Orders of magnitude (time)

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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[edit]

Unit (s) Multiple Symbol Definition Comparative examples & common units
yoctosecond 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 tP = 5.39×10−44 s[1] is the briefest physically meaningful span of time. It is the unit of time in the natural units system known as Planck units.
10−24 1 yoctosecond ys[2] Yoctosecond, (yocto- + second), is one septillionth of a second 0.3 ys: mean lifetime of W and Z bosons
156 ys: mean lifetime of a Higgs Boson
10−21 1 zeptosecond zs Zeptosecond, (zepto- + second), is one sextillionth of one second 2 zs: representative cycle time of gamma ray radiation released in the decay of a radioactive atomic nucleus (here as 2 MeV per emitted photon)
10−18 1 attosecond as One quintillionth of one second 12 attoseconds: best timing control of laser pulses.[3]
10−15 1 femtosecond fs One quadrillionth of one second 1 fs: Cycle time for 300 nanometre light; ultraviolet light; light travels 0.3 micrometres (µm).
140 fs: Electrons have localized onto individual bromine atoms 6Å apart after laser dissociation of Br2.[4]
10−12 1 picosecond ps One trillionth of one second 1 ps: mean lifetime of a bottom quark; light travels 0.3 millimeters (mm)
1 ps: typical lifetime of a transition state
4 ps: Time to execute one machine cycle by an IBM Silicon-Germanium transistor
10−9 1 nanosecond ns One billionth of one second 1 ns: Time to execute one machine cycle by a 1 GHz microprocessor
1 ns: Light travels 30 centimetres (12 in)
10−6 1 microsecond µs One millionth of one second 1 µs: Time to execute one machine cycle by an Intel 80186 microprocessor
2.2 µs: Lifetime of a muon
4–16 µs: Time to execute one machine cycle by a 1960s minicomputer
10−3 1 millisecond ms One thousandth of one second 1 ms: time for a neuron in human brain to fire one impulse and return to rest[5]
4–8 ms: typical seek time for a computer hard disk
10−2 1

centisecond

cs One hundredth of one second 18–30 cs (=0.02–0.3 s): Human reflex response to visual stimuli

1.6667 cs period of a frame at a frame rate of 60 Hz.
2 cs: cycle time for European 50 Hz AC electricity

10−1 1

decisecond

ds One tenth of a second 1–4 ds (=0.1–0.4 s): Blink of an eye[6]

One second and longer[edit]

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)

6 das: one minute (min), the time it takes a second hand to cycle around a clock face
102 1 hectosecond hs minutes
(1 hs = 1 min 40 s = 100 s)
2.6 hs (4 min 20 s): average length of the most popular YouTube videos as of January 2017[7]
5.55 hs (9 min 12 s): longest videos in above study

7.1 hs: time for a human walking at average speed of 1.4 m/s to walk 1 kilometre

103 1 kilosecond ks minutes, hours, days

(1 ks = 16 min 40 s = 1,000 s)

1 ks: record confinement time for antimatter, specifically antihydrogen, in electrically neutral state as of 2011[8]

3.6 ks: one hour (h), time for the minute hand of a clock to cycle once around the face, approximately 1/24 of one mean solar day
7.2 ks (2 h): typical length of feature films
86.399 ks (23 h 59 min 59 s): one day with a removed leap second on UTC time scale. Such has not yet occurred.
86.4 ks (24 h): one day of Earth by standard. More exactly, the mean solar day is 86.400 002 ks due to tidal braking, and increasing at the rate of approximately 2 ms/century; to correct for this time standards like UTC use leap seconds with the interval described as "a day" on them being most often 86.4 ks exactly by definition but occasionally one second more or less so that every day contains a whole number of seconds while preserving alignment with astronomical time. The hour hand of an analogue clock will typically cycle twice around the dial in this period as most analogue clocks are 12 hour, less common are analogue 24-hour clocks in which it cycles around once.
86.401 ks (24 h 0 min 1 s): one day with an added leap second on UTC time scale. Note that while this is strictly 24 hours and 1 second in conventional units, a digital clock of suitable capability level will most often display the leap second as 23:59:60 and not 24:00:00 before rolling over to 00:00:00 the next day, as though the last "minute" of the day were crammed with 61 seconds and not 60, and similarly the last "hour" 3601 s instead of 3600.
88.775 ks (24 h 39 min 35 s): one sol of Mars
604.8 ks (7 d): one week of the Gregorian calendar

106 1 megasecond Ms weeks to years

(1 Ms = 11 d 13 h 46 min 40 s = 1,000,000 s)

1.641 6 Ms (19 d): length of a "month" of the Baha'i calendar

2.36 Ms (27.32 d): length of the true month, the orbital period of the Moon
2.419 2 Ms (28 d): length of February, the shortest month of the Gregorian calendar
2.592 Ms (30 d): 30 days, a common interval used in legal agreements and contracts as a proxy for a month
2.678 4 Ms (31 d): - length of the longest months of the Gregorian calendar
23 Ms (270 d): approximate length of typical human gestational period
31.557 6 Ms (365.25 d): length of the Julian year, also called the annum, symbol a.
31.558 15 Ms (365 d 6 h 9 min 10 s): length of the true year, the orbital period of the Earth

109 1 gigasecond Gs decades, centuries, millennia

(1 Gs = over 31 years and 287 days = 1,000,000,000 s)

1.5 Gs: UNIX time as of Jul 14 02:40:00 UTC 2017. UNIX time being the number of seconds since 1970-01-01T00:00:00Z ignoring leap seconds.

2.5 Gs: (79 a): typical human life expectancy in the developed world
3.16 Gs: (100 a): one century
31.6 Gs: (1000 a, 1 ka): one millennium, also called a kilo-annum (ka)
63.7 Gs: approximate time since the beginning of the Anno Domini era as of 2018 - 2,018 years, and traditionally the time since the birth of Jesus Christ
194.67 Gs: Approximate lifespan of time capsule Crypt of Civilization, 28 May 1940 - 28 May 8113
363 Gs: (11.5 ka): time since the beginning of the Holocene epoch

1012 1 terasecond Ts millennia to geological epochs

(1 Ts = over 31,600 years = 1,000,000,000,000 s)

3.1 Ts (100 ka): approximate length of a glacial period of the current Quaternary glaciation epoch

31.6 Ts (1000 ka, 1 Ma): one mega-annum (Ma), or one million years
79 Ts (2.5 Ma): approximate time since earliest hominids of genus Australopithecus
130 Ts (4 Ma): the typical lifetime of a biological species on Earth
137 Ts (4.32 Ma): the length of the mythic unit of mahayuga, the Great Age, in Hindu mythology.

1015 1 petasecond Ps geological eras, history of Earth and the Universe 2 Ps: approximate time since the Cretaceous-Paleogene extinction event, believed to be caused by the impact of a large asteroid into Chicxulub in modern-day Mexico. This extinction was one of the largest in Earth's history and marked the demise of most dinosaurs, with the only known exception being the ancestors of today's birds.

7.9 Ps (250 Ma): approximate time since the Permian-Triassic extinction event, the actually largest known mass extinction in Earth history which wiped out 95% of all extant species and believed to have been caused by the consequences of massive long-term volcanic eruptions in the area of the Siberian Traps. Also, the approximate time to the supercontinent of Pangaea. Also, the length of one galactic year or cosmic year, the time required for the Sun to complete one orbit around the Milky Way Galaxy.
16 Ps (510 Ma): approximate time since the Cambrian explosion, a massive evolutionary diversification of life which led to the appearance of most existing multicellular organisms and the replacement of the previous Ediacaran biota.
22 Ps (704 Ma): approximate half-life of the uranium isotope 235U.
31.6 Ps (1000 Ma, 1 Ga): one giga-annum (Ga), one billion years, the largest fixed time unit used in the standard geological time scale, approximately the order of magnitude of an eon, the largest division of geological time.
+1 Ga: The estimated remaining habitable lifetime of Earth, according to some models. At this point in time the stellar evolution of the Sun will have increased its luminosity to the point that enough energy will be reaching the Earth to cause the evaporation of the oceans and their loss into space (due to the uv flux from the Sun at the top of the atmosphere dissociating the molecules), making it impossible for any life to continue.
136 Ps (4.32 Ga): The length of the legendary unit kalpa in Hindu mythology, or one day (but not including the following night) of the life of Brahma.
143 Ps (4.5 Ga): The age of the Earth by our best estimates. Also the approximate half-life of the uranium isotope 238U.
315 Ps (10 Ga): approximate lifetime of a main-sequence star similar to our 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.

1.08 Es (+34 Ga): time to the Big Rip according to some models, but this is not favored by existing data. This is one possible scenario for the ultimate fate of the Universe. Under this scenario, dark energy increases in strength and power in a feedback loop that eventually results in the tearing apart of all matter down to subatomic scale due to the rapidly increasing negative pressure thereupon
300 - 600 Es (10 000 - 20 000 Ga): The estimate lifetime of low-mass stars (red dwarfs)

1021 1 zettasecond Zs 3 Zs (+100 000 Ga): The remaining time until the end of Stelliferous Era of the universe under the heat death scenario for the ultimate fate of the Universe which is the most commonly-accepted model in the current scientific community. This is marked by the cooling-off of the last low-mass dwarf star to a black dwarf. After this time has elapsed, the Degenerate Era begins.

9.85 Zs (311 000 Ga): The entire lifetime of Brahma in Hindu mythology.

1024 and onward 1 yottasecond and beyond Ys and on 600 Ys (9 × 1018 a): The radioactive half-life of bismuth-209 by alpha decay, one of the slowest-observed radioactive decay processes.

1.310 019 × 1012 Ys (4.134 105 × 1028 years) – The time period equivalent to the value of 13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.13.0.0.0.0 in the Mesoamerican Long Count, a date discovered on a stela at the Coba Maya site, believed by archaeologist Linda Schele to be the absolute value for the length of one cycle of the universe[9][10]
2.6 × 1017 Ys (8.2 × 1033 years) – the smallest possible value for proton half-life consistent with experiment[11]

1029 Ys (3.2×1045 years) – the largest possible value for the proton half-life, assuming that the Big Bang was inflationary and that the same process that made baryons predominate over antibaryons in the early Universe also makes protons decay[12]
6 × 1053 Ys (2×1066 years) – approximate lifespan of a black hole with the mass of the Sun[13]
5.4×1093 Ys (1.7×10106 years) – approximate lifespan of a supermassive black hole with a mass of 20 trillion solar masses[13]
Ys ( years) – Scale of an estimated Poincaré recurrence time for the quantum state of a hypothetical box containing an isolated black hole of stellar mass[14] This time assumes a statistical model subject to Poincaré recurrence. A much simplified way of thinking about this time is that in a model in which history repeats itself arbitrarily many times due to properties of statistical mechanics, this is the time scale when it will first be somewhat similar (for a reasonable choice of "similar") to its current state again.
Ys ( years) – Scale of an estimated Poincaré recurrence time for the quantum state of a hypothetical box containing a black hole with the mass of the observable Universe.[14]
Ys ( years) – Scale of an estimated Poincaré recurrence time for the quantum state of a hypothetical box containing a black hole with the estimated mass of the entire Universe, observable or not, assuming Linde's chaotic inflationary model with an inflaton whose mass is 10−6 Planck masses.[14]

See also[edit]

Footnotes[edit]

Notes
References
  1. ^ "CODATA Value: Planck time". The NIST Reference on Constants, Units, and Uncertainty. NIST. Retrieved October 1, 2011.
  2. ^ 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
  3. ^ "12 attoseconds is the world record for shortest controllable time".
  4. ^ Li, Wen; et al. (November 23, 2010). "Visualizing electron rearrangement in space and timeduring the transition from a molecule to atoms". PNAS. 107 (47): 20219–20222. Bibcode:2010PNAS..10720219L. doi:10.1073/pnas.1014723107. PMC 2996685. PMID 21059945. Retrieved 12 July 2015.
  5. ^ http://www.noteaccess.com/APPROACHES/ArtEd/ChildDev/1cNeurons.htm
  6. ^ Eric H. Chudler. "Brain Facts and Figures: Sensory Apparatus: Vision". Retrieved October 10, 2011.
  7. ^ https://www.minimatters.com/youtube-best-video-length/
  8. ^ "Confinement of antihydrogen for 1,000 seconds". Nature Physics. 7: 558–564. 5 June 2011. arXiv:1104.4982. Bibcode:2011NatPh...7..558A. doi:10.1038/nphys2025. Archived from the original on 6 June 2011. Retrieved 12 May 2012.
  9. ^ Falk, Dan (2013). In search of time the science of a curious dimension. New York: St. Martin's Press. ISBN 1429987863.
  10. ^ G. Jeffrey MacDonald "Does Maya calendar predict 2012 apocalypse?" USA Today 3/27/2007.
  11. ^ Nishino, H. et al. (Super-K Collaboration) (2009). "Search for Proton Decay via
    p+

    e+

    π0
    and
    p+

    μ+

    π0
    in a Large Water Cherenkov Detector". Physical Review Letters. 102 (14): 141801. arXiv:0903.0676. Bibcode:2009PhRvL.102n1801N. doi:10.1103/PhysRevLett.102.141801. PMID 19392425.
  12. ^ A Dying Universe: the Long-term Fate and Evolution of Astrophysical Objects, Adams, Fred C. and Laughlin, Gregory, Reviews of Modern Physics 69, #2 (April 1997), pp. 337–372. Bibcode1997RvMP...69..337A. doi:10.1103/RevModPhys.69.337.
  13. ^ a b Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole, Don N. Page, Physical Review D 13 (1976), pp. 198–206. doi:10.1103/PhysRevD.13.198. See in particular equation (27).
  14. ^ a b c Page, Don N. (1995). "Information Loss in Black Holes and/or Conscious Beings?". In Fulling, S.A. Heat Kernel Techniques and Quantum Gravity. Discourses in Mathematics and its Applications. Texas A&M University. p. 461. arXiv:hep-th/9411193. Bibcode:1994hep.th...11193P. ISBN 978-0-9630728-3-2.

External links[edit]