what is time?

Albert Einstein
:   Zeit ist das, was man an der Uhr abliest.
[Time is what a clock measures.]
Isaac Newton
:   Nam Tempus, Spatium, Locum & Motum, ut omnibus notiſſima, non definio.
[I do not define time, space, place, and motion, as being well known to all.]
(480–411 BCE)
:   τὸ πολυτελέστατον ἀνάλωμα τὸν χρόνον.
[The most precious thing a man can spend is time.]
(384–322 BCE)
:   ὥσπερ οὖν εἰ μὴ ἦν ἕτερον τὸ νῦν ἀλλὰ ταὐτὸ καὶ ἕν, οὐκ ἂν ἦν χρόνος.
[As, if the now had remained the same, time would not have existed.]
Augustinus Hipponensis
[Augustine of Hippo]
:   quid est ergo tempus? si nemo ex me quaerat, scio; si quaerenti explicare velim, nescio.
[What, then, is time? If no one asks me, I know; if I wish to explain to him who asks, I know not.]
Marcus Aurelius
:   Time is like a river made up of the events which happen, and a violent stream; for as soon as a thing has been seen, it is carried away, and another comes in its place, and this will be carried away too. Ποταμός τίς ἐστι τῶν γινομένων καὶ ῥεῦμα βίαιον ὁ αἰών· ἅμα τε γὰρ ὤφθη ἕκαστον, καὶ παρενήνεκται καὶ ἄλλο παραφέρεται, τὸ δὲ ἐνεχθήσεται.
Julian Barbour
:   We shall come to see that time does not exist.
Henri Bergson
:   Le temps est ce qui empêche que tout soit donné tout d'un coup.
[Time keeps everything from happening all at once.]
Hector Berlioz
:   Le temps est un grand maître, dit-on; le malheur est qu'il soit un maître inhumain qui tue ses élèves.
[Time is a great teacher, but unfortunately it kills all its pupils.]
Carol Burnett
:   Comedy is tragedy plus time.
David Byrne
:   Time isn't holding us.Time isn't after us. Same as it ever was. Same as it ever was.
Charles Chesnutt
:   Time touches all things with destroying hand.
Benjamin Disraeli
:   Time is precious, but truth is more precious than time.
Benjamin Franklin
:   You may delay, but time will not.
Benjamin Franklin
:   Remember that time is money.
Merrick Furst
:   The biggest difference between time and space is that you can't reuse time.
Ben Hecht
:   Time is a circus, always packing up and moving away.
(460–370 BCE)
:   Χρόνος ἐστὶν ἐν ᾧ καιρός, καὶ καιρὸς ἐν ᾧ χρόνος οὐ πολύς‧
[Time is that wherein there is opportunity, and opportunity is that wherein there is no great time.]
Aldous Huxley
:   Time, as we know it, is a very recent invention. The modern time-sense is hardly older than the United States. It is a by-product of industrialism — a sort of psychological analogue of synthetic perfumes and aniline dyes.
Franklin P. Jones
:   Time is a versatile performer. It flies, marches on, heals all wounds, runs out, and will tell.
Stanisław Lec
:   Życie zabiera ludziom zbyt wiele czasu.
[People find life entirely too time consuming.]
Abraham Lincoln
:   The best thing about the future is that it comes only one day at a time.
Groucho Marx
:   Time flies like an arrow. Fruit flies like a banana.
David B. Norris
:   How you spend your time is more important than how you spend your money. Money mistakes can be corrected, but time is gone forever.
:   Tempus edax rerum.
[Time is the devourer of all things.]
Theodore Roethke
:   Time marks us while we are marking time.
William Shakespeare
:   But thought's the slave of life, and life time's fool;and time, that takes survey of all the world,must have a stop.
William Shakespeare
:   I wasted time, and now doth time waste me
Bob Talbert
:   Time neither subtracts nor divides, but adds at such a pace it seems like multiplication.
Henry David Thoreau
:   As if we could kill time without injuring eternity!
H.G. Wells
:   Clearly…any real body must have extension in four directions: it must have length, breadth, thickness, and duration….There are really four dimensions, three which we call the three planes of space, and a fourth, time. There is, however, a tendency to draw an unreal distinction between the former three dimensions and the latter, because it happens that our consciousness moves intermittently in one direction along the latter from the beginning to the end of our lives.
Steven Wright
:   Everywhere is in walking distance if you have the time.
unknown: :   An inch of gold cannot buy an inch of time. 寸金难买寸光阴
unknown: :   The speed of time is one second per second.
unknown: :   Time heals all wounds — except deadly ones.
unknown: :   Wasting time is an important part of living.
unknown: :   Time is an illusion perpetrated by the manufacturers of space.
unknown: :   What does "it" mean in the sentence, "What time is it?"
Tom Stoppard
:   Eternity is a terrible thought. I mean, where's it going to end?

Lots of fancy words for what could be stated more simply, or can it? Simple concepts are often the most difficult to explain. Many times, there's one notion that we carry around with us and another, more technical and specific, that's used in physics. What time is it? Pretty simple question, no? . Now tell me again what time is. Is my definition any good? Well, of course it is. Otherwise I wouldn't have written it down. Time in the physical sense is always relative and never absolute. That is to say, we always consider time as the interval between two events and not as some cumulative measure of this abstract thing we talk about when when ask, "What time is it?" When did time begin? In the year 1 CE? Hardly. That's just a cultural fixed point. Do you think Socrates walked around thinking, "I can't believe it's 535 BCE already. I can't stop writing 536 BCE on my checks"? When the aliens land on Mount Shasta they'll have a different chronometer reading in their spaceships, using different units and a different zero point. Furthermore, why is it in London and in Seattle? This idea of local time is not usually what we mean by time in physics.

Have you ever heard people say "Daylight Saving Time is ending so we'll gain an hour Saturday night"? Well let me tell you right now that nobody ever gained an hour when Daylight Saving Time ended, not literally anyway. If you were in the hospital, nearing death at 1:59 AM on the last Saturday of October in the United States would you have lived an extra hour if you died two minutes later at 1:01 AM? Would you say you went back in time? No way. There's time — in the sense of how long it takes for something to happen — and then there's time -- in the sense of "What time is it?". Time in the former sense, as used in physics, is measured with a stopwatch or an interval timer, while time in the latter sense is determined with a wristwatch or clock. In the course of your study of physics you'll have to understand the difference between the two meanings of this one word.

Time is a measure of the interval between two events. Time is also a cultural construct whereby an event can be associated with a series of numbers. When the quantity called time appears in a physical equation, it is always referring to the measure of the interval between two events.

natural units

year month day

The length of a year depends on your choice of calendars or how you define a year.

type in days in seconds notes
standard 365 31,536,000  
leap 366 31,622,400  
julian 365.25 31,557,600 adopted by Julius Caesar in 46 BCE
gregorian 365.2425 31,556,952 adopted by Pope Gregory XIII in 1582
tropical 365.242189… 31,556,925.16… period between vernal equinoxes
sidereal 365.256363… 31,558,149.76… orbital period relative to the stars
anomalistic 365.259635… 31,558,432.46… period between perihelia
eclipse 346.620075… 29,947,974.48… period of lunar node passages
How long is a year?

cultural units

hour minute second


decade century millennium eon



time zones

Greenwich Mean Time (GMT)

international atomic time (tai)

The SI unit of time is the second [s].


The hyperfine transition is the basis of International Atomic Time (TAI). By definition, the outermost electron in an ordinary cesium 133 atom cycles through this transition 9,192,631,770 times in one second.

International Atomic Time (abbreviated TAI after the French Temps Atomique International) began at midnight GMT on the first day of 1958 and has continued advancing forward at the rate of one second every 9,192,631,770 periods of the hyperfine transition in 133Cs. TAI is maintained by the Bureau International des Poids et Mesures (BIPM) in Paris, which periodically averages the time kept by various atomic clocks around the world. The BIPM then disseminates correction factors needed to synchronize these clocks with the master clock in the Observatoire de Paris.

coordinated universal time (utc)

Coordinated Universal Time (abbreviated UTC) is the basis of legal time throughout the world. All local civil times differ from UTC by either a whole number of hours or an odd number of half hours, but never by any other amount. One second of Coordinated Universal Time is the same as one second of International Atomic Time, but UTC and TAI are slightly out of step. TAI marches forward uniformly, while UTC is adjusted from time to time to keep it synchronized with the earth's rotation.

The earth is not an effective timekeeper. For most of the last two hundred years the mean solar day has been slightly longer than the 86,400 s currently defined by the International System. Universal Time UT, or more specifically UT1, is in effect the mean solar time. It is continuous (i.e. there are no leap seconds) but has a variable rate because of the Earth's non-uniform rotation period. It is needed for computing the sidereal time, an essential part of pointing a telescope at a celestial source. The quantity UT1-UTC, which typically changes by 1 or 2 ms per year, can only be obtained by observation, though seasonal trends are known and the IERS listings are able to predict some way into the future with adequate accuracy for pointing telescopes.



When UT1 lags too far behind UTC, a leap second is inserted at the end of the day before January 1 or July 1 as appropriate. When this happens, 23:59:59 is followed by the unusual time of 23:59:60 before turning over to 00:00:00 and starting the next day. In the unlikely event that UT1 were to lead UTC (that is, if the earth's rate of rotation were to increase) the provision exists for the insertion of a negative leap second. Were this to ever occur, 23:59:58 of one day would be followed by 00:00:00 of the next, skipping 23:59:59 altogether. In any case the absolute difference between UTC and UT1 must never exceed 0.9 s.

The decision on when to insert a leap second is made by the International Earth Rotation Service (IERS) in Frankfurt based on observations of the Earth's orientation in space.


Adding leap seconds to Coordinated Universal Time (UTC) keeps it in line with the rotation of the earth as measured by Universal Time (UT1).

Coordinated Universal Time, CUT — Temps universel coordonné, TUC

Are leap seconds even necessary?

What would be so wrong with that? Does it really matter what number we assign to a position of the sun in the sky?

In 1582 Pope Gregory XIII managed to extract ten days from the calendar. On 4 October 1582 the Catholic world went to sleep. When they woke up it was 15 October 1582. By 1752 the protestant nation of England and her American colonies also accepted the change. (They needed to add 11 days to catch up.) In 1873 Japan made the switch. (They needed 12 days.) Then Russia in 1917 and China in 1949. (13 days.) The Greek Orthodox Church is possibly the only European agency that has not accepted this change (although the nation of Greece made the switch in 1923).

I think the big thing is that everyone agrees what time (or day) it is. Not that the time is any particular number. Time is a social construct, remember.

year month offset   year month offset   year month offset
1961 January 0   1986   23   2002   32
1971 * 10   1987   23   2003   32
1972 July 11   1988 January 24   2004   32
1973 January 12   1989   24   2005   32
1974 January 13   1990 January 25   2006 January 33
1975 January 14   1991 January 26   2007   33
1976 January 15   1992 July 27   2008   33
1977 January 16   1993 July 28   2009 January 34
1978 January 17   1994 July 29   2010   34
1979 January 18   1995   29   2011   34
1980 January 19   1996 January 30   2012 July 35
1981 July 20   1997 July 31   2013   ?
1982 July 21   1998   31   2014   ?
1983 July 22   1999 January 32   2015   ?
1984   22   2000   32   2016   ?
1985 July 23   2001   32   2017   ?
Leap seconds and cumulative adjustments to UTC
Adjustments from 1961 to 1971 followed a more complicated protocol and were omitted. Only the final offset is shown.

network time protocol (ntp)

Network Time Protocol (NTP) is a 64 bit binary counter that advances in synchrony with International Atomic Time (TAI). The first 32 bits (binary digits) count the seconds and the second 32 bits count the fractions of a second.

The first 32 bits divide NTP into eras lasting 136 years, since…

232 s = 4,294,967,296 s ≈ 136 years

or more precisely…

232 s = 4,294,967,296 s ≈ 136 years, 36 days, 6 hours, 28 minutes, 16 seconds

but don't quote me on the number of days. The years shift between normal years with 365 days and leap years with 366 days in a roughly four year cycle. The exceptions that made me write "roughly" make this an exact number that is a pain to determine. My guess is that for most eras there'd be 136 years and 36 days plus the fractions in this cycle and for exceptional eras (like those containing the years 2400 or 2800) there'd be 136 years and 37 days plus the fractions. But all this is idle speculation. NTP is probably the longest continuously running protocol on the Internet, but it would be astounding if it lasted four hundred years.

The first era of NTP began 1 January 1900 at midnight Greenwich Mean Time (GMT) — the predecessor of Coordinated Universal Time (UTC). No NTP clock literally began ticking at this time, of course. The necessary technology hadn't been invented. (Digital computers first appeared in the late 1930s and the first atomic clock was built in 1949.) It's just a convenient place to put the zero for us humans who are used to years, days, hours and minutes. When UTC went into effect at 00:00:00 on 1 January 1972 the NTP time was 2,272,060,800; the first 32 bits of which looks like this…


or with all 64 bits, like this…


The second 32 bits allows for a precision of about one quarter of a nanosecond since…

2−32 s = 2.328 × 10−10 s ≈ ¼ ns

This is a ridiculous level of precision given that the maximum speed at which any signal can propagate through a network is the speed of light. To take advantage of the last bit in the 64 bit NTP code, the time server would have to be closer than the distance traveled by a beam of light in 2−32 s.

s = ct = (299,792,458 m/s)(2−32 s) = 0.06980 m ≈ 7 cm

My favorite NTP server is time.nist.gov at the Time and Frequency Division of the National Institute of Standards and Technology in Boulder, Colorado. This is roughly 2900 km from my desktop computer in New York City. The signal that I get is delayed by at least…

t = s/c = (2,900,000 m)/(299,792,458 m/s) = 0.009673 s ≈ 10 ms

I could get increased accuracy by switching to time-a.nist.gov located in Gaithersburg, Maryland; which is only 380 km away. This signal would have a maximum delay of only…

t = s/c = (380,000 m)/(299,792,458 m/s) = 0.001268 s ≈ 1 ms

This increase in accuracy is meaningless given the way signals propagate over the Internet. Data (like email, web pages, streaming video, and time signals) are broken up into packets that are free to take whatever path the network allows. Unlike a classical telephone network where information is sent along a single dedicated channel, the packets of an Internet message need not follow the same path. Each one is free to negotiate its own journey. The path each packet follows is determined by the architecture of the network and the instantaneous traffic at every node and through every link. Packets can even get lost or "dropped" along the way. Only after they've all arrived are the packets reassembled into the original message.

The electronic act of chopping up a message into packets and reassembling them back into a message takes time, as does the negotiation that each packet makes at the junctions or nodes in the network. The overall result is that the actual transmission time is several times the speed-of-light time. Typical ping times across the United States are on the order of 10 to 100 ms. For NTP this means a deviation from TAI of around 10 to 100 ms in practice. Erring on the side of caution, most software companies will only claim accuracy to within a second.

event common era ntp era ntp time
julian day number zero begins 1 January 4713 BCE −49 1,795,583,104
common era begins 1 January 1 CE −14 202,934,144
gregorian calendar begins 15 October 1582   −3 2,874,597,888
ntp begins 1 January 1900   0 0
unix time begins 1 January 1970   0 2,208,988,800
utc synched to tai minus 10 s 1 January 1972   0 2,272,060,800
last second of second millennium 31 December 1999   0 3,155,673,599
first second of third millennium 1 January 2000   0 3,155,673,600
unix time reaches one billion seconds 9 September 2001   0 3,208,988,800
ntp era change 7 February 2036   1 0
fourth millennium begins 1 January 3000   8 352,930,432
Some events in Network Time Protocol (NTP) Adapted from: David Mills, University of Delaware