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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. Therefore, it is said "a million years" instead of "a megayear". Clock time and calendar time have duodecimal or sexagesimal orders of magnitude rather than decimal, e.g., 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.[1]

The largest realized amount of time, based on 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.[2] Those amounts of time together span 60 decimal orders of magnitude. Metric prefixes are defined spanning 10−30 to 1030, 60 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 the author. For everyday use and most other scientific contexts, the common units of minutes, hours (3,600 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 lengths depend on the choice of calendar and are 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 which version is being used.

Because of this, the table below does not include weeks, months, and years. Instead, the table uses the annum or astronomical Julian year (365.25 days of 86,400 seconds), denoted with the symbol a. Its definition is based on the average length of a year according to the Julian calendar, which has one leap year every four years. According to the geological science convention, this is used 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

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Units of measure less than a second
Multiple
of a
second 		Unit Symbol Definition Comparative examples & common units
10−44 Planck time tP Presumed to be the shortest theoretically measurable time interval
(but not necessarily the shortest increment of time—see quantum gravity) 		10−14 qs: The length of one Planck time (tP = ≈ 5.39×10−44 s)[3] is the briefest physically meaningful span of time. It is the unit of time in the natural units system known as Planck units.
10−30 quectosecond qs Quectosecond, (quecto- + second), is one nonillionth of a second
10−27 rontosecond rs Rontosecond, (ronto- + second), is one octillionth of a second 300 rs: The mean lifetime of W and Z bosons
10−24 yoctosecond ys[4] Yoctosecond, (yocto- + second), is one septillionth of a second 23 ys: The lower estimated bound on the half-life of isotope 7 of hydrogen (Hydrogen-7)
143 ys: The half-life of the Nitrogen-10 isotope of Nitrogen
156 ys: The mean lifetime of a Higgs Boson
10−21 zeptosecond zs Zeptosecond, (zepto- + second), is one sextillionth of one second 1.3 zs: Smallest experimentally controlled time delay in a photon field.[5]
2 zs: The representative cycle time of gamma ray radiation released in the decay of a radioactive atomic nucleus (here as 2 MeV per emitted photon)
4 zs: The cycle time of the zitterbewegung of an electron ()
247 zs: The experimentally-measured travel time of a photon across a hydrogen molecule, "for the average bond length of molecular hydrogen"[6]
10−18 attosecond as One quintillionth of one second 12 as: The best timing control of laser pulses.[7]
43 as: The shortest X-ray laser pulse[8]
53 as: The shortest electron laser pulse[9][10]
10−15 femtosecond fs One quadrillionth of one second 1 fs: The cycle time for ultraviolet light with a wavelength of 300 nanometres; The time it takes light to travel a distance of 0.3 micrometres (μm).
7.58fs: The period of vibration of a hydrogen molecule.
140 fs: The time needed for electrons to have localized onto individual bromine atoms 6 Ångstrom apart after laser dissociation of Br2.[11]
290 fs: The lifetime of a tauon
10−12 picosecond ps One trillionth of one second 1 ps: The mean lifetime of a bottom quark; the time needed for light to travel 0.3 millimetres (mm)
1 ps: The typical lifetime of a transition state one machine cycle by an IBM silicon-germanium transistor
109 ps: The period of the photon corresponding to the hyperfine transition of the ground state of cesium-133, and one 9,192,631,770th of one second by definition
114.6 ps: The time for the fastest overclocked processor as of 2014 to execute one machine cycle.[12]
696 ps: How much more a second lasts far away from Earth's gravity due to the effects of General Relativity
10−9 nanosecond ns One billionth of one second 1 ns: The time needed to execute one machine cycle by a 1 GHz microprocessor
1 ns: The time light takes to travel 30 cm (11.811 in)
10−6 microsecond μs One millionth of one second 1 μs: The time needed to execute one machine cycle by an Intel 80186 microprocessor
2.2 μs: The lifetime of a muon
4–16 μs: The time needed to execute one machine cycle by a 1960s minicomputer
10−3 millisecond ms One thousandth of one second 1 ms: The time for a neuron in the human brain to fire one impulse and return to rest[13]
4–8 ms: The typical seek time for a computer hard disk
10−2 centisecond cs One hundredth of one second 1.6667 cs: The period of a frame at a frame rate of 60 Hz.
2 cs: The cycle time for European 50 Hz AC electricity

10–20 cs (=0.1–0.2 s): The human reflex response to visual stimuli

10−1 decisecond ds One tenth of a second 1–4 ds (=0.1–0.4 s): The length of a single blink of an eye[14]

More than one second

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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.

Units of measure greater than one second
Multiple of a second Unit Symbol Common units Comparative examples and common units
101 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 hectosecond hs minutes
(1 hs = 1 min 40 s = 100 s) 		2 hs (3 min 20 s): The average length of the most popular YouTube videos as of January 2017[15]
5.55 hs (9 min 12 s): The longest videos in the above study

7.1 hs (11 m 50 s): The time for a human walking at average speed of 1.4 m/s to walk 1 kilometre

103 kilosecond ks minutes, hours, days

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

1 ks: The record confinement time for antimatter, specifically antihydrogen, in electrically neutral state as of 2011;[16] 1.477 ks: The longest period in which a person has not taken a breath.

1.8 ks: The time slot for the typical situation comedy on television with advertisements included
2.28 ks: The duration of the Anglo-Zanzibar War, the shortest war in recorded history.
3.6 ks: The length of one hour (h), the 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): The typical length of feature films

35.73 ks: the rotational period of planet Jupiter, fastest planet to rotate

38.0196 ks: rotational period of Saturn, second shortest rotational period

57.996 ks: one day on planet Neptune.

62.064 ks: one day on Uranus.
86.399 ks (23 h 59 min 59 s): The length of one day with a removed leap second on UTC time scale. Such has not yet occurred.
86.4 ks (24 h): The length of 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. 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 megasecond Ms weeks to years

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

1.6416 Ms (19 d): The length of a month of the Baha'i calendar

2.36 Ms (27.32 d): The length of the true month, the orbital period of the Moon
2.4192 Ms (28 d): The length of February, the shortest month of the Gregorian calendar, in common years
2.5056 Ms (29 d): The length of February in leap years
2.592 Ms (30 d): The length of April, June, September, and November in the Gregorian calendar; common interval used in legal agreements and contracts as a proxy for a month
2.6784 Ms (31 d): The length of the longest months of the Gregorian calendar
23 Ms (270 d): The approximate length of typical human gestational period
31.5576 Ms (365.25 d): The length of the Julian year, also called the annum, symbol a.

5.06703168 Ms: The rotational period of Mercury.

7.600544064 Ms: One year on Mercury.

19.41414912 Ms: One year on Venus.

20.9967552 Ms: The rotational period of Venus.
31.55815 Ms (365 d 6 h 9 min 10 s): The length of the true year, the orbital period of the Earth
126.2326 Ms (1461 d 0 h 34 min 40 s): The elected term of the President of the United States or one Olympiad

109 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): The 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)
63.8 Gs: The approximate time since the beginning of the Anno Domini era as of 2019 – 2,019 years, and traditionally the time since the birth of Jesus Christ
194.67 Gs: The approximate lifespan of time capsule Crypt of Civilization, 28 May 1940 – 28 May 8113
363 Gs: (11.5 ka): The time since the beginning of the Holocene epoch
814 Gs: (25.8 ka): The approximate time for the cycle of precession of the Earth's axis

1012 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): The 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 petasecond Ps geological eras, history of Earth and the Universe 2 Ps: The 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): The 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): The 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): The 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): The approximate lifetime of a main-sequence star similar to the Sun.
434.8 Ps (13.787 Ga): The approximate age of the Universe

1018 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 – 20 Ta): The estimated lifetime of low-mass stars (red dwarfs)

1021 zettasecond Zs 3 Zs (+100 Ta): 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 Ta): The entire lifetime of Brahma in Hindu mythology.

1024 yottasecond Ys 600 Ys (2×1019 a): The radioactive half-life of bismuth-209 by alpha decay, one of the slowest-observed radioactive decay processes.
1027 ronnasecond Rs 3.16 Rs (1×1020 a): The estimated time until all stars are ejected from their galaxies or consumed by black holes.

32 Rs (1×1021 a): Highest estimate of the time until all stars are ejected from galaxies or consumed by black holes.

1030 and onward quettasecond and beyond Qs and on 69 Qs (2.2×1024 a): The radioactive half-life of tellurium-128, the longest known half-life of any elemental isotope.

1,340,009 Qs (4.134105×1028 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 stele at the Coba Maya site, believed by archaeologist Linda Schele to be the absolute value for the length of one cycle of the universe[17][18]
2.6×1011 Qs (8.2×1033 years): The smallest possible value for proton half-life consistent with experiment[19]

1023 Qs (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[20]
6×1043 Qs (2×1066 years): The approximate lifespan of a black hole with the mass of the Sun[21]
4×1063 Qs (1.3×1086 years): The approximate lifespan of Sagittarius A*, if uncharged and non-rotating[21]
5.4×1083 Qs (1.7×10106 years): The approximate lifespan of a supermassive black hole with a mass of 20 trillion solar masses[21]
Qs: The scale of an estimated Poincaré recurrence time for the quantum state of a hypothetical box containing an isolated black hole of stellar mass[22] 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.
Qs: The 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.[22]
Qs ( years): The 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.[22]

Other
Multiples Unit Symbol
6×101 seconds 1 minute min
6×101 minutes 1 hour h (hr)
2.4×101 hours 1 day d

See also

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References

[edit]
  1. ^ "Planck Time | COSMOS". astronomy.swin.edu.au. Retrieved 12 October 2021.
  2. ^ "WMAP- Age of the Universe". wmap.gsfc.nasa.gov. Retrieved 12 October 2021.
  3. ^ "CODATA Value: Planck time". The NIST Reference on Constants, Units, and Uncertainty. NIST. Retrieved 1 October 2011.
  4. ^ The American Heritage Dictionary of the English Language: Fourth Edition. 2000. Available at: http://www.bartleby.com/61/21/Y0022100.html Archived 10 March 2008 at the Wayback Machine. Accessed 19 December 2007. note: abbr. ys or ysec
  5. ^ Bocklage, Lars; et al. (29 January 2021). "Coherent control of collective nuclear quantum states via transient magnons". Science Science Advances. 7: eabc3991. doi:10.1126/sciadv.abc3991. PMC 7846183. PMID 33514541. Retrieved 19 April 2023.
  6. ^ Grundmann, Sven; Trabert, Daniel; et al. (16 October 2020). "Zeptosecond birth time delay in molecular photoionization". Science. 370 (6514): 339–341. arXiv:2010.08298. Bibcode:2020Sci...370..339G. doi:10.1126/science.abb9318. PMID 33060359. S2CID 222412229. Retrieved 17 October 2020.
  7. ^ "12 attoseconds is the world record for shortest controllable time". phys.org.
  8. ^ Gaumnitz, Thomas; Jain, Arohi; Pertot, Yoann; Huppert, Martin; Jordan, Inga; Ardana-Lamas, Fernando; Wörner, Hans Jakob (2017). "Streaking of 43-attosecond soft-X-ray pulses generated by a passively CEP-stable mid-infrared driver". Optics Express. 25 (22): 27506–27518. Bibcode:2017OExpr..2527506G. doi:10.1364/OE.25.027506. hdl:20.500.11850/211882. PMID 29092222.
  9. ^ Kim, H. Y.; Garg, M.; Mandal, S.; Seiffert, L.; Fennel, T.; Goulielmakis, E. (January 2023). "Attosecond field emission". Nature. 613 (7945): 662–666. doi:10.1038/s41586-022-05577-1. ISSN 1476-4687. PMC 9876796.
  10. ^ "Attosecond electron pulses are claimed as shortest ever". Physics World. 17 February 2023. Retrieved 17 February 2023.
  11. ^ Li, Wen; et al. (23 November 2010). "Visualizing electron rearrangement in space and time during the transition from a molecule to atoms". PNAS. 107 (47): 20219–20222. Bibcode:2010PNAS..10720219L. doi:10.1073/pnas.1014723107. PMC 2996685. PMID 21059945.
  12. ^ Chiappetta, Marco (23 September 2011). "AMD Breaks 8 GHz Overclock with Upcoming FX Processor, Sets World Record. The record has been surpassed with 8794 MHz of overclocking with AMD FX 8350". HotHardware. Archived from the original on 10 March 2015. Retrieved 28 April 2012.
  13. ^ "Notebook". www.noteaccess.com.
  14. ^ Eric H. Chudler. "Brain Facts and Figures: Sensory Apparatus: Vision". Retrieved 10 October 2011.
  15. ^ "YouTube Statistics and Your Best Video Length for Different Videos". Video Production Washington DC - MiniMatters. 11 March 2014.
  16. ^ Alpha Collaboration; Andresen, G. B.; Ashkezari, M. D.; Baquero-Ruiz, M.; Bertsche, W.; Bowe, P. D.; Butler, E.; Cesar, C. L.; Charlton, M.; Deller, A.; Eriksson, S.; Fajans, J.; Friesen, T.; Fujiwara, M. C.; Gill, D. R.; Gutierrez, A.; Hangst, J. S.; Hardy, W. N.; Hayano, R. S.; Hayden, M. E.; Humphries, A. J.; Hydomako, R.; Jonsell, S.; Kemp, S. L.; Kurchaninov, L.; Madsen, N.; Menary, S.; Nolan, P.; Olchanski, K.; et al. (5 June 2011). "Confinement of antihydrogen for 1,000 seconds". Nature Physics. 7 (7): 558–564. arXiv:1104.4982. Bibcode:2011NatPh...7..558A. doi:10.1038/nphys2025. S2CID 17151882.
  17. ^ Falk, Dan (2013). In search of time the science of a curious dimension. New York: St. Martin's Press. ISBN 978-1429987868.
  18. ^ G. Jeffrey MacDonald "Does Maya calendar predict 2012 apocalypse?" USA Today 27 March 2007.
  19. ^ 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. S2CID 32385768.
  20. ^ Adams, Fred C.; Laughlin, Gregory (1 April 1997). "A dying universe: the long-term fate and evolution of astrophysical objects". Reviews of Modern Physics. 69 (2): 337–372. arXiv:astro-ph/9701131. Bibcode:1997RvMP...69..337A. doi:10.1103/revmodphys.69.337. ISSN 0034-6861. S2CID 12173790.
  21. ^ a b c Page, Don N. (15 January 1976). "Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole". Physical Review D. 13 (2). American Physical Society (APS): 198–206. Bibcode:1976PhRvD..13..198P. doi:10.1103/physrevd.13.198. ISSN 0556-2821. See in particular equation (27).
  22. ^ a b c Page, Don N. (25 November 1994). "Information Loss in Black Holes and/or Conscious Beings?". In Fulling, S.A. (ed.). 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. S2CID 18633007.
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