Orders of magnitude (time)

An order of magnitude of time is (usually) a decimal prefix or decimal order-of-magnitude quantity together with a base unit of time, like a microsecond or a million years. In some cases, the order of magnitude may be implied (usually 1), like a "second" or "year". In other cases, the quantity name implies the base unit, like "century". In most cases, the base unit is seconds or years. Prefixes are not usually used with a base unit of years, so we say "a million years", not "a megayear". Clock time and calendar time have duodecimal or sexagesimal orders of magnitude rather than decimal, i.e. a year is 12 months, and a minute is 60 seconds.

The smallest meaningful increment of time is the Planck time, the time light takes to traverse the Planck distance, many decimal orders of magnitude smaller than a second. The largest realized amount of time, given known scientific data, is the age of the universe, about 13.8 billion years - the time since the Big Bang as measured in the cosmic microwave background rest frame. Those amounts of time together span 60 decimal orders of magnitude. Metric prefixes are defined spanning 10−24 to 1024, 48 decimal orders of magnitude which may be used in conjunction with the metric base unit of second. Metric units of time larger than the second are most commonly seen only in a few scientific contexts such as observational astronomy and materials science although this depends on author; for everyday usage and most other scientific contexts the common units of minutes (60 s), hours (3600 s or 3.6 ks), days (86 400 s), weeks, months, and years (of which there are a number of variations) are commonly used. Weeks, months and years are significantly variable units whose length crucially depends on the choice of calendar and is often not regular even with a calendar, e.g. leap years versus regular years in the Gregorian calendar. This makes them problematic for use against a linear and regular time scale such as that defined by the SI since it is not clear as to which version of these units we are to be using. Because of this, in the table below we will not use weeks and months and the year we will use is the Julian year of astronomy, or 365.25 days of 86 400 s exactly, also called an annum and denoted with the symbol a, whose definition is based on the average length of a year of the Julian calendar which had one leap year every and always every 4 years against common years of 365 days each. This unit is used, following the convention of geological science, to form larger units of time by the application of SI prefixes to it at least up to giga-annum, or Ga, equal to 1 000 000 000 a (short scale: one billion years, long scale: one milliard years).

Less than one second

Unit (s) Multiple Symbol Definition Comparative examples & common units
1044 1 Planck time tP Presumed to be the shortest theoretically measurable time interval (but not necessarily the shortest increment of time - see quantum gravity) 10−20 ys = 10−44 s: One Planck time

10−20 ys = 10−44 s: estimate time of the Big Bang
10−20 ys = 10−44 s: the temperature of the universe has arisen 1032 K.

1024 1 yoctosecond ys[1] Yoctosecond, (yocto- + second), is one septillionth of a second 1 ys: estimate lifetime of a top quark.

200 ys: estimate lifetime of an electroweak photon.
300 ys: estimate lifetime of a preon.

1021 1 zeptosecond zs Zeptosecond, (zepto- + second), is one sextillionth of one second 3 zs: estimate lifetime of an up quark.
1018 1 attosecond as One quintillionth of one second 900 as: estimate lifetime of a down quark.
1015 1 femtosecond fs One quadrillionth of one second 550 fs: estimate half-life of hydrogen-7.

600 fs: Light travels 20 micrometres (0.00079 in)
800 fs: estimate lifetime of a muon.

1012 1 picosecond ps One trillionth of one second 12 ps: estimate lifetime of a bottom quark.
109 1 nanosecond ns One billionth of one second 1 ns: Light travels 30 centimetres (12 in)
106 1 microsecond µs One millionth of one second 1 µs: estimate half-life of oxygen-16.

5.28 µs: Light travels 1 mile (1.6 km)

103 1 millisecond ms One thousandth of one second 1 ms: the temperature of the universe has arisen 1018 K.
102 1

centisecond

cs One hundredth of one second 16.667 ms period of a frame at a frame rate of 60 Hz.
101 1

decisecond

ds One tenth of a second 100400 ms (=0.10.4 s): Blink of an eye[2]

One second and longer

In this table, large intervals of time surpassing one second are catalogued in order of the SI multiples of the second as well as their equivalent in common time units of minutes, hours, days, and Julian years.

Unit (s) Multiple Symbol Common units Comparative examples & common units
101 1 decasecond das single seconds

(1 das = 10 s)

60 s: the time it takes a second hand to cycle around a clock face
102 1 hectosecond hs minutes
(1 hs = 1 min 40 s)
500 s: Light travels from Earth to Sun.

900 s: Light travels from Sun to Mars.

103 1 kilosecond ks minutes, hours, days

(1 ks = 16 min 40 s)

3.6 ks (1 h): one hour

86.4 ks (24 h): one day
604.8 ks (7 d): one week

106 1 megasecond Ms weeks to years

(1 Ms = 11 d 13 h 46 min 40 s)

2.419 2 Ms (28 d): length of February, the shortest month of the Gregorian calendar

2.678 4 Ms (31 d): - length of the longest months of the Gregorian calendar
31.557 6 Ms (365.25 d): the orbital period of Earth.

109 1 gigasecond Gs decades, centuries, millennia

(1 Gs = over 31 years and 287 days)

2.52 Gs (80 a): typical human life on Earth from birth to death.

3.16 Gs (100 a): one century
31.6 Gs (1000 a, 1 ka): one millennium
89.4 Gs (2837 a, 2.83 ka): average sea level was arisen one meter.

1012 1 terasecond Ts millennia to geological epochs

(1 Ts = over 31,600 years)

89.4 Ts (2.83 Ma): average sea level was arisen one kilometer.

144 Ts (4.56 Ma): average sea level was arisen one mile.

1015 1 petasecond Ps geological eras, history of Earth and the Universe 7.9 Ps (250 Ma): the orbital period of the Sun around the Milky Way Galaxy.

143 Ps (4.5 Ga): The approximate age of the Earth.
315 Ps (10 Ga): approximate lifetime of the Sun.
435 Ps (13.8 Ga): The approximate age of the Universe

1018 1 exasecond Es future cosmological time All times of this length and beyond are currently theoretical as they surpass the elapsed lifetime of the known universe.

30 Es (1 Ta): average lifetime of a star formation.
300 - 600 Es (10 - 20 Ta): The estimate lifetime of red dwarf stars.

1021 1 zettasecond Zs 2.4 Zs (80 Ta): time can let go of the sun was forming a black dwarf.

3 Zs (100 Ta): the Degenerate Era begins.

1024 and onward 1 yottasecond and beyond Ys and on 1018 Ys (1.5×1034 years) – all protons decayed.

1064 Ys (3.2×1080 years) – the Black Hole Era begins.
3.2×1084 Ys (1×10100 years) – the last supermassive black hole was evaporated by Hawking Radiation.
5.4×1090 Ys (1.7×10106 years) – the Dark Era begins.
3.2×10104 Ys (1.7×10120 years) – the universe was released by the Big Bang, assuming the Big Freeze of the universe.
1.2×101484 Ys (1.8×101500 years) – all neutron stars decayed but iron-56 was detected by protons.
Ys ( years) – a Boltzmann brain could appear.
Ys ( years) – a perfect vacuum was seen in the universe with the Big Crunch.
Ys ( years) – created a new universe with the Big Bang was a quantum tunneling, assuming the inflation of the new universe.

See also

Footnotes

Notes
    References
    1. The American Heritage Dictionary of the English Language: Fourth Edition. 2000. Available at: http://www.bartleby.com/61/21/Y0022100.html. Accessed December 19, 2007. note: abbr. ys or ysec
    2. Eric H. Chudler. "Brain Facts and Figures: Sensory Apparatus: Vision". Retrieved October 10, 2011.
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