The Physics
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what is time?

Zeit ist das, was man an der Uhr abliest.

[Time is what a clock measures.]

Albert Einstein (1879–1955)

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.]

Isaac Newton (1642–1727)

τὸ πολυτελέστατον ἀνάλωμα τὸν χρόνον.

[The most precious thing a man can spend is time.]

Ἀντιφῶν [Antiphon] (480–411 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.]

Αριστοτέλης [Aristotle] (384–322 BCE)

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.]

Augustinus Hipponensis [Augustine of Hippo] (354–430)

Ποταμός τίς ἐστι τῶν γινομένων καὶ ῥεῦμα βίαιον ὁ αἰών· ἅμα τε γὰρ ὤφθη ἕκαστον, καὶ παρενήνεκται καὶ ἄλλο παραφέρεται, τὸ δὲ ἐνεχθήσεται.

[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.]

Marcus Aurelius (121–180)

We shall come to see that time does not exist.

Julian Barbour (1937–0000)

Le temps est ce qui empêche que tout soit donné tout d'un coup.

[Time keeps everything from happening all at once.]

Henri Bergson (1859–1941)

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.]

Hector Berlioz (1803–1869)

Comedy is tragedy plus time.

Carol Burnett (1933–0000)

Time isn't holding us. Time isn't after us. Same as it ever was. Same as it ever was.

David Byrne (1952–0000)

Time touches all things with destroying hand.

Charles Chesnutt (1858–1932)

Time is precious, but truth is more precious than time.

Benjamin Disraeli (1804–1881)

You may delay, but time will not.

Benjamin Franklin (1706–1790)

Remember that time is money.

Benjamin Franklin (1706–1790)

The biggest difference between time and space is that you can't reuse time.

Merrick Furst (1956–0000)

Time is a circus, always packing up and moving away.

Ben Hecht (1894–1964)

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.]

Ιπποκράτης [Hippocrates] (460–370 BCE)

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.

Aldous Huxley (1894–1963)

Time is a versatile performer. It flies, marches on, heals all wounds, runs out, and will tell.

Franklin P. Jones (1939–2008)

Życie zabiera ludziom zbyt wiele czasu.

[People find life entirely too time consuming.]

Stanisław Lec (1909–1966)

The best thing about the future is that it comes only one day at a time.

Abraham Lincoln (1809–1865)

Time flies like an arrow. Fruit flies like a banana.

Groucho Marx (1890–1977)

How you spend your time is more important than how you spend your money. Money mistakes can be corrected, but time is gone forever.

David B. Norris (1944–0000)

Tempus edax rerum.

[Time is the devourer of all things.]

Ovid (43–18 BCE)

Time marks us while we are marking time.

Theodore Roethke (1908–1963)

I wasted time, and now doth time waste me.

William Shakespeare (1564–1616)

Time neither subtracts nor divides, but adds at such a pace it seems like multiplication.

Bob Talbert (1936–1999)

As if we could kill time without injuring eternity!

Henry David Thoreau (1817–1862)

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.

H.G. Wells (1866–1946)

Everywhere is in walking distance if you have the time.

Steven Wright (1955–0000)

Time is. Time was. Time is past.

Robert Greene (1558–1592)


[An inch of gold cannot buy an inch of time.]


The speed of time is one second per second.


Time heals all wounds — except deadly ones.


Wasting time is an important part of living.


Time is an illusion perpetrated by the manufacturers of space.


What does "it" mean in the sentence, "What time is it?"


Eternity is a terrible thought. I mean, where's it going to end?

Tom Stoppard (1937–0000)

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? Why it's . Well it's in Sierra Leone, but it's in South Carolina. This idea of local time is not usually what we mean by time in physics.

When did time begin? In the year 1 CE? Hardly. That's just a cultural fixed point. This wouldn't have made sense to people who lived before what we now call the common era. 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 alien overlords land on Mount Shasta their calendars will count the number of extraterrestrial time units starting from a different first event — and we will learn to love it or be incinerated.

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 United States in a hospital, nearing death at 1:59 AM on the last Saturday of October you would not have gained an hour of life if you died two minutes later at 1:01 AM. The duration of your life is independent of the time zone or calendar you live by.

There's time in the sense of "What time is it?" And then there's time in the sense of how long did it take for something to happen. Time in the former sense is determined with a wristwatch or clock. Time in the latter sense is measured with a stopwatch or an interval timer. In day to day living, time is a cultural construct whereby an event can be associated with a series of numbers. In physics, time is a measure of the interval between two events.

natural units

In the International System of Units the second is the base unit of time, but for most of human existence (for as long as there have been things that looked and acted like humans) the natural units of time have been the day, the year, and the month.

the day

From the view of someone stuck on the surface of the Earth, day is the time when the Sun is visible in the sky. The day begins when the Sun appears to rise above and it ends when the Sun appears to settle below the apparent boundary between the Earth and the sky called the horizon. The middle of one of these days is the moment when the Sun it at its highest position above the horizon called noon (from an archaic term meaning "ninth hour") or midday (since it occurs in the middle of the day, halfway between sunrise and sunset).

Night is the time when the Sun isn't visible because it is below the horizon. The day can also be thought of as extending into the night. For most of us alive in the 21st century, the transition from one day to the next takes place when we sleep (or when we probably should be sleeping). When we wake up, a new day is already underway. For people who follow this convention, the end of one day and the beginning of the next occurs when the Sun it at its lowest position below the horizon called midnight (since it occurs in the middle of the night, halfway between the sunset of one day and the sunrise of the next). This solar midnight marks the boundary of what is called the solar day. In many places, a legally agreed upon time called midnight marks the boundary of what is called the civil day. Solar midnight and civil midnight are usually less than an hour apart at most locations.

Even when the Sun isn't visible, we know it's still there. That's because we now know that the Earth is a rotating sphere. Day occurs when we're on the side of the Earth facing the Sun. Noon or midday occurs when the side of the Earth we're on is closest to the Sun for that day. Similarly, night occurs when we're on the side of the Earth facing away from the Sun and midnight occurs when that side is farthest from the Sun for that night. We say the Sun is up in the day and down at night because these are the directions we'd have to head to reach it from a location on the surface of the Earth (or at least the words up and down give the general sense of the vertical component of that direction).

the year

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

How long is 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 CE
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

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 transition9,192,631,770times 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 every9,192,631,770periods 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 the variant known as 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 sidereal time, which is an essential part of pointing telescopes in the right direction. 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.

Leap seconds and other time adjustments (TAI − UTC)
1960s, 1970s, 1980s
year month offset
1961 January 0
1971 * 10
1972 July 11
1973 January 12
1974 January 13
1975 January 14
1976 January 15
1977 January 16
1978 January 17
1979 January 18
1980 January 19
1981 July 20
1982 July 21
1983 July 22
1984   22
1985 July 23
1986   23
1987   23
1988 January 24
1989   24
1990s, 2000s
year month offset
1990 January 25
1991 January 26
1992 July 27
1993 July 28
1994 July 29
1995   29
1996 January 30
1997 July 31
1998   31
1999 January 32
2000   32
2001   32
2002   32
2003   32
2004   32
2005   32
2006 January 33
2007   33
2008   33
2009 January 34
2010s, 2020s
year month offset
2010   34
2011   34
2012 July 35
2013   35
2014   35
2015 July 36
2016   36
2017 January 37
2018   37
2019   37
2020   37
2021   37
2022   37
2023   37
2024   37
* 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
232 s ≈ 136 years

or more precisely…

232 s =  4,294,967,296 s
232 s =  136 years, 37 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 are years ending in double zeroes, like 1800 or 1900, which are not leap years. The exceptions to the exceptions are years divisible by 400, like 2000 or 2400, which are leap years. 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 to the year 2400.

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

My favorite NTP server is at the Time and Frequency Division of the National Institute of Standards and Technology in Boulder, Colorado. This is roughly 2,900 km from my desktop computer in New York City. The signal that I get is delayed by at least…

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

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

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

An expanded version of NTP (NTPv4) that was backward compatible was proposed in 2010 and fully defined in 2016. It added 32 digits to the front to allow for a possible 232 eras of 232 seconds each. That will allow NTP to continue for another 584 billion years.

264 s = 18,446,744,073,709,551,616 s
264 s ≈ 584,554,545,395 years

This expanded version of NTP similarly increased in precision, doubling the binary digits in the fractional portion to 64. This allows for the reporting of times to 54 zeptoseconds of precision. (A zepto of something is 10−21 of that thing.)

2−64 s = 5.421 × 10−20 s
2−64 s ≈ 54 zs

In this amount of time, a photon would travel a little over 16 picometers (pico being 10−12).

s = ct
s = (299,792,458 m/s)(2−64 s)
s = 1.625 × 10−11 m
s ≈ 16¼ pm

For comparison, the diameter of a hydrogen atom is about 100 picometers.

Some events in Network Time Protocol (NTP) Adapted from David Mills, University of Delaware.
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
00:00:00 GMT
0 0
Unix time begins 1 January 1970
00:00:00 GMT
0 2,208,988,800
UTC synced to TAI minus 10 s 1 January 1972
00:00:00 UTC
0 2,272,060,800
last second of second millennium 31 December 1999
23:59:59 UTC
0 3,155,673,599
first second of third millennium 1 January 2000
00:00:00 UTC
0 3,155,673,600
Unix time reaches one billion seconds 9 September 2001
01:46:40 UTC
0 3,208,988,800
time you accessed this page 20 May 2024
18:12:00 UTC
0 3,925,217,520
first NTP era ends 7 February 2036
06:28:15 UTC
0 4,294,967,295
second NTP era begins 7 February 2036
06:28:16 UTC
1 0
fourth millennium begins 1 January 3000
00:00:00 UTC
8 352,930,432
end of final NTP era some day in the year
584,554,547,295 ± 5,000 years
4,294,967,295 4,294,967,295

cosmological timeline

Timeline of the universe