the speed of light for all observers. He showed that this postulate, together with a reasonable definition for what it means for two events to be simultaneous, requires that distances appear compressed and time intervals appear lengthened for events associated with objects in motion relative to an inertial observer.

[edit] Time in Classical Mechanics

In classical mechanics Newton's concept of "relative, apparent, and common time" can be used in the formulation of a prescription for the synchronization of clocks. Events seen by two different observers in motion relative to each other can be synchronized in terms of signals passed back and forth between these observers. Implicit in the classical description is the assumption that these signals can travel with infinite velocity (as opposed to the finite maximum signal velocity, the speed of light, in modern physics).

Newton's first law of motion states that every object remains at rest or continues in a state of uniform linear motion unless acted upon by an outside force. A careful analysis of this principle provokes the second underlying assumption about classical time: There must exist some absolute spatial metric with respect to which one can define some absolute time metric such that the acceleration (second derivative of spatial position with respect to time) can be defined and is always zero in the absence of forces.

These two underlying assumptions (the existence of infinite signal velocities and absolute space and time metrics shared by all observers) produce a mathematical concept of time that works pretty well for describing the everyday phenomena of most people's experience.

[edit] Time in Modern Physics

In the late nineteenth century physicists encountered problems with the classical understanding of time, in connection with the behavior of electricity and magnetism. Einstein resolved these problems by invoking a method of synchronizing clocks using the constant, finite speed of light as the maximum signal velocity. This led directly to the result that time appears to elapse at different rates relative to different observers in motion relative to one another.

[edit] Spacetime
A tesseract, a cube in 3 dimensions extended to a fourth, as a description of time; adhering to defined finite bounds, all possibilities for this configuration are conceptually representable.
A tesseract, a cube in 3 dimensions extended to a fourth, as a description of time; adhering to defined finite bounds, all possibilities for this configuration are conceptually representable.
Main article: Spacetime
See also: Time in physics

Modern physics views the curvature of spacetime around an object as much a feature of that object as are its mass and volume.

Time has historically been closely related with space, the two together comprising spacetime in Einstein's special relativity and general relativity. According to these theories, the concept of time depends on the spatial reference frame of the observer(s), and the human perception as well as the measurement by instruments such as clocks are different for observers in relative motion. Even the temporal order of events can change, but the past and future are defined by the backward and forward light cones, which never change. The past is the set of events that can send light signals to the observer, the future the events to which she can send light signals. All else is the present and within that set of events the very time-order differs for different observers.

[edit] Block time
Main article: Block time

Block time consists of an unchanging four-dimensional spacetime. This does away with the idea of the past, present and future.

[edit] Natural unit of time
Main article: Planck time

Planck time (~ 5.4 × 10−44 seconds) is the unit of time in the system of natural units known as Planck units. Current established physical theories are believed to fail at this time scale, and many physicists expect that the Planck time might be the smallest unit of time that could ever be measured, even in principle. Tentative physical theories that describe this time scale exist; see for instance loop quantum gravity.

[edit] Time quanta
See also: Chronon

Time quanta is a hypothetical concept.

In the modern quantum theory (Standard Model of particle physics) and in general relativity time is not quantized.

[edit] Time dilation
Main article: Time dilation

Einstein said that "The only reason for time is so that everything does not happen at once". In this regard, Einstein said that time was basically what a clock reads; the clock can be any action or change, like the movement of the sun. Einstein showed that people traveling at different speeds will measure different times for events and different distances between objects, though these differences are minute unless one is traveling at a speed close to that of light. Many subatomic particles exist for only a fixed fraction of a second in a lab relatively at rest, but some that travel close to the speed of light can be measured to travel further and survive longer than expected (a muon is one example). According to the special theory of relativity, in the high-speed particle's frame of reference, it exists, on the average, for a standard amount of time known as its mean lifetime, and the distance it travels in that time is zero, because its velocity is zero. Relative to a frame of reference at rest, time seems to "slow down" for the particle. Relative to the high-speed particle, distances seems to shorten. Even in Newtonian terms time may be considered the fourth dimension of motion; but Einstein showed how both temporal and spatial dimensions can be altered (or "warped") by high-speed motion.

Einstein (The Meaning of Relativity): "Two events taking place at the points A and B of a system K are simultaneous if they appear at the same instant when observed from the middle point, M, of the interval AB. Time is then defined as the ensemble of the indications of similar clocks, at rest relatively to K, which register the same simultaneously."

Einstein wrote in his book, Relativity, that simultaneity is also relative, i.e., two events that appear simultaneous to an observer in a particular inertial reference frame need not be judged as simultaneous by a second observer in a different inertial frame of reference.

[edit] Arrow of time
Main article: Arrow of time

Time appears to have a direction - the past lies behind, fixed and incommutable, while the future lies ahead and is not necessarily fixed. Yet the majority of the laws of physics don't provide this arrow of time. The exceptions include the Second law of thermodynamics, which states that entropy must increase over time (see Entropy (arrow of time)); the cosmological arrow of time, which points away from the Big Bang, and the radiative arrow of time, caused by light only traveling forwards in time. In particle physics, there is also the weak arrow of time, from CPT symmetry, and also measurement in quantum mechanics (see Measurement in quantum mechanics).

[edit] Time and the "Big Bang"

According to some of the latest scientific theories, time began with the Big Bang. Stephen Hawking has commented that statements about what happened "before" time began are self-contradictory, and thus without meaning. Other theorists have contended that even if there were another time frame "before" the Big Bang, no information from events then would be accessible to us. Scientists have come to some agreement on descriptions of events that happened 10−35 seconds after the Big Bang, but generally agree that descriptions about what happened before one Planck time after the Big Bang will likely remain pure speculations.

[edit] Time travel in science fiction

Main article: Time travel
See also: Time travel in fiction

Time travel is the concept of moving backward or forward to different points in time, in a manner analogous to moving through space. Additionally, some interpretations of time travel take the form of travel between parallel realities or universes. A central problem with time travel is that of logic - say, violation of causality (when effect precedes the cause it is the consequence of) — which has given rise to a number of paradoxes (see grandfather paradox).

[edit] Psychology

See also: Mental chronometry and Mental chronometry

Different people may judge identical lengths of time quite differently. Time can "fly"; that is, a long period of time can seem to go by very quickly. Likewise, time can seem to "drag," as in when one performs a boring task. The psychologist Jean Piaget called this form of time perception "lived time."

Time also appears to pass more quickly as one gets older. For example, a year for a five-year-old child is 20% of his entire life so far, however for a 50 year old adult a year is only 2% of his entire life so far; so with increasing age, each segment of time is a decreasing percentage of the person's total experience.

Altered states of consciousness are sometimes characterized by a different estimation of time. Some psychoactive substances--such as entheogens--may also dramatically alter a person's temporal judgement. When viewed under the influence of such substances as LSD, psychedelic mushrooms and peyote, a clock may appear to be a strange reference point and a useless tool for measuring the passage of events as it does not correlate with the user's experience. At higher doses, time may appear to slow down, stop, speed up, and even go backwards when under the influence of these agents. A typical thought might be "I can't believe it's only 8 o'clock, but then again, what does 8 o'clock mean?" As the boundaries for experiencing time are removed, so is its relevance. Many users claim this unbounded timelessness feels like a glimpse into spiritual infinity. To imagine that one exists somewhere "outside" of time is one of the hallmark experiences of a psychedelic voyage. Marijuana may also distort the perception of time, although, to a lesser degree than psychedelics.

The practice of meditation, central to all Buddhist traditions, takes as its goal the reflection of the mind back upon itself, thus altering the subjective experience of time; the so called, 'entering the now', or 'the moment'.

In explaining his theory of relativity, Albert Einstein is often quoted as saying that although sitting next to a pretty girl for an hour feels like a minute, placing one's hand on a hot stove for a minute feels like an hour. This is intended to introduce the listener to the concept of the interval between two events being perceived differently by different observers.

[edit] Use of time

See also: Time management and Time discipline

The use of time is an important issue in understanding human behaviour, education, and travel behaviour. Time use research is a developing field of study. The question concerns how time is allocated across a number of activities (such as time spent at home, at work, shopping, etc.). Time use changes with technology, as the television or the Internet created new opportunities to use time in different ways. However, some aspects of time use are relatively stable over long periods of time, such as the amount of time spent traveling to work, which despite major changes in transport, has been observed to be about 20-30 minutes one-way for a large number of cities over a long period of time. This has led to the disputed time budget hypothesis.

Time management is the organization of tasks or events by first estimating how much time a task will take to be completed, when it must be completed, and then adjusting events that would interfere with its completion so that completion is reached in the appropriate amount of time. Calendars and day planners are common examples of time management tools.

Arlie Russell Hochschild and Norbert Elias have written on the use of time from a sociological perspective.

[edit] References

  1. ^ Newton's Views on Space, Time, and Motion - Stanford University http://plato.stanford.edu/entries/newton-stm/
  2. ^ Leibniz on Space, Time, and Indiscernibles - Against the Absolute Theory -- Internet Encyclopedia of Philosophy http://www.iep.utm.edu/l/leib-met.htm#H7
  3. ^ Critique of Pure Reason - Lecture notes of G. J. Mattey, UC Davis http://www-philosophy.ucdavis.edu/mattey/kant/TIMELEC.HTM
  4. ^ Kant's Transcendental Idealism - Internet Encyclopedia of Philosophy http://www.iep.utm.edu/k/kantmeta.htm#H4
  5. ^ Jo Ellen Barnett, Time's Pendulum ISBN 0-306-45787-3 p.28
  6. ^ Jo Ellen Barnett, Time's Pendulum p.31
  7. ^ Jo Ellen Barnett, Time's Pendulum p.38
  8. ^ Jo Ellen Barnett, Time's Pendulum p.37
  9. ^ Laurence Bergreen, Over the Edge of the World: Magellan's Terrifying Circumnavigation of the Globe, HarperCollins Publishers, 2003, hardcover 480 pages, ISBN 0-06-621173-5
  10. ^ North, J. (2004) God's Clockmaker: Richard of Wallingford and the Invention of Time. Oxbow Books. ISBN 1-85285-451-0
  11. ^ Watson, E (1979) "The St Albans Clock of Richard of Wallingford". Antiquarian Horology 372-384.
  12. ^ a b Organisation Intergouvernementale de la Convention du Métre (1998). The International System of Units (SI), 7th Edition (PDF). Retrieved on June 13, 2006. 
  13. ^ Base unit definitions: Second. NIST. Retrieved on June 13, 2006.
  14. ^ Newton, Isaac (1726). The Principia, 3rd edition.  Translated by I. Bernard Cohen and Anne Whitman, University of California Press, Berkeley, 1999.
  15. ^ Tarthang Tulku. Opening time. (In Dimensions of Thought. Current Explorations in Time, Space, and Knowledge. Volume 1, Dharma Publishing, Berkeley, USA, 1980, ISBN 0-913546-77-1, p. 54)
  16. ^ Edward S. Casey. Time out of Mind. (In Dimensions of Thought. Current Explorations in Time, Space, and Knowledge. Volume 1, Dharma Publishing, Berkeley, USA, 1980, ISBN 0-913546-77-1, p. 141ff)
  17. ^ Herman M. Schwartz, Introduction to Special Relativity, McGraw-Hill Book Company, 1968, hardcover 442 pages, see ISBN 0882754785 (1977 edition), pp. 10-13
  18. ^ A. Einstein, H. A. Lorentz, H. Weyl, H. Minkowski, The Principle of Relativity, Dover Publications, Inc, 2000, softcover 216 pages, ISBN 0486600815, See pp. 37-65 for an English translation of Einstein's original 1905 paper.

[edit] See also

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[edit] Special units of time

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[edit] Perception of time

[edit] Physics

[edit] Philosophy

[edit] Timekeeping

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