Time (Orders of magnitude)

In the context of time, an order of magnitude is a description of the quantity of a time in respect to comparison between differing magnitudes. In common usage, the scale is usually the base10 or base−10 exponent being applied to an amount, making the order of magnitude 10 times greater or smaller.[1] As the differences are measured in factors of 10, a logarithmic scale is applied. In terms of time, the relationship between the smallest limit of time, the Planck time, and the next order of magnitude larger is 10.

Low order of magnitude - measures by the unit second (s)

Unit (s) Multiple Symbol Definition Comparative examples & common units Orders of magnitude
10−44 1 Planck time tP The time required to travel one Planck length at the speed of light (c) 5.4×10−20 ys = 5.4×10−44 s: One Planck time tP = \sqrt{\hbar G/c^5} ≈ 5.4×10−44 s[2] is the briefest physically meaningful span of time. It is the unit of time in the natural units system known as Planck units. 10−20 ys, 10−19 ys (10−44 s, 10−43 s)
10−24 1 yoctosecond ys[3] Yoctosecond, (yocto- + second), is one septillionth of a second 0.3 ys: mean life of the W and Z bosons.[4][5][lower-alpha 1]
0.5 ys: time for top quark decay, according to the Standard Model.
1 ys: time taken for a quark to emit a gluon.
23 ys: half-life of 7H.		 1 ys and less, 10 ys, 100 ys
10−21 1 zeptosecond zs Zeptosecond, (zepto- + second), is one sextillionth of one second 7 zs: half-life of helium-9's outer neutron in the second nuclear halo.
17 zs: approximate period of electromagnetic radiation at the boundary between gamma rays and X-rays.
300 zs: approximate typical cycle time of X-rays, on the boundary between hard and soft X-rays.
500 zs: current resolution of tools used to measure speed of chemical bonding[6]		 1 zs, 10 zs, 100 zs
10−18 1 attosecond as One quintillionth of one second 12 attoseconds: shortest measured period of time.[7] 1 as, 10 as, 100 as
10−15 1 femtosecond fs One quadrillionth of one second 1 fs: Cycle time for 390 nanometre light; transition from visible light to ultraviolet; light travels 0.3 micrometers (µm).
140 fs: Electrons have localized onto individual bromine atoms 6Å apart after laser dissociation of Br2.[8]		 1 fs, 10 fs, 100 fs
10−12 1 picosecond ps One trillionth of one second 1 ps: half-life of a bottom quark; light travels 0.3 millimeters (mm)
1 ps: lifetime of a transition state
4 ps: Time to execute one machine cycle by an IBM Silicon-Germanium transistor		 1 ps, 10 ps, 100 ps
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)		 1 ns, 10 ns, 100 ns
10−6 1 microsecond µs One millionth of one second 1 µs: Time to execute one machine cycle by an Intel 80186 microprocessor
4–16 µs: Time to execute one machine cycle by a 1960s minicomputer		 1 µs, 10 µs, 100 µs
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[9]
4–8 ms: typical seek time for a computer hard disk
100–400 ms (=0.1–0.4 s): Blink of an eye[10]
18–300 ms (=0.02–0.3 s): Human reflex response to visual stimuli		 1 ms, 10 ms, 100 ms
100 1 second s The duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. 1 s: 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom.[11]

60 s: 1 minute

 1 s, 10 s, 100 s
103 1 kilosecond
(16.7 minutes)		 ks One thousand seconds 3.6 ks: 3600 s or 1 hour
86.4 ks: 86 400 s or 1 day
604.8 ks: 1 week		 103 s, 104 s, 105 s
106 1 megasecond
(11.6 days)		 Ms One million seconds

2.6 Ms: approximately 1 month
31.6 Ms: approximately 1 year ≈ 107.50 s

 106 s, 107 s, 108 s
109 1 gigasecond
(32 years)		 Gs One billion seconds

2.1 Gs: average human life expectancy at birth (2011 estimate)[12]
3.16 Gs: approximately 1 century
31.6 Gs: approximately 1 millennium

 109 s, 1010 s, 1011 s
1012 1 terasecond
(32 000 years)		 Ts One trillion seconds

6 Ts: Time since the appearance of Homo sapiens (approximately)
80 Ts: Time it takes for light to travel from the Andromeda Galaxy to the Milky Way.[13]
160–220 Ts: Time since the divergence of the human and chimpanzee lineages.[14]

 1012 s, 1013 s, 1014 s
1015 1 petasecond
(32 million years)		 Ps One quadrillion seconds 2.1 Ps: (66 million years) Time elapsed since the Cretaceous–Paleogene extinction event, during which all non-avian dinosaurs became extinct. [15]

7.1–7.9 Ps: 1 galactic year (225-250 million years)[16]
143 Ps: the age of the Earth[17][18][19]
144 Ps: the approximate age of the Solar system[20] and the Sun.[21]
430 Ps: the approximate age of the Universe
440 Ps: the half-life of thorium 232

 1015 s, 1016 s, 1017 s
1018 1 exasecond
(32 billion years)		 Es One quintillion seconds 312 Es: Estimated lifespan of a 0.1 solar mass red dwarf star. 1018 s, 1019 s, 1020 s
1021 1 zettasecond
(32 trillion years)		 Zs One sextillion seconds 3 Zs: Estimated duration of Stelliferous Era. 1021 s, 1022 s, 1023 s
1024 1 yottasecond
(32 quadrillion years)		 Ys One septillion seconds 1.6416 Ys: Estimated half-life of the meta-stable 20983Bi radioactive isotope.

6.616×1050 Ys: Time required for a 1 solar mass black hole to evaporate completely due to Hawking radiation, if nothing more falls in.

 1024 s, 1025 s, 1026 s and more

High order of magnitude - measures by the unit year (a)

Unit (a) Multiple Common units
10−50 1 Planck Annum Planck time, the shortest physically meaningful interval of time ≈ 1.71×10−50 a
10−24 1 yoctoannum —
10−21 1 zeptoannum —
10−18 1 attoannum —
10−15 1 femtoannum —
10−12 1 picoannum —
10−9 1 nanoannum 1 second = 3.17 × 10−8 a ≈ 10−7.50 a
10−6 1 microannum 1 minute = 1.90 × 10−6 a
1 hour = 1.40 × 10−4 a
10−3 1 milliannum 1 day = 2.73 × 10−3 a
1 week = 1.91 × 10−2 a
100 1 annum 1 average year = 1 annum (= 365.24219 SI days)
1 decade = 10 a
1 century = 100 a
103 1 kiloannum millennium = 1000 a
106 1 megaannum epoch = 1,000,000 a
109 1 gigaannum aeon = 1,000,000,000 a
13.8 Ga = 1.38×1010 a ≈ 13.8 billion years, the approximate age of the Universe
1012 1 teraannum —
1015 1 petaannum —
1018 1 exaannum 19 exaannum, the estimated half-life of the "stable" 20983Bi radioactive isotope
1021 1 zettaannum —
1024 1 yottaannum —

The pages linked in the right-hand column contain lists of times that are of the same order of magnitude (power of ten). Rows in the table represent increasing powers of a thousand (3 orders of magnitude).

Conversion from year to second is year × 31 557 600 (approximately \pi * 10^7) using the Julian year. Conversion from \log_{10} \mbox{ year} to \log_{10} \mbox{ second} is approximately \log_{10} \mbox{ year} + 7.50. Example conversion; 1 \mbox{ year} =10^0 \mbox{ year} = 10^{0+7.50} \mbox{ seconds } = 10^{0.50 + 7} s = 3.16 * 10^7 s.

See also

Footnotes

Notes
  1. ↑ PDG reports the resonance width (Γ). Here the conversion τ = ħ⁄Γ is given instead.
References
  1. ↑ Brians, Paus. "Orders of Magnitude" (8/4/2013)
  2. ↑ "CODATA Value: Planck time". The NIST Reference on Constants, Units, and Uncertainty. NIST. Retrieved October 1, 2011.
  3. ↑ 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
  4. ↑ C. Amsler et al. (2009): Particle listings – W boson
  5. ↑ C. Amsler et al. (2009): Particle listings – Z boson
  6. ↑ esciencenews (2010)
  7. ↑ "12 attoseconds is the world record for shortest controllable time".
  8. ↑ 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. doi:10.1073/pnas.1014723107. Retrieved 12 July 2015.
  9. ↑ http://www.noteaccess.com/APPROACHES/ArtEd/ChildDev/1cNeurons.htm
  10. ↑ Eric H. Chudler. "Brain Facts and Figures: Sensory Apparatus: Vision". Retrieved October 10, 2011.
  11. ↑ http://tycho.usno.navy.mil/leapsec.html
  12. ↑ CIA - The World Factbook -- Rank Order - Life expectancy at birth
  13. ↑ Ribas, I.; et al. (2005). "First Determination of the Distance and Fundamental Properties of an Eclipsing Binary in the Andromeda Galaxy". Astrophysical Journal Letters 635 (1): L37–L40. arXiv:astro-ph/0511045. Bibcode:2005ApJ...635L..37R. doi:10.1086/499161.
  14. ↑ Patterson N, Richter DJ, Gnerre S, Lander ES, Reich D (June 2006). "Genetic evidence for complex speciation of humans and chimpanzees". Nature 441 (7097): 1103–8. doi:10.1038/nature04789. PMID 16710306.
  15. ↑ Renne, Paul R.; Deino, Alan L.; Hilgen, Frederik J.; Kuiper, Klaudia F.; Mark, Darren F.; Mitchell, William S.; Morgan, Leah E.; Mundil, Roland; Smit, Jan (7 February 2013). "Time Scales of Critical Events Around the Cretaceous-Paleogene Boundary". Science 339 (6120): 684–687. Bibcode:2013Sci...339..684R. doi:10.1126/science.1230492. PMID 23393261.
  16. ↑ Leong, Stacy (2002). "Period of the Sun's Orbit around the Galaxy (Cosmic Year)". The Physics Factbook.
  17. ↑ "Age of the Earth". U.S. Geological Survey. 1997. Retrieved January 10, 2006.
  18. ↑ Dalrymple, G. Brent (2001). "The age of the Earth in the twentieth century: a problem (mostly) solved". Special Publications, Geological Society of London 190 (1): 205–221. Bibcode:2001GSLSP.190..205D. doi:10.1144/GSL.SP.2001.190.01.14.
  19. ↑ Manhesa, Gérard; Allègrea, Claude J.; Dupréa, Bernard; and Hamelin, Bruno (1980). "Lead isotope study of basic-ultrabasic layered complexes: Speculations about the age of the earth and primitive mantle characteristics". Earth and Planetary Science Letters 47 (3): 370–382. Bibcode:1980E&PSL..47..370M. doi:10.1016/0012-821X(80)90024-2.
  20. ↑ Bouvier, Audrey and Meenakshi Wadhwa, "The age of the solar system redefined by the oldest Pb-Pb age of a meteoritic inclusion". Nature Geoscience, Nature Publishing Group, a division of Macmillan Publishers Limited. Published online August 22, 2010, retrieved August 26, 2010, doi:10.1038/NGEO941.
  21. ↑ Bonanno, A.; Schlattl, H.; Paternò, L. (2008). "The age of the Sun and the relativistic corrections in the EOS". Astronomy and Astrophysics 390 (3): 1115–1118. arXiv:astro-ph/0204331. Bibcode:2002A&A...390.1115B. doi:10.1051/0004-6361:20020749.

External links

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