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| {{About|the astronomical phenomenon}}
| | Hi there, I am Andrew Berryhill. Ohio is where her home is. The favorite pastime for him and his kids is to perform lacross and he would never give it up. Distributing manufacturing has been his occupation for some time.<br><br>my site psychic phone readings ([http://www.tv-world.us/users/EGqq www.tv-world.us]) |
| {{cosmology}}
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| [[File:Redshift.png|thumb|upright|[[spectral line|Absorption lines]] in the [[visible spectrum|optical spectrum]] of a [[supercluster]] of distant galaxies (right), as compared to absorption lines in the optical spectrum of the Sun (left). Arrows indicate redshift. Wavelength increases up towards the red and beyond (frequency decreases).]]
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| In [[physics]], '''redshift''' happens when [[light]] or other [[electromagnetic radiation]] from an object moving away from the [[Observer (physics)|observer]] is increased in [[wavelength]], or shifted to the red end of the [[electromagnetic spectrum|spectrum]]. In general, whether or not the radiation is within the [[visible spectrum]], "redder" means an increase in [[wavelength]] – equivalent to a lower [[frequency]] and a lower [[photon]] energy, in accordance with, respectively, the [[Wave theory of light|wave]] and [[Light#Quantum theory|quantum]] theories of light.
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| Redshifts are an example of the [[Doppler effect]], familiar in the change in the apparent [[Pitch (music)|pitches]] of sirens and [[frequency]] of the [[sound|sound waves]] emitted by speeding vehicles. A redshift occurs whenever a light source moves away from an observer. [[Cosmology|Cosmological]] redshift is seen due to the [[Metric expansion of space|expansion of the universe]], and sufficiently distant light sources (generally more than a few million [[Light-year|light years]] away) show redshift corresponding to the rate of increase in their distance from Earth. Finally, [[gravitational redshift]]s are a [[general relativity|relativistic]] effect observed in electromagnetic radiation moving out of [[gravitational field]]s. Conversely, a ''decrease'' in wavelength is called [[blueshift]] and is generally seen when a light-emitting object moves toward an observer or when electromagnetic radiation moves into a gravitational field.
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| Although knowledge of redshifts and blueshifts has been applied to develop several terrestrial technologies (such as [[Doppler radar]] and [[radar gun]]s),<ref>See Feynman, Leighton and Sands (1989) or any introductory undergraduate (and many high school) [[Physics/Further reading|physics textbooks]]. See Taylor (1992) for a relativistic discussion.</ref> redshifts are most famously seen in the [[astronomical spectroscopy|spectroscopic]] observations of astronomical objects.<ref name=basicastronomy>See Binney and Merrifeld (1998), Carroll and Ostlie (1996), Kutner (2003) for applications in astronomy.</ref>
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| A [[special relativity|special relativistic]] [[#Redshift formulae|redshift formula]] (and its [[classical physics|classical approximation]]) can be used to calculate the redshift of a nearby object when [[spacetime]] is [[Minkowski space|flat]]. However, in many contexts, such as [[black hole]]s and [[Big Bang cosmology]], redshifts must be calculated using [[general relativity]].<ref>See Misner, Thorne and Wheeler (1973) and Weinberg (1971) or any of the [[physical cosmology#Textbooks|physical cosmology textbooks]]</ref> Special relativistic, gravitational, and cosmological redshifts can be understood under the umbrella of [[Frame of reference|frame transformation laws]]. There exist other physical processes that can lead to a shift in the frequency of electromagnetic radiation, including [[scattering]] and [[physical optics|optical effects]]; however, the resulting changes are distinguishable from true redshift and are not generally referred to as such (see section on [[#Effects due to physical optics or radiative transfer|physical optics and radiative transfer]]).
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| [[Image:Redshift blueshift.svg|thumb|Redshift and blueshift]]
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| ==History==
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| The history of the subject began with the development in the 19th century of [[wave|wave mechanics]] and the exploration of phenomena associated with the [[Doppler effect]]. The effect is named after [[Christian Doppler]], who offered the first known physical explanation for the phenomenon in 1842.<ref>
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| {{cite journal
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| |author=Doppler, Christian
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| |year=1846
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| |title=Beiträge zur fixsternenkunde
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| |publisher=Prag, Druck von G. Haase sohne<!--Prag = Prague? -->
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| |doi=
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| |bibcode=1846QB815.D69......
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| |volume=69
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| |journal=Prag
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| }}</ref> The hypothesis was tested and confirmed for [[sound wave]]s by the [[Netherlands|Dutch]] scientist [[C.H.D. Buys Ballot|Christophorus Buys Ballot]] in 1845.<ref>
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| {{cite book
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| |author=Maulik, Dev
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| |chapter=Doppler Sonography: A Brief History
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| |chapterurl=http://books.google.com/books?id=HedeGJms0n4C&vid=ISBN3540230882&dq=%22Buys+Ballot%22&pg=PA3&lpg=PA3&q=%22Ballot%22
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| |editor=Maulik, Dev; Zalud, Ivica
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| |year=2005
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| |title=Doppler Ultrasound in Obstetrics And Gynecology
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| |url= http://www.springer.com/west/home/medicine/gynecology?SGWID=4-10066-22-46625046-0
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| |isbn=978-3-540-23088-5
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| }}</ref> Doppler correctly predicted that the phenomenon should apply to all [[wave]]s, and in particular suggested that the varying [[color]]s of [[star]]s could be attributed to their motion with respect to the Earth.<ref>
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| {{cite web
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| |author=O'Connor, John J.; Roberston, Edmund F.
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| |year=1998
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| |url=http://www-history.mcs.st-andrews.ac.uk/Biographies/Doppler.html
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| |title=Christian Andreas Doppler
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| |work=[[MacTutor History of Mathematics archive]]
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| |publisher=[[University of St Andrews]]
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| }}</ref> Before this was verified, however, it was found that stellar colors were primarily due to a star's [[color temperature|temperature]], not motion. Only later was Doppler vindicated by verified redshift observations.
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| The first Doppler redshift was described by French physicist [[Hippolyte Fizeau]] in 1848, who pointed to the shift in [[spectral line]]s seen in stars as being due to the Doppler effect. The effect is sometimes called the "Doppler–Fizeau effect". In 1868, British astronomer [[William Huggins]] was the first to determine the velocity of a star moving away from the Earth by this method.<ref name=Huggins>
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| {{cite journal
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| |author=Huggins, William
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| |year=1868
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| |title=Further Observations on the Spectra of Some of the Stars and Nebulae, with an Attempt to Determine Therefrom Whether These Bodies are Moving towards or from the Earth, Also Observations on the Spectra of the Sun and of Comet II
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| |journal=[[Philosophical Transactions of the Royal Society of London]]
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| |volume= 158 |pages=529–564
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| |bibcode=1868RSPT..158..529H
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| |doi=10.1098/rstl.1868.0022
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| }}</ref> In 1871, optical redshift was confirmed when the phenomenon was observed in [[Fraunhofer lines]] using solar rotation, about 0.1 Å in the red.<ref>
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| {{cite journal
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| |author=Reber, G.
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| |year=1995
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| |title=Intergalactic Plasma
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| |journal=[[Astrophysics and Space Science]]
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| |volume=227
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| |issue=1–2 |pages=93–96
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| |doi=10.1007/BF00678069
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| |bibcode=1995Ap&SS.227...93R
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| }}</ref>
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| In 1887, Vogel and Scheiner discovered the ''annual Doppler effect'', the yearly change in the Doppler shift of stars located near the ecliptic due to the orbital velocity of the Earth.<ref>{{cite book|last=Pannekoek|first=A|title=A History of Astronomy |year=1961|publisher=Dover|page=451|isbn=0-486-65994-1}}</ref> In 1901, [[Aristarkh Apollonovich Belopolsky|Aristarkh Belopolsky]] verified optical redshift in the laboratory using a system of rotating mirrors.<ref>
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| {{cite journal
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| |author=Bélopolsky, A.
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| |year=1901
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| |bibcode=1901ApJ....13...15B
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| |title=On an Apparatus for the Laboratory Demonstration of the Doppler-Fizeau Principle
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| |journal=[[Astrophysical Journal]]
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| |volume=13 |page=15
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| |doi=10.1086/140786
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| }}</ref>
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| The earliest occurrence of the term "red-shift" in print (in this hyphenated form), appears to be by American astronomer [[Walter S. Adams]] in 1908, where he mentions "Two methods of investigating that nature of the nebular red-shift".<ref>
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| {{cite journal
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| |author=Adams, Walter S.
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| |year=1908
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| |title=Preliminary catalogue of lines affected in sun-spots
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| |place=Contributions from the Solar Observatory of the Carnegie Institution of Washington
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| |publisher=[[Carnegie Institution of Washington]]
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| |volume=22 |pages=1–21
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| |bibcode=1908CMWCI..22....1A
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| |journal=Contributions from the Mount Wilson Observatory / Carnegie Institution of Washington
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| }} Reprinted in {{cite journal|doi=10.1086/141524|last1=Adams|first1=Walter S.|title=Preliminary Catalogue of Lines Affected in Sun-Spots Region λ 4000 TO λ 4500|year=1908|journal=[[Astrophysical Journal]] |volume=27 |page=45|bibcode=1908ApJ....27...45A}}</ref> The word doesn't appear unhyphenated until about 1934 by [[Willem de Sitter]], perhaps indicating that up to that point its German equivalent, ''Rotverschiebung'', was more commonly used.<ref>
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| {{cite journal
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| |author=de Sitter, W.
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| |year=1934
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| |title=On distance, magnitude, and related quantities in an expanding universe
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| |journal=[[Bulletin of the Astronomical Institutes of the Netherlands]]
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| |volume=7 |page=205
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| |doi=
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| |bibcode=1934BAN.....7..205D
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| |quote=It thus becomes urgent to investigate the effect of the redshift and of the metric of the universe on the apparent magnitude and observed numbers of nebulae of given magnitude
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| }}</ref>
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| Beginning with observations in 1912, [[Vesto Slipher]] discovered that most [[Spiral galaxy|spiral galaxies]], then mostly thought to be [[Spiral_galaxy#Spiral_nebula|spiral nebulae]], had considerable redshifts. Slipher first reports on his measurement in the inaugural volume of the ''[[Lowell Observatory Bulletin]]''.<ref>
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| {{cite journal
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| |author=Slipher, Vesto
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| |year=1912
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| |title=The radial velocity of the Andromeda Nebula
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| |journal=[[Lowell Observatory Bulletin]]
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| |volume=1 |pages=2.56–2.57
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| |bibcode=1913LowOB...1b..56S
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| |quote=The magnitude of this velocity, which is the greatest hitherto observed, raises the question whether the velocity-like displacement might not be due to some other cause, but I believe we have at present no other interpretation for it
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| }}</ref> Three years later, he wrote a review in the journal ''[[Popular Astronomy (US magazine)|Popular Astronomy]]''.<ref>
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| {{cite journal
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| |author=Slipher, Vesto
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| |year=1915
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| |title=Spectrographic Observations of Nebulae
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| |journal=[[Popular Astronomy (US magazine)|Popular Astronomy]]
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| |volume=23 |pages=21–24
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| |bibcode=1915PA.....23...21S
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| }}</ref> In it he states, "[...] the early discovery that the great Andromeda spiral had the quite exceptional velocity of –300 km(/s) showed the means then available, capable of investigating not only the spectra of the spirals but their velocities as well."<ref>
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| {{cite journal |author=Slipher, Vesto |authorlink=Vesto Slipher |year=1915 |title=Spectrographic Observations of Nebulae |journal=[[Popular Astronomy (US magazine)|Popular Astronomy]] |volume=23 |page=22 |bibcode=1915PA.....23...21S}}</ref> Slipher reported the velocities for 15 spiral nebulae spread across the entire [[celestial sphere]], all but three having observable "positive" (that is recessional) velocities. Subsequently, [[Edwin Hubble]] discovered an approximate relationship between the redshifts of such "nebulae" and the [[distance]]s to them with the formulation of his eponymous [[Hubble's law]].<ref>
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| {{cite journal
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| |doi=10.1073/pnas.15.3.168
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| |author=Hubble, Edwin
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| |year=1929
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| |bibcode=1929PNAS...15..168H
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| |title=A Relation between Distance and Radial Velocity among Extra-Galactic Nebulae
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| |url=http://www.pnas.org/cgi/reprint/15/3/168
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| |journal=[[Proceedings of the National Academy of Sciences of the United States of America]]
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| |volume=15 |issue=3 |pages=168–173
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| |pmid=16577160
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| |pmc=522427
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| }}</ref> These observations corroborated [[Alexander Friedmann|Alexander Friedmann's]] 1922 work, in which he derived the famous [[Friedmann equations]].<ref>
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| {{cite journal
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| |author=Friedman, A. A.
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| |year=1922
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| |title=Über die Krümmung des Raumes
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| |journal=[[Zeitschrift fur Physik]]
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| |volume=10
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| |issue=1 |pages=377–386
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| |doi=10.1007/BF01332580
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| |bibcode = 1922ZPhy...10..377F }} English translation in {{cite journal |doi=10.1023/A:1026751225741 |last1=Friedman |year=1999 |first1=A. |journal=[[General Relativity and Gravitation]] |volume=31 |issue=12 |pages=1991–2000 |bibcode=1999GReGr..31.1991F}})</ref> They are today considered strong evidence for an [[expanding universe]] and the [[Big Bang]] theory.<ref name=Eddington>This was recognized early on by physicists and astronomers working in cosmology in the 1930s. The earliest layman publication describing the details of this correspondence is {{cite book
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| |author=Eddington, Arthur
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| |year=1933
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| |title=The Expanding Universe: Astronomy's 'Great Debate', 1900–1931
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| |publisher=[[Cambridge University Press]]
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| }} (Reprint: ISBN 978-0-521-34976-5)</ref>
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| ==Measurement, characterization, and interpretation==
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| [[File:High-redshift galaxy candidates in the Hubble Ultra Deep Field 2012.jpg|thumb|High-redshift galaxy candidates in the [[Hubble Ultra Deep Field]] 2012.<ref>{{cite news|title=Hubble census finds galaxies at redshifts 9 to 12|url=http://www.spacetelescope.org/news/heic1219/|accessdate=13 December 2012|newspaper=ESA/Hubble Press Release}}</ref> ]]
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| The [[visible spectrum|spectrum]] of light that comes from a single source (see idealized spectrum illustration top-right) can be measured. To determine the redshift, one searches for features in the spectrum such as [[spectral line|absorption lines]], [[spectral line|emission lines]], or other variations in [[Light intensity (disambiguation)|light intensity]]<!--Intentionally ambiguous-->. If found, these features can be compared with known features in the spectrum of various chemical compounds found in experiments where that compound is located on earth. A very common [[chemical element|atomic element]] in space is [[hydrogen]]. The spectrum of originally featureless light shone through hydrogen will show a [[hydrogen spectrum|signature spectrum]] specific to hydrogen that has features at regular intervals. If restricted to absorption lines it would look similar to the illustration (top right). If the same pattern of intervals is seen in an observed spectrum from a distant source but occurring at shifted wavelengths, it can be identified as hydrogen too. If the same spectral line is identified in both spectra but at different wavelengths then the redshift can be calculated using the table below. Determining the redshift of an object in this way requires a frequency- or wavelength-range. In order to calculate the redshift one has to know the wavelength of the emitted light in the rest frame of the source, in other words, the wavelength that would be measured by an observer located adjacent to and comoving with the source. Since in astronomical applications this measurement cannot be done directly, because that would require travelling to the distant star of interest, the method using spectral lines described here is used instead. Redshifts cannot be calculated by looking at unidentified features whose rest-frame frequency is unknown, or with a spectrum that is featureless or [[white noise]] (random fluctuations in a spectrum).<ref>See, for example, this 25 May 2004 [http://heasarc.gsfc.nasa.gov/docs/swift/about_swift/redshift.html press release] from [[NASA]]'s [[Swift Gamma-Ray Burst Mission|Swift]] [[space telescope]] that is researching [[gamma-ray burst]]s: "Measurements of the gamma-ray spectra obtained during the main outburst of the GRB have found little value as redshift indicators, due to the lack of well-defined features. However, optical observations of GRB afterglows have produced spectra with identifiable lines, leading to precise redshift measurements."</ref>
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| Redshift (and blueshift) may be characterized by the relative difference between the observed and emitted wavelengths (or frequency) of an object. In astronomy, it is customary to refer to this change using a [[dimensionless]] quantity called ''z''. If ''λ'' represents wavelength and ''f'' represents frequency (note, ''λf'' = ''c'' where ''c'' is the [[speed of light]]), then ''z'' is defined by the equations:<ref>See [http://ned.ipac.caltech.edu/help/zdef.html] for a tutorial on how to define and interpret large redshift measurements.</ref>
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| {| class="wikitable" style="margin:auto;"
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| |+ '''Calculation of redshift, <math>z</math>'''
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| ! '''Based on wavelength''' !! '''Based on frequency'''
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| |- align=center
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| | <math>z = \frac{\lambda_{\mathrm{obsv}} - \lambda_{\mathrm{emit}}}{\lambda_{\mathrm{emit}}}</math>
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| | <math>z = \frac{f_{\mathrm{emit}} - f_{\mathrm{obsv}}}{f_{\mathrm{obsv}}}</math>
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| |- align=center
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| | <math>1+z = \frac{\lambda_{\mathrm{obsv}}}{\lambda_{\mathrm{emit}}}</math>
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| | <math>1+z = \frac{f_{\mathrm{emit}}}{f_{\mathrm{obsv}}}</math>
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| |}
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| After ''z'' is measured, the distinction between redshift and blueshift is simply a matter of whether ''z'' is positive or negative. See the [[#Redshift formulae|formula section]] below for some basic interpretations that follow when either a redshift or blueshift is observed. For example, [[Doppler effect]] blueshifts (''z'' < 0) are associated with objects approaching (moving closer to) the observer with the light shifting to greater [[energy|energies]]. Conversely, Doppler effect redshifts (''z'' > 0) are associated with objects receding (moving away) from the observer with the light shifting to lower energies. Likewise, gravitational blueshifts are associated with light emitted from a source residing within a weaker [[gravitational field]] as observed from within a stronger gravitational field, while gravitational redshifting implies the opposite conditions.
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| ==Redshift formulae==
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| In general relativity one can derive several important special-case formulae for redshift in certain special spacetime geometries, as summarized in the following table. In all cases the magnitude of the shift (the value of ''z'') is independent of the wavelength.<ref name=basicastronomy />
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| {| class="wikitable" style="margin:auto;"
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| |+ '''Redshift summary'''
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| ! Redshift type !! Geometry !! Formula<ref>Where z = redshift; v<sub>||</sub> = [[velocity]] parallel to line-of-sight (positive if moving away from receiver); c = [[speed of light]]; ''γ'' = [[Lorentz factor]]; ''a'' = [[scale factor (Universe)|scale factor]]; G = [[gravitational constant]]; M = object [[mass]]; r = [[Schwarzschild coordinates|radial Schwarzschild coordinate]], g<sub>tt</sub> = t,t component of the [[metric tensor]]</ref>
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| |- align=center
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| | Relativistic Doppler || [[Minkowski space]] (flat spacetime) || <math>1 + z = \gamma \left(1 + \frac{v_{\parallel}}{c}\right)</math><br><math>z \approx \frac{v_{\parallel}}{c}</math> for small <math>v</math><br>
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| <math>1 + z = \sqrt{\frac{1+\frac{v}{c}}{1-\frac{v}{c}}}</math> for motion completely in the radial direction.<br>
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| <math>1 + z=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}</math> for motion completely in the transverse direction.
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| |- align=center
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| | Cosmological redshift || [[Friedmann-Lemaître-Robertson-Walker|FLRW spacetime]] (expanding Big Bang universe) || <math>1 + z = \frac{a_{\mathrm{now}}}{a_{\mathrm{then}}}</math>
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| |- align=center
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| | Gravitational redshift || any [[stationary spacetime]] (e.g. the [[Schwarzschild geometry]]) || <math>1 + z = \sqrt{\frac{g_{tt}(\text{receiver})}{g_{tt}(\text{source})}}</math><br>(for the Schwarzschild geometry, <math>1 + z = \sqrt{\frac{1 - \frac{2GM}{ c^2 r_{\text{receiver}}}}{1 - \frac{2GM}{ c^2 r_{\text{source} }}}}</math>
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| |}
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| ===Doppler effect===
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| {{main|Doppler effect|Relativistic Doppler effect}}
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| [[Image:Suzredshift.gif|thumb|Doppler effect, [[yellow]] (~575 [[nanometer|nm]] wavelength) ball appears [[green]]ish (blueshift to ~565 nm wavelength) approaching observer, turns [[Orange (colour)|orange]] (redshift to ~585 nm wavelength) as it passes, and returns to yellow when motion stops. To observe such a change in color, the object would have to be traveling at approximately 5200 [[kilometer per second|km/s]], or about 75 times faster than the speed record for the [[Helios II|fastest manmade space probe]].]]
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| If a source of the light is moving away from an observer, then redshift (''z'' > 0) occurs; if the source moves towards the observer, then [[blueshift]] (''z'' < 0) occurs. This is true for all electromagnetic waves and is explained by the [[Doppler effect]]. Consequently, this type of redshift is called the ''Doppler redshift''. If the source moves away from the observer with [[velocity]] ''v'', which is much less than the speed of light (<math>v \ll c</math>), the redshift is given by
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| :<math>z \approx \frac{v}{c}</math> (since <math>\gamma \approx 1</math>)
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| where ''c'' is the [[speed of light]]. In the classical Doppler effect, the frequency of the source is not modified, but the recessional motion causes the illusion of a lower frequency.
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| A more complete treatment of the Doppler redshift requires considering relativistic effects associated with motion of sources close to the speed of light. A complete derivation of the effect can be found in the article on the [[relativistic Doppler effect]]. In brief, objects moving close to the speed of light will experience deviations from the above formula due to the [[time dilation]] of [[special relativity]] which can be corrected for by introducing the [[Lorentz factor]] ''γ'' into the classical Doppler formula as follows:
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| :<math>1 + z = \left(1 + \frac{v}{c}\right) \gamma.</math>
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| This phenomenon was first observed in a 1938 experiment performed by Herbert E. Ives and G.R. Stilwell, called the [[Ives–Stilwell experiment]].<ref>H. Ives and G. Stilwell, An Experimental study of the rate of a moving atomic clock, J. Opt. Soc. Am. 28, 215–226 (1938) [http://www.opticsinfobase.org/abstract.cfm?URI=josa-28-7-215]</ref>
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| Since the Lorentz factor is dependent only on the [[magnitude (mathematics)|magnitude]] of the velocity, this causes the redshift associated with the relativistic correction to be independent of the orientation of the source movement. In contrast, the classical part of the formula is dependent on the [[scalar resolute|projection]] of the movement of the source into the [[Line-of-sight propagation|line-of-sight]] which yields different results for different orientations. If ''θ'' is the angle between the direction of relative motion and the direction of emission in the observer's frame<ref>{{cite book|last=Freund|first=Jurgen|title=Special Relativity for Beginners|year=2008|publisher=World Scientific|pages=120|isbn=981-277-160-3}}</ref> (zero angle is directly away from the observer), the full form for the relativistic Doppler effect becomes:
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| :<math>1+ z = \frac{1 + v \cos (\theta)/c}{\sqrt{1-v^2/c^2}}</math>
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| and for motion solely in the line of sight (θ = 0°), this equation reduces to:
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| :<math>1 + z = \sqrt{\frac{1 + \frac{v}{c}}{1 - \frac{v}{c}}}</math>.
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| For the special case that the light is approaching at [[right angle]]s (θ = 90°) to the direction of relative motion in the observer's frame,<ref>{{cite book|last=Ditchburn|first=R|title=Light|year=1961|publisher=Dover|pages=329|isbn=0-12-218101-8}}</ref> the relativistic redshift is known as the [[Transverse Doppler effect|transverse redshift]], and a redshift:
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| :<math>1 + z = \frac{1}{\sqrt{1-v^2/c^2}}</math>
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| is measured, even though the object is not moving away from the observer. Even when the source is moving towards the observer, if there is a transverse component to the motion then there is some speed at which the dilation just cancels the expected blueshift and at higher speed the approaching source will be redshifted.<ref>See "[http://www.physics.uq.edu.au/people/ross/phys2100/doppler.htm Photons, Relativity, Doppler shift]" at the University of Queensland</ref>
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| ===Expansion of space===
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| {{main|Metric expansion of space}}
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| In the early part of the twentieth century, Slipher, Hubble and others made the first measurements of the redshifts and blueshifts of galaxies beyond the [[Milky Way]]. They initially interpreted these redshifts and blueshifts as due solely to the Doppler effect, but later Hubble discovered a rough correlation between the increasing redshifts and the increasing distance of galaxies. Theorists almost immediately realized that these observations could be explained by a different mechanism for producing redshifts. [[Hubble's law]] of the correlation between redshifts and distances is required by models of cosmology derived from general relativity that have a [[metric expansion of space]].<ref name=Eddington /> As a result, photons propagating through the expanding space are stretched, creating the [[cosmological redshift]].
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| There is a distinction between a redshift in cosmological context as compared to that witnessed when nearby objects exhibit a [[Local reference frame|local]] Doppler-effect redshift. Rather than cosmological redshifts being a consequence of relative velocities, the photons instead increase in wavelength and redshift because of a [[Spacetime topology|feature of the spacetime]] through which they are traveling that causes space to [[metric expansion of space|expand]].<ref>The distinction is made clear in {{cite book |last=Harrison |first=Edward Robert |year= 2000 |title=Cosmology: The Science of the Universe |publisher=Cambridge University Press |edition=2 |url=http://books.google.com/?id=-8PJbcA2lLoC&pg=PA315#PPA306,M1 |pages=306''ff'' |isbn=0-521-66148-X |ref=harv}}</ref> Due to the expansion increasing as distances increase, the distance between two remote galaxies can increase at more than 3{{e|8}} m/s, but this does not imply that the galaxies move faster than the speed of light at their present location (which is forbidden by [[Lorentz covariance]]).
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| ====Mathematical derivation====
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| The observational consequences of this effect can be derived using [[Friedmann-Robertson-Walker metric|the equations]] from [[general relativity]] that describe a [[cosmological principle|homogeneous and isotropic universe]].
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| To derive the redshift effect, use the [[geodesic equation]] for a light wave, which is
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| :<math>ds^2=0=-c^2dt^2+\frac{a^2 dr^2}{1-kr^2}</math>
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| where
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| * <math>ds^2</math> is the [[spacetime interval]]
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| * <math>dt^2</math> is the time interval
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| * <math>dr^2</math> is the spatial interval
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| * <math>c</math> is the speed of light
| |
| * <math>a</math> is the time-dependent cosmic [[scale factor (Universe)|scale factor]]
| |
| * <math>k</math> is the [[curvature]] per unit area.
| |
| | |
| For an observer observing the crest of a light wave at a position <math>r=0</math> and time <math>t=t_\mathrm{now}</math>, the crest of the light wave was emitted at a time <math>t=t_\mathrm{then}</math> in the past and a distant position <math>r=R</math>. Integrating over the path in both space and time that the light wave travels yields:
| |
| | |
| :<math>
| |
| c \int_{t_\mathrm{then}}^{t_\mathrm{now}} \frac{dt}{a}\; =
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| \int_{R}^{0} \frac{dr}{\sqrt{1-kr^2}}\,.
| |
| </math>
| |
| | |
| In general, the wavelength of light is not the same for the two positions and times considered due to the changing properties of the metric. When the wave was emitted, it had a wavelength <math>\lambda_\mathrm{then}</math>. The next crest of the light wave was emitted at a time
| |
| | |
| :<math>t=t_\mathrm{then}+\lambda_\mathrm{then}/c\,.</math>
| |
| | |
| The observer sees the next crest of the observed light wave with a wavelength <math>\lambda_\mathrm{now}</math> to arrive at a time
| |
| | |
| :<math>t=t_\mathrm{now}+\lambda_\mathrm{now}/c\,.</math>
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| | |
| Since the subsequent crest is again emitted from <math>r=R</math> and is observed at <math>r=0</math>, the following equation can be written:
| |
| | |
| :<math>
| |
| c \int_{t_\mathrm{then}+\lambda_\mathrm{then}/c}^{t_\mathrm{now}+\lambda_\mathrm{now}/c} \frac{dt}{a}\; =
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| \int_{R}^{0} \frac{dr}{\sqrt{1-kr^2}}\,.
| |
| </math>
| |
| | |
| The right-hand side of the two integral equations above are identical which means
| |
| | |
| :<math>
| |
| c \int_{t_\mathrm{then}+\lambda_\mathrm{then}/c}^{t_\mathrm{now}+\lambda_\mathrm{now}/c} \frac{dt}{a}\; =
| |
| c \int_{t_\mathrm{then}}^{t_\mathrm{now}} \frac{dt}{a}\,
| |
| </math>
| |
| | |
| or, alternatively,
| |
| | |
| :<math>
| |
| \int_{t_\mathrm{now}}^{t_\mathrm{now}+\lambda_\mathrm{now}/c} \frac{dt}{a}\; =
| |
| \int_{t_\mathrm{then}}^{t_\mathrm{then}+\lambda_\mathrm{then}/c} \frac{dt}{a}\,.
| |
| </math>
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| | |
| For very small variations in time (over the period of one cycle of a light wave) the scale factor is essentially a constant (<math>a=a_\mathrm{now}</math> today and <math>a=a_\mathrm{then}</math> previously). This yields
| |
| | |
| :<math>\frac{t_\mathrm{now}+\lambda_\mathrm{now}/c}{a_\mathrm{now}}-\frac{t_\mathrm{now}}{a_\mathrm{now}}\; = \frac{t_\mathrm{then}+\lambda_\mathrm{then}/c}{a_\mathrm{then}}-\frac{t_\mathrm{then}}{a_\mathrm{then}}
| |
| </math>
| |
| | |
| which can be rewritten as
| |
| | |
| :<math>\frac{\lambda_\mathrm{now}}{\lambda_\mathrm{then}}=\frac{a_\mathrm{now}}{a_\mathrm{then}}\,.</math>
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| | |
| Using the definition of redshift provided [[#Measurement, characterization, and interpretation|above]], the equation
| |
| | |
| :<math>1+z = \frac{a_\mathrm{now}}{a_\mathrm{then}}</math>
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| | |
| is obtained. In an expanding universe such as the one we inhabit, the scale factor is [[monotonic function|monotonically increasing]] as time passes, thus, z is positive and distant galaxies appear redshifted.
| |
| | |
| ----
| |
| | |
| Using a model of the expansion of the universe, redshift can be related to the age of an observed object, the so-called ''[[cosmic time]]–redshift relation''. Denote a density ratio as Ω<sub>0</sub>:
| |
| | |
| :<math>\Omega_0 = \frac {\rho}{ \rho_{crit}} \ , </math>
| |
| | |
| with ρ<sub>crit</sub> the critical density demarcating a universe that eventually crunches from one that simply expands. This density is about three hydrogen atoms per thousand liters of space.<ref Name=Weinberg>{{cite book |author=Steven Weinberg |edition=2 |title=The First Three Minutes: A Modern View of the Origin of the Universe |url=http://books.google.com/?id=oxfoF_gasvsC&pg=PA34 |page=34 |isbn=0-465-02437-8 |year=1993 |publisher=Basic Books}}</ref> At large redshifts one finds:
| |
| | |
| :<math> t(z) = \frac {2}{3 H_0 {\Omega_0}^{1/2} (1+ z )^{3/2}} \ , </math>
| |
| | |
| where ''H<sub>0</sub>'' is the present-day [[Hubble constant]], and ''z'' is the redshift.<ref name="Bergström">{{cite book |author=[[Lars Bergström (physicist)|Lars Bergström]], [[Ariel Goobar]] |title=Cosmology and Particle Astrophysics |url=http://books.google.com/?id=CQYu_sutWAoC&pg=PA77 |page=77, Eq.4.79 |isbn=3-540-32924-2 |publisher=Springer |edition=2|year=2006}}</ref><ref name = Longair>{{cite book |title=Galaxy Formation |author=M.S. Longair |url=http://books.google.com/?id=2ARuLT-tk5EC&pg=PA161 |page=161 |isbn=3-540-63785-0 |publisher=Springer |year=1998}}</ref><ref name=Sanchez>{{cite book |editor=Norma Sanchez |page=223 |title=Current Topics in Astrofundamental Physics |url=http://books.google.com/?id=GOJoas-Dg7QC&pg=PA223 |isbn=0-7923-6856-8 |year=2001 |publisher=Springer |chapter=The High Redshift Radio Universe |author=Yu N Parijskij}}</ref>
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| | |
| ====Distinguishing between cosmological and local effects====
| |
| For cosmological redshifts of z < 0.01 additional Doppler redshifts and blueshifts due to the [[peculiar velocity|peculiar motions]] of the galaxies relative to one another cause a wide [[variance|scatter]] from the standard [[Hubble Law]].<ref>Measurements of the peculiar velocities out to 5 [[parsec|Mpc]] using the [[Hubble Space Telescope]] were reported in 2003 by Karachentsev et al. ''Local galaxy flows within 5 Mpc''. 02/2003 ''[[Astronomy and Astrophysics]]'', '''398''', 479-491.[http://arxiv.org/abs/astro-ph/0211011]</ref> The resulting situation can be illustrated by the [[Metric expansion of space#Other models of expansion|Expanding Rubber Sheet Universe]], a common cosmological analogy used to describe the expansion of space. If two objects are represented by ball bearings and spacetime by a stretching rubber sheet, the Doppler effect is caused by rolling the balls across the sheet to create peculiar motion. The cosmological redshift occurs when the ball bearings are stuck to the sheet and the sheet is stretched.<ref name=Kuhn>{{cite book |title=In Quest of the Universe |author=Theo Koupelis, Karl F. Kuhn |edition=5 |url=http://books.google.com/?id=6rTttN4ZdyoC&pg=PA556#PPA557,M1 |page=557 |publisher=Jones & Bartlett Publishers |year=2007 |isbn=0-7637-4387-9}}</ref><ref name=Lewis>"It is perfectly valid to interpret the equations of relativity in terms of an expanding space. The mistake is to push analogies too far and imbue space with physical properties that are not consistent with the equations of relativity." {{cite journal |title=Cosmological Radar Ranging in an Expanding Universe |arxiv=0805.2197 |journal=Monthly Notices of the Royal Astronomical Society |author=Geraint F. Lewis ''et al.'' |year=2008 |pages=960–964 |issue=3 |volume=388 |doi=10.1111/j.1365-2966.2008.13477.x |bibcode=2008MNRAS.388..960L}}</ref><ref name=Chodorowski>{{Cite journal |author=Michal Chodorowski |title=Is space really expanding? A counterexample |year=2007 |arxiv=astro-ph/0601171 |journal=Concepts Phys |volume=4 |pages=17–34|bibcode = 2007ONCP....4...15C |doi = 10.2478/v10005-007-0002-2 }}</ref>
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| | |
| The redshifts of galaxies include both a component related to recessional velocity from expansion of the universe, and a component related to [[peculiar motion]] (Doppler shift).<ref>Bedran,M.L.(2002)http://www.df.uba.ar/users/sgil/physics_paper_doc/papers_phys/cosmo/doppler_redshift.pdf "A comparison between the Doppler and cosmological redshifts"; Am.J.Phys.'''70''', 406–408 (2002)</ref> The redshift due to expansion of the universe depends upon the recessional velocity in a fashion determined by the cosmological model chosen to describe the expansion of the universe, which is very different from how Doppler redshift depends upon local velocity.<ref name=Harrison2>{{cite journal |title=The redshift-distance and velocity-distance laws |author=Edward Harrison |year=1992 |bibcode=1993ApJ...403...28H |journal=Astrophysical Journal, Part 1 |pages=28–31 |volume=403 |doi=10.1086/172179}}. A pdf file can be found here [http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1993ApJ...403...28H&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf].</ref> Describing the cosmological expansion origin of redshift, cosmologist [[Edward Robert Harrison]] said, "Light leaves a galaxy, which is stationary in its local region of space, and is eventually received by observers who are stationary in their own local region of space. Between the galaxy and the observer, light travels through vast regions of expanding space. As a result, all wavelengths of the light are stretched by the expansion of space. It is as simple as that....<ref>{{Harvnb|Harrison|2000|p=315}}.</ref> [[Steven Weinberg]] clarified, "The increase of wavelength from emission to absorption of light does not depend on the rate of change of ''a(t)'' [here ''a(t)'' is the [[cosmic scale factor|Robertson-Walker scale factor]]] at the times of emission or absorption, but on the increase of ''a(t)'' in the whole period from emission to absorption."<ref name=Weinberg_Cosmology>{{cite book |url=http://books.google.com/?id=48C-ym2EmZkC&pg=PA11 |author=Steven Weinberg |title=Cosmology |publisher=Oxford University Press |page=11 |year=2008 |isbn=978-0-19-852682-7}}</ref>
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| | |
| Popular literature often uses the expression "Doppler redshift" instead of "cosmological redshift" to describe the redshift of galaxies dominated by the expansion of spacetime, but the cosmological redshift is not found using the relativistic Doppler equation<ref>Odenwald & Fienberg 1993</ref> which is instead characterized by [[special relativity]]; thus ''v > c'' is impossible while, in contrast, ''v > c'' is possible for cosmological redshifts because the space which separates the objects (for example, a quasar from the Earth) can expand faster than the speed of light.<ref>Speed faster than light is allowed because the [[metric expansion of space|expansion]] of the [[spacetime]] [[Metric (mathematics)|metric]] is described by [[general relativity]] in terms of sequences of only locally valid inertial frames as opposed to a global [[Minkowski metric]]. Expansion faster than light is an integrated effect over many local inertial frames and is allowed because no single inertial frame is involved. The speed-of-light limitation applies only locally. See {{cite journal |author=Michal Chodorowski |title=Is space really expanding? A counterexample |year=2007 |arxiv=astro-ph/0601171 |journal=Concepts Phys |volume=4 |pages=17–34|bibcode = 2007ONCP....4...15C |doi = 10.2478/v10005-007-0002-2 }}</ref> More mathematically, the viewpoint that "distant galaxies are receding" and the viewpoint that "the space between galaxies is expanding" are related by changing [[coordinate system]]s. Expressing this precisely requires working with the mathematics of the [[Friedmann-Robertson-Walker metric]].<ref>M. Weiss, What Causes the Hubble Redshift?, entry in the Physics [[FAQ]] (1994), available via [[John Baez]]'s [http://math.ucr.edu/home/baez/physics/Relativity/GR/hubble.html website]</ref>
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| | |
| If the universe were contracting instead of expanding, we would see distant galaxies blueshifted by an amount proportional to their distance instead of redshifted.<ref>This is only true in a universe where there are no [[peculiar velocity|peculiar velocities]]. Otherwise, redshifts combine as
| |
| :<math>1+z=(1+z_{\mathrm{Doppler}})(1+z_{\mathrm{expansion}})</math>
| |
| which yields solutions where certain objects that "recede" are blueshifted and other objects that "approach" are redshifted. For more on this bizarre result see Davis, T. M., Lineweaver, C. H., and Webb, J. K. "[http://arxiv.org/abs/astro-ph/0104349/ Solutions to the tethered galaxy problem in an expanding universe and the observation of receding blueshifted objects]", ''[[American Journal of Physics]]'' (2003), '''71''' 358–364.</ref>
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| | |
| ===Gravitational redshift===
| |
| {{main|Gravitational redshift}}
| |
| In the theory of [[general relativity]], there is time dilation within a gravitational well. This is known as the [[gravitational redshift]] or ''Einstein Shift''.<ref>{{cite journal | author = Chant, C. A. | bibcode = 1930JRASC..24..390C | title = Notes and Queries (Telescopes and Observatory Equipment – The Einstein Shift of Solar Lines) | year = 1930 | journal = [[Journal of the Royal Astronomical Society of Canada]] | volume = 24 | page = 390 }}</ref> The theoretical derivation of this effect follows from the [[Schwarzschild solution]] of the [[Einstein field equations|Einstein equations]] which yields the following formula for redshift associated with a photon traveling in the [[gravitational field]] of an [[electrical charge|uncharged]], [[rotation|nonrotating]], [[spherical symmetry|spherically symmetric]] mass:
| |
| | |
| :<math>1+z=\frac{1}{\sqrt{1-\frac{2GM}{rc^2}}},</math>
| |
| | |
| where
| |
| * <math>G\,</math> is the [[gravitational constant]],
| |
| * <math>M\,</math> is the [[mass]] of the object creating the gravitational field,
| |
| * <math>r\,</math> is the radial coordinate of the source (which is analogous to the classical distance from the center of the object, but is actually a [[Schwarzschild coordinates|Schwarzschild coordinate]]), and
| |
| * <math>c\,</math> is the [[speed of light]].
| |
| | |
| This gravitational redshift result can be derived from the assumptions of [[special relativity]] and the [[equivalence principle]]; the full theory of general relativity is not required.<ref>{{cite journal | last = Einstein | first = A | authorlink = Albert Einstein | year = 1907 | title = Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen | journal = Jahrbuch der Radioaktivität und Elektronik | volume = 4 | pages = 411–462}}</ref>
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| | |
| The effect is very small but measurable on Earth using the [[Mössbauer effect]] and was first observed in the [[Pound-Rebka experiment]].<ref>{{cite journal | doi = 10.1103/PhysRevLett.4.337 | title = Apparent Weight of Photons | year = 1960 | last1 = Pound | first1 = R. | last2 = Rebka | first2 = G. | journal = Physical Review Letters | volume = 4 | issue = 7 | pages = 337 | bibcode=1960PhRvL...4..337P}}. This paper was the first measurement.</ref> However, it is significant near a [[black hole]], and as an object approaches the [[event horizon]] the red shift becomes infinite. It is also the dominant cause of large angular-scale temperature fluctuations in the [[cosmic microwave background radiation]] (see [[Sachs-Wolfe effect]]).<ref>{{cite journal | last = Sachs | first = R. K. | authorlink = Rainer Kurt Sachs|coauthors = [[Arthur Michael Wolfe|Wolfe, A. M.]] | year = 1967 | title = Perturbations of a cosmological model and angular variations of the cosmic microwave background | journal = Astrophysical Journal | volume = 147 | issue = 73 | doi = 10.1086/148982 | page = 73 | bibcode=1967ApJ...147...73S}}</ref><ref>[http://astroreview.com/issue/2012/article/black-hole-horizons-and-how-they-begin Dieter Brill, “Black Hole Horizons and How They Begin”, Astronomical Review (2012); Online Article, cited Sept.2012.]</ref>
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| ==Observations in astronomy==
| |
| The redshift observed in astronomy can be measured because the [[emission spectrum|emission]] and [[absorption spectrum|absorption]] spectra for [[atom]]s are distinctive and well known, calibrated from [[spectroscopy|spectroscopic experiments]] in [[laboratory|laboratories]] on Earth. When the redshift of various absorption and emission lines from a single astronomical object is measured, ''z'' is found to be remarkably constant. Although distant objects may be slightly blurred and lines broadened, it is by no more than can be explained by [[thermal motion|thermal]] or [[motion (physics)|mechanical motion]] of the source. For these reasons and others, the consensus among astronomers is that the redshifts they observe are due to some combination of the three established forms of Doppler-like redshifts. Alternative hypotheses and explanations for redshift such as [[tired light]] are not generally considered plausible.<ref name=reboul>When cosmological redshifts were first discovered, [[Fritz Zwicky]] proposed an effect known as tired light. While usually considered for historical interests, it is sometimes, along with [[intrinsic redshift]] suggestions, utilized by [[nonstandard cosmologies]]. In 1981, H. J. Reboul summarised many [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1981A%26AS...45..129R&db_key=AST&data_type=HTML&format=&high=42ca922c9c23806 alternative redshift mechanisms] that had been discussed in the literature since the 1930s. In 2001, [[Geoffrey Burbidge]] remarked in a [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2001PASP..113..899B&db_key=AST&data_type=HTML review] that the wider astronomical community has marginalized such discussions since the 1960s. Burbidge and [[Halton Arp]], while investigating the mystery of [[Quasar#History of quasar observation|the nature of quasars]], tried to develop alternative redshift mechanisms, and very few of their fellow scientists acknowledged let alone accepted their work. Moreover, Goldhaber ''et al.'' 2001; "Timescale Stretch Parameterization of Type Ia Supernova B-Band Lightcurves", ApJ, 558:359–386, 2001 September 1 pointed out that alternative theories are unable to account for timescale stretch observed in [[type Ia supernovae]]</ref>
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| Spectroscopy, as a measurement, is considerably more difficult than simple [[photometry (astronomy)|photometry]], which measures the [[brightness]] of astronomical objects through certain [[filter (optics)|filters]].<ref>For a review of the subject of photometry, consider Budding, E., ''Introduction to Astronomical Photometry'', Cambridge University Press (September 24, 1993), ISBN 0-521-41867-4</ref> When photometric data is all that is available (for example, the [[Hubble Deep Field]] and the [[Hubble Ultra Deep Field]]), astronomers rely on a technique for measuring [[photometric redshift]]s.<ref>The technique was first described by Baum, W. A.: 1962, in G. C. McVittie (ed.), ''Problems of extra-galactic research'', p. 390, IAU Symposium No. 15</ref> Due to the broad wavelength ranges in photometric filters and the necessary assumptions about the nature of the spectrum at the light-source, [[observational error|errors]] for these sorts of measurements can range up to δ''z'' = 0.5, and are much less reliable than spectroscopic determinations.<ref>Bolzonella, M.; Miralles, J.-M.; Pelló, R., [http://arxiv.org/abs/astro-ph/0003380 Photometric redshifts based on standard SED fitting procedures], ''[[Astronomy and Astrophysics]]'', '''363''', p.476–492 (2000).</ref> However, photometry does at least allow a qualitative characterization of a redshift. For example, if a sun-like spectrum had a redshift of ''z'' = 1, it would be brightest in the [[infrared]] rather than at the yellow-green color associated with the peak of its [[blackbody spectrum]], and the light intensity will be reduced in the filter by a factor of four, <math>{(1+z)^2}</math>. Both the photon count rate and the photon energy are redshifted. (See [[K correction]] for more details on the photometric consequences of redshift.)<ref>A pedagogical overview of the K-correction by David Hogg and other members of the [[Sloan Digital Sky Survey|SDSS]] collaboration can be found at [http://arxiv.org/abs/astro-ph/0210394 astro-ph].</ref>
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| ===Local observations===
| |
| [[Image:LASCO C1a.png|thumb|200px|A picture of the solar corona taken with the [[Large Angle and Spectrometric Coronagraph|LASCO]] C1 coronagraph. The picture is a color-coded image of the doppler shift of the FeXIV 5308 Å line, caused by the coronal plasma velocity towards or away from the satellite.]]
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| In nearby objects (within our [[Milky Way]] galaxy) observed redshifts are almost always related to the [[Line-of-sight propagation|line-of-sight]] velocities associated with the objects being observed. Observations of such redshifts and blueshifts have enabled astronomers to measure [[velocity|velocities]] and parametrize the [[mass]]es of the [[orbit (celestial mechanics)|orbiting]] [[star]]s in [[spectroscopic binaries]], a method first employed in 1868 by British astronomer [[William Huggins]].<ref name=Huggins /> Similarly, small redshifts and blueshifts detected in the spectroscopic measurements of individual stars are one way astronomers have been able to [[Methods of detecting extrasolar planets#Radial velocity|diagnose and measure]] the presence and characteristics of [[extrasolar planet|planetary systems]] around other stars and have even made very [[Rossiter-McLaughlin effect|detailed differential measurements]] of redshifts during [[Transiting extrasolar planet|planetary transits]] to determine precise orbital parameters.<ref>The [[Exoplanet Tracker]] is the newest observing project to use this technique, able to track the redshift variations in multiple objects at once, as reported in {{cite journal | doi = 10.1086/505699 | title = The First Extrasolar Planet Discovered with a New‐Generation High‐Throughput Doppler Instrument | year = 2006 | last1 = Ge | first1 = Jian | last2 = Van Eyken | first2 = Julian | last3 = Mahadevan | first3 = Suvrath | last4 = Dewitt | first4 = Curtis | last5 = Kane | first5 = Stephen R. | last6 = Cohen | first6 = Roger | last7 = Vanden Heuvel | first7 = Andrew | last8 = Fleming | first8 = Scott W. | last9 = Guo | first9 = Pengcheng | journal = The Astrophysical Journal | volume = 648 | pages = 683 | bibcode=2006ApJ...648..683G |arxiv = astro-ph/0605247 }}</ref> Finely detailed measurements of redshifts are used in [[helioseismology]] to determine the precise movements of the [[photosphere]] of the [[Sun]].<ref>{{cite journal | doi = 10.1007/BF00243557 | title = Solar and stellar seismology | year = 1988 | last1 = Libbrecht | first1 = Keng. | journal = Space Science Reviews | volume = 47 | issue = 3–4 |bibcode=1988SSRv...47..275L | pages=275–301}}</ref> Redshifts have also been used to make the first measurements of the [[Period of revolution|rotation rates]] of [[planet]]s,<ref>In 1871 [[Hermann Carl Vogel]] measured the rotation rate of [[Venus]]. [[Vesto Slipher]] was working on such measurements when he turned his attention to spiral nebulae.</ref> velocities of [[interstellar cloud]]s,<ref>An early review by [[Jan Hendrik Oort|Oort, J. H.]] on the subject: {{cite journal | title = The formation of galaxies and the origin of the high-velocity hydrogen|journal= [[Astronomy and Astrophysics]]|volume=7|page= 381 |year=1970| bibcode=1970A&A.....7..381O | author1 = Oort | first1 = J. H. }}</ref> the [[galaxy rotation problem|rotation of galaxies]],<ref name=basicastronomy /> and the [[dynamics (mechanics)|dynamics]] of [[accretion theory|accretion]] onto [[neutron star]]s and [[black hole]]s which exhibit both Doppler and gravitational redshifts.<ref>{{cite journal| last=Asaoka |first= Ikuko|bibcode=1989PASJ...41..763A|title= X-ray spectra at infinity from a relativistic accretion disk around a Kerr black hole|journal=Astronomical Society of Japan|issn= 0004-6264|volume=41|issue= 4|year= 1989|pages=763–778 }}</ref> Additionally, the [[temperature]]s of various emitting and absorbing objects can be obtained by measuring [[Doppler broadening]] – effectively redshifts and blueshifts over a single emission or absorption line.<ref>Rybicki, G. B. and A. R. Lightman, ''Radiative Processes in Astrophysics'', John Wiley & Sons, 1979, p. 288 ISBN 0-471-82759-2</ref> By measuring the broadening and shifts of the 21-centimeter [[hydrogen line]] in different directions, astronomers have been able to measure the [[recessional velocity|recessional velocities]] of [[interstellar gas]], which in turn reveals the [[rotation curve]] of our Milky Way.<ref name=basicastronomy /> Similar measurements have been performed on other galaxies, such as [[Andromeda (galaxy)|Andromeda]].<ref name=basicastronomy /> As a diagnostic tool, redshift measurements are one of the most important [[astronomical spectroscopy|spectroscopic measurements]] made in astronomy.
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| ===Extragalactic observations===
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| The most distant objects exhibit larger redshifts corresponding to the [[Hubble's law|Hubble flow]] of the universe. The largest observed redshift, corresponding to the greatest distance and furthest back in time, is that of the [[cosmic microwave background radiation]]; the numerical value of its redshift is about {{nowrap|''z'' {{=}} 1089}} ({{nowrap|''z'' {{=}} 0}} corresponds to present time), and it shows the state of the [[Universe]] about 13.8 billion years ago,<ref>{{cite web
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| |last =
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| |first =
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| |title = Cosmic Detectives
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| |url=http://www.esa.int/Our_Activities/Space_Science/Cosmic_detectives
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| |authorlink =
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| |coauthors =
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| |work =
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| |publisher = The European Space Agency (ESA)
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| |date = 2013-04-02
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| |doi =
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| |accessdate = 2013-04-25}}
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| </ref> and 379,000 years after the initial moments of the [[Big Bang]].<ref>An accurate measurement of the cosmic microwave background was achieved by the [[Cosmic Background Explorer|COBE]] experiment. The final published temperature of 2.73 K was reported in this paper: Fixsen, D. J.; Cheng, E. S.; Cottingham, D. A.; Eplee, R. E., Jr.; Isaacman, R. B.; Mather, J. C.; Meyer, S. S.; Noerdlinger, P. D.; Shafer, R. A.; Weiss, R.; Wright, E. L.; Bennett, C. L.; Boggess, N. W.; Kelsall, T.; Moseley, S. H.; Silverberg, R. F.; Smoot, G. F.; Wilkinson, D. T.. (1994). "Cosmic microwave background dipole spectrum measured by the COBE FIRAS instrument", ''Astrophysical Journal'', 420, 445. The most accurate measurement as of 2006 was achieved by the [[Wilkinson Microwave Anisotropy Probe|WMAP]] experiment.</ref>
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| The luminous point-like cores of [[quasar]]s were the first "high-redshift" ({{nowrap|''z'' > 0.1}}) objects discovered before the improvement of telescopes allowed for the discovery of other high-redshift galaxies.
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| For galaxies more distant than the [[Local Group]] and the nearby [[Virgo Cluster]], but within a thousand [[parsec|megaparsecs]] or so, the redshift is approximately proportional to the galaxy's distance. This correlation was first observed by [[Edwin Hubble]] and has come to be known as [[Hubble's law]]. [[Vesto Slipher]] was the first to discover galactic redshifts, in about the year 1912, while Hubble correlated Slipher's measurements with distances he [[cosmic distance ladder|measured by other means]] to formulate his Law. In the widely accepted cosmological model based on [[general relativity]], redshift is mainly a result of the expansion of space: this means that the farther away a galaxy is from us, the more the space has expanded in the time since the light left that galaxy, so the more the light has been stretched, the more redshifted the light is, and so the faster it appears to be moving away from us. [[Hubble's law]] follows in part from the [[Copernican principle]].<ref name="Peebles-1993">Peebles (1993).</ref> Because it is usually not known how [[luminosity|luminous]] objects are, measuring the redshift is easier than more direct distance measurements, so redshift is sometimes in practice converted to a crude distance measurement using Hubble's law.
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| [[Gravitation|Gravitational interactions]] of galaxies with each other and clusters cause a significant [[variance|scatter]] in the normal plot of the Hubble diagram. The [[peculiar velocity|peculiar velocities]] associated with galaxies superimpose a rough trace of the [[mass]] of [[virial theorem|virialized objects]] in the universe. This effect leads to such phenomena as nearby galaxies (such as the [[Andromeda Galaxy]]) exhibiting blueshifts as we fall towards a common [[Barycentric coordinates (astronomy)|barycenter]], and redshift maps of clusters showing a [[Fingers of God]] effect due to the scatter of peculiar velocities in a roughly spherical distribution.<ref name="Peebles-1993"/> This added component gives cosmologists a chance to measure the masses of objects independent of the ''[[mass to light ratio]]'' (the ratio of a galaxy's mass in solar masses to its brightness in solar luminosities), an important tool for measuring [[dark matter]].<ref>{{cite book|first=James|last=Binney|coauthors=and Scott Treimane|title=Galactic dynamics|publisher=Princeton University Press|isbn=0-691-08445-9|year=1994}}</ref>
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| The Hubble law's linear relationship between distance and redshift assumes that the rate of expansion of the universe is constant. However, when the universe was much younger, the expansion rate, and thus the Hubble "constant", was larger than it is today. For more distant galaxies, then, whose light has been travelling to us for much longer times, the approximation of constant expansion rate fails, and the Hubble law becomes a non-linear integral relationship and dependent on the history of the expansion rate since the emission of the light from the galaxy in question. Observations of the redshift-distance relationship can be used, then, to determine the expansion history of the universe and thus the matter and energy content.
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| While it was long believed that the expansion rate has been continuously decreasing since the Big Bang, recent observations of the redshift-distance relationship using [[Type Ia supernova]]e have suggested that in comparatively recent times the expansion rate of the universe has [[Accelerating universe|begun to accelerate]].
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| ===Highest redshifts===
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| [[Image:Distance compared to z.png|thumb|400px|Plot of distance (in [[giga]] [[light-year]]s) vs. redshift according to the [[Lambda-CDM model]]. <math>d_H</math> (in solid black) is the [[comoving distance]] from Earth to the location with the Hubble redshift ''z'' while <math>ct_{LB}</math> (in dotted red) is the speed of light multiplied by the lookback time to Hubble redshift ''z''. The comoving distance is the physical [[Space-like#Space-like interval|space-like]] distance between here and the distant location, [[asymptote|asymptoting]] to the [[Universe#Size, age, contents, structure, and laws|size of the observable universe]] at some 47 billion light years. The lookback time is the distance a photon traveled from the time it was emitted to now divided by the speed of light, with a maximum distance of 13.8 billion light years corresponding to the [[age of the universe]].]]
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| {{see also|List of the most distant astronomical objects#List of most distant objects by type{{!}}List of most distant objects by type}}
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| Currently, the objects with the highest known redshifts are galaxies and the objects producing gamma ray bursts. The most reliable redshifts are from [[spectroscopic]] data, and the highest confirmed [[spectroscopic]] redshift of a galaxy is that of
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| [[UDFy-38135539]]
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| <ref>
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| {{cite journal
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| | author=M.D.Lehnert, ''et al.''
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| | last2=Nesvadba
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| | first2=NP
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| | last3=Cuby
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| | first3=JG
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| | last4=Swinbank
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| | first4=AM
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| | last5=Morris
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| | first5=S
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| | last6=Clément
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| | first6=B
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| | last7=Evans
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| | first7=CJ
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| | last8=Bremer
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| | first8=MN
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| | last9=Basa
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| | first9=S
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| | title=Spectroscopic Confirmation of a galaxy at redshift z = 8.6
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| | url=http://www.nature.com/news/2010/101020/full/news.2010.552.html
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| | journal=Nature
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| | volume=467
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| | issue=7318
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| | pages=940–942
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| | doi=10.1038/nature09462
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| | pmid=20962840
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| | year=2010
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| | bibcode=2010Natur.467..940L
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| |arxiv = 1010.4312 }}</ref>
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| at a redshift of <math>z=8.6</math>, corresponding to just 600 million years after the Big Bang.
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| The previous record was held by
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| [[IOK-1]],<ref>
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| {{cite journal
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| | author=Masanori Iye, ''et al.''
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| | title=A galaxy at a redshift z = 6.96
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| | url=http://www.nature.com/nature/journal/v443/n7108/abs/nature05104.html
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| | journal=Nature
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| | volume=443
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| | issue=7108
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| | pages=186–188
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| | doi=10.1038/nature05104
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| | year=2006
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| | pmid=16971942
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| |arxiv = astro-ph/0609393 |bibcode = 2006Natur.443..186I }}</ref> at a redshift <math>z = 6.96</math>, corresponding to just 750 million years after the Big Bang. Slightly less reliable are [[Lyman-break galaxy|Lyman-break]] redshifts, the highest of which is the lensed galaxy A1689-zD1 at a redshift <math>z = 7.6</math><ref>Bradley, L.., et al., Discovery of a Very Bright Strongly Lensed Galaxy Candidate at z ~ 7.6, ''[[Astrophysical Journal|The Astrophysical Journal]]'' (2008), Volume 678, Issue 2, pp. 647-654. [http://adsabs.harvard.edu/abs/2008ApJ...678..647B</ref> and the next highest being <math>z=7.0</math>.<ref>Egami, E., et al., Spitzer and Hubble Space Telescope Constraints on the Physical Properties of the z~7 Galaxy Strongly Lensed by A2218, ''[[Astrophysical Journal|The Astrophysical Journal]]'' (2005), v. 618, Issue 1, pp. L5–L8 [http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2005ApJ...618L...5E&db_key=AST&data_type=HTML&format=&high=43a73989ff16910].</ref> The most distant observed [[gamma ray burst]] was [[GRB 090423]], which had a redshift of <math>z = 8.2</math>.<ref>
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| {{cite journal
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| |author= Salvaterra, R. ''et al.''
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| |year=2009
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| |title=GRB 090423 reveals an exploding star at the epoch of re-ionization
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| |journal=[[Nature (journal)|Nature]]
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| |volume=461 |issue=7268 |doi=10.1038/nature08445
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| |pmid=19865166
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| |bibcode = 2009Natur.461.1258S |arxiv = 0906.1578
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| |pages= 1258–60 }}</ref> The most distant known quasar, [[ULAS J1120+0641]], is at <math>z = 7.1 </math>.<ref>http://www.universetoday.com/87175/most-distant-quasar-opens-window-into-early-universe/</ref><ref name=SciAm-2011-06-29>Scientific American, [http://www.scientificamerican.com/article.cfm?id=farthest-quasar "Brilliant, but Distant: Most Far-Flung Known Quasar Offers Glimpse into Early Universe"], '''John Matson''', ''29 June 2011''</ref> The highest known redshift radio galaxy (TN J0924-2201) is at a redshift <math>z = 5.2</math><ref>{{cite journal | doi = 10.1086/429147 | title = CO (1-0) and CO (5-4) Observations of the Most Distant Known Radio Galaxy atz = 5.2 | year = 2005 | last1 = Klamer | first1 = I. J. | last2 = Ekers | first2 = R. D. | last3 = Sadler | first3 = E. M. | last4 = Weiss | first4 = A. | last5 = Hunstead | first5 = R. W. | last6 = De Breuck | first6 = C. | journal = The Astrophysical Journal | volume = 621 | pages = L1 | arxiv=astro-ph/0501447v1 | bibcode=2005ApJ...621L...1K}}</ref> and the highest known redshift molecular material is the detection of emission from the CO molecule from the quasar SDSS J1148+5251 at <math>z = 6.42</math><ref>{{cite journal | doi = 10.1038/nature01821 | title = Molecular gas in the host galaxy of a quasar at redshift z = 6.42 | year = 2003 | last1 = Walter | first1 = Fabian | last2 = Bertoldi | first2 = Frank | last3 = Carilli | first3 = Chris | last4 = Cox | first4 = Pierre | last5 = Lo | first5 = K. Y. | last6 = Neri | first6 = Roberto | last7 = Fan | first7 = Xiaohui | last8 = Omont | first8 = Alain | last9 = Strauss | first9 = Michael A. | journal = Nature | volume = 424 | issue = 6947 | pages = 406–8 | pmid = 12879063 |bibcode=2003Natur.424..406W|arxiv = astro-ph/0307410 }}</ref>
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| ''Extremely red objects'' (EROs) are [[Radio astronomy#Astronomical sources|astronomical sources]] of radiation that radiate energy in the red and near infrared part of the electromagnetic spectrum. These may be starburst galaxies that have a high redshift accompanied by reddening from intervening dust, or they could be highly redshifted elliptical galaxies with an older (and therefore redder) stellar population.<ref>
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| {{cite journal
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| | author=Smail, Ian; Owen, F. N.; Morrison, G. E.; Keel, W. C.; Ivison, R. J.; Ledlow, M. J.
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| | journal=The Astrophysical Journal | volume=581 | issue=2
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| | pages=844–864 | doi=10.1086/344440 | bibcode=2002ApJ...581..844S
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| | title=The Diversity of Extremely Red Objects
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| | year=2002
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| |arxiv = astro-ph/0208434 }}</ref> Objects that are even redder than EROs are termed ''hyper extremely red objects'' (HEROs).<ref>
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| {{cite journal
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| | author=Totani, Tomonori; Yoshii, Yuzuru; Iwamuro, Fumihide; Maihara, Toshinori; Motohara, Kentaro
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| | title=Hyper Extremely Red Objects in the Subaru Deep Field: Evidence for Primordial Elliptical Galaxies in the Dusty Starburst Phase
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| | journal=The Astrophysical Journal | volume=558 | issue=2
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| | year=2001 | pages=L87–L91 | doi=10.1086/323619
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| | bibcode=2001ApJ...558L..87T
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| |arxiv = astro-ph/0108145 }}</ref>
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| The [[cosmic microwave background]] has a redshift of <math>z=1089</math>, corresponding to an age of approximately 379,000 years after the Big Bang and a [[comoving distance]] of more than 46 billion light years.<ref name="ly93">
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| {{cite web | last = Lineweaver | first = Charles | coauthors = Tamara M. Davis | year = 2005 | url = http://www.sciam.com/article.cfm?id=misconceptions-about-the-2005-03&page=5 | title = Misconceptions about the Big Bang | publisher = Scientific American | accessdate = 2008-11-06}}</ref> The yet-to-be-observed first light from the oldest [[Population III stars]], not long after atoms first formed and the CMB ceased to be absorbed almost completely, may have redshifts in the range of <math>20<z<100</math>.<ref>{{cite journal|bibcode=2006MNRAS.373L..98N|arxiv = astro-ph/0604050 |doi = 10.1111/j.1745-3933.2006.00251.x|title=The first stars in the Universe|year=2006|last1=Naoz|first1=S.|last2=Noter|first2=S.|last3=Barkana|first3=R.|journal=Monthly Notices of the Royal Astronomical Society: Letters|volume=373|pages=L98–L102 }}</ref> Other high-redshift events predicted by physics but not presently observable are the [[cosmic neutrino background]] from about two seconds after the Big Bang (and a redshift in excess of <math>z>10^{10}</math>)<ref>{{cite journal|bibcode=2006PhR...429..307L|arxiv = astro-ph/0603494 |doi = 10.1016/j.physrep.2006.04.001|title=Massive neutrinos and cosmology|year=2006|last1=Lesgourgues|first1=J|last2=Pastor|first2=S|journal=Physics Reports|volume=429|issue=6|pages=307–379 }}</ref> and the [[cosmic gravitational wave background]] emitted directly from [[inflation (cosmology)|inflation]] at a redshift in excess of <math>z>10^{25}</math>.<ref>{{cite journal|bibcode=2005PhyU...48.1235G|arxiv = gr-qc/0504018 |doi = 10.1070/PU2005v048n12ABEH005795|title=Relic gravitational waves and cosmology|year=2005|last1=Grishchuk|first1=Leonid P|journal=Physics-Uspekhi|volume=48|issue=12|pages=1235–1247 }}</ref>
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| ===Redshift surveys===
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| [[File:2dfgrs.png|thumb|Rendering of the 2dFGRS data]]
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| {{main|Redshift survey}}
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| With advent of automated [[telescope]]s and improvements in [[astronomical spectroscopy|spectroscopes]], a number of collaborations have been made to map the universe in redshift space. By combining redshift with angular position data, a redshift survey maps the 3D distribution of matter within a field of the sky. These observations are used to measure properties of the [[large-scale structure of the cosmos|large-scale structure]] of the universe. The [[Great Wall (astronomy)|Great Wall]], a vast [[supercluster]] of galaxies over 500 million [[light-year]]s wide, provides a dramatic example of a large-scale structure that redshift surveys can detect.<ref>M. J. Geller & J. P. Huchra, ''Science'' '''246''', 897 (1989). [http://www.sciencemag.org/cgi/content/abstract/246/4932/897 online]</ref>
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| The first redshift survey was the [[CfA Redshift Survey]], started in 1977 with the initial data collection completed in 1982.<ref>See the official CfA [http://cfa-www.harvard.edu/~huchra/zcat/ website] for more details.</ref> More recently, the [[2dF Galaxy Redshift Survey]] determined the large-scale structure of one section of the Universe, measuring redshifts for over 220,000 galaxies; data collection was completed in 2002, and the final [[data set]] was released 30 June 2003.<ref>{{cite journal|doi=10.1111/j.1365-2966.2005.09318.x|title=The 2dF galaxy redshift survey: Power-spectrum analysis of the final dataset and cosmological implications|author=Shaun Cole ''et al.'' (The 2dFGRS Collaboration)|journal=Mon. Not. Roy. Astron. Soc.|volume=362|issue=2|pages=505–34|year=2005|bibcode=2005MNRAS.362..505C|arxiv = astro-ph/0501174 }} [http://msowww.anu.edu.au/2dFGRS/ 2dF Galaxy Redshift Survey homepage]</ref> The [[Sloan Digital Sky Survey]] (SDSS), is ongoing as of 2013 and aims to measure the redshifts of around 3 million objects.<ref>[http://www.sdss3.org/ SDSS Homepage]</ref> SDSS has recorded redshifts for galaxies as high as 0.8, and has been involved in the detection of [[quasar]]s beyond ''z'' = 6. The [[DEEP2 Redshift Survey]] uses the [[Keck telescopes]] with the new "DEIMOS" [[spectrograph]]; a follow-up to the pilot program DEEP1, DEEP2 is designed to measure faint galaxies with redshifts 0.7 and above, and it is therefore planned to provide a high redshift complement to SDSS and 2dF.<ref>{{cite conference|title=Science objectives and early results of the DEEP2 redshift survey|author=Marc Davis ''et al.'' (DEEP2 collaboration)|year=2002|booktitle=Conference on Astronomical Telescopes and Instrumentation, Waikoloa, Hawaii, 22–28 Aug 2002| arxiv=astro-ph/0209419 }}</ref>
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| ==Effects due to physical optics or radiative transfer==
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| The interactions and phenomena summarized in the subjects of [[radiative transfer]] and [[physical optics]] can result in shifts in the wavelength and frequency of electromagnetic radiation. In such cases the shifts correspond to a physical energy transfer to matter or other photons rather than being due to a transformation between reference frames. These shifts can be due to such physical phenomena as [[Wolf effect|coherence effects]] or the [[scattering]] of [[electromagnetic radiation]] whether from [[electric charge|charged]] [[elementary particle]]s, from particulates, or from fluctuations of the [[index of refraction]] in a [[dielectric medium]] as occurs in the radio phenomenon of [[Whistler (radio)|radio whistlers]].<ref name=basicastronomy /> While such phenomena are sometimes referred to as "redshifts" and "blueshifts", in astrophysics light-matter interactions that result in energy shifts in the radiation field are generally referred to as "reddening" rather than "redshifting" which, as a term, is normally reserved for the [[#Redshift formulae|effects discussed above]].<ref name=basicastronomy />
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| In many circumstances scattering causes radiation to redden because [[entropy]] results in the predominance of many low-[[energy]] photons over few high-energy ones (while [[conservation of energy|conserving total energy]]).<ref name=basicastronomy /> Except possibly under carefully controlled conditions, scattering does not produce the same relative change in wavelength across the whole spectrum; that is, any calculated ''z'' is generally a [[function (mathematics)|function]] of wavelength. Furthermore, scattering from [[randomness|random]] [[matter|media]] generally occurs at many [[angle]]s, and ''z'' is a function of the scattering angle. If multiple scattering occurs, or the scattering particles have relative motion, then there is generally distortion of [[spectral line]]s as well.<ref name=basicastronomy />
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| In [[interstellar medium|interstellar astronomy]], [[visible spectrum|visible spectra]] can appear [[red]]der due to scattering processes in a phenomenon referred to as [[interstellar reddening]]<ref name=basicastronomy /> – similarly [[Rayleigh scattering]] causes the [[Earth's atmosphere|atmospheric]] reddening of the [[Sun]] seen in the [[sunrise]] or [[sunset]] and causes the rest of the [[sky]] to have a [[blue]] color. This phenomenon is distinct from red''shift''ing because the [[atomic spectral line|spectroscopic lines]] are not shifted to other wavelengths in reddened objects and there is an additional [[extinction (astronomy)|dimming]] and distortion associated with the phenomenon due to photons being scattered in and out of the [[Line-of-sight propagation|line-of-sight]].
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| ''For a list of scattering processes, see [[Scattering]].''
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| ==References==
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| ===Notes===
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| {{Reflist|colwidth=30em}}
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| ===Articles===
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| * Odenwald, S. & Fienberg, RT. 1993; "Galaxy Redshifts Reconsidered" in ''Sky & Telescope'' Feb. 2003; pp31–35 (This article is useful further reading in distinguishing between the 3 types of redshift and their causes.)
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| * Lineweaver, Charles H. and Tamara M. Davis, "[http://www.sciam.com/article.cfm?chanID=sa006&colID=1&articleID=0009F0CA-C523-1213-852383414B7F0147 Misconceptions about the Big Bang]", ''[[Scientific American]]'', March 2005. (This article is useful for explaining the cosmological redshift mechanism as well as clearing up misconceptions regarding the physics of the expansion of space.)
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| ===Book references===
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| * {{cite book | last=Nussbaumer|first=Harry|coauthors=and Lydia Bieri|title=Discovering the Expanding Universe|publisher=Cambridge University Press|year=2009|isbn=978-0-521-51484-2}}
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| * {{cite book | last=Binney|first=James|coauthors=and Michael Merrifeld|title=Galactic Astronomy|publisher=Princeton University Press|year=1998|isbn=0-691-02565-7}}
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| * {{cite book | author=Carroll, Bradley W. and Dale A. Ostlie| title=An Introduction to Modern Astrophysics| publisher=Addison-Wesley Publishing Company, Inc.| year=1996| isbn=0-201-54730-9}}
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| * {{cite book | author=Feynman, Richard; Leighton, Robert; Sands, Matthew | title=[[The Feynman Lectures on Physics|Feynman Lectures on Physics]]. Vol. 1 | publisher=Addison-Wesley | year=1989 | isbn=0-201-51003-0}}
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| * {{cite book | last = Grøn | first = Øyvind |authorlink=Øyvind Grøn| coauthors = Hervik, Sigbjørn | title = Einstein's General Theory of Relativity | location = New York | publisher = Springer | year = 2007 | isbn = 978-0-387-69199-2}}
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| * {{cite book | author=Kutner, Marc | title=Astronomy: A Physical Perspective | publisher=Cambridge University Press | year=2003 | isbn=0-521-52927-1}}
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| * {{cite book | last = Misner | first = Charles | coauthors = Thorne, Kip S. and Wheeler, John Archibald | title = Gravitation | location = San Francisco | publisher = W. H. Freeman | year = 1973 | isbn = 0-7167-0344-0}}
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| * {{cite book | first = P. J. E. | last = Peebles | title = Principles of Physical Cosmology | publisher = Princeton University Press | year = 1993 | isbn = 0-691-01933-9 }}
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| * {{cite book | author=Taylor, Edwin F.; [[John Archibald Wheeler|Wheeler, John Archibald]] | title=Spacetime Physics: Introduction to Special Relativity (2nd ed.) | publisher=W.H. Freeman | year=1992 | isbn=0-7167-2327-1}}
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| * {{cite book | first = Steven | last = Weinberg | title = Gravitation and Cosmology | publisher = John Wiley | year = 1971 | isbn = 0-471-92567-5}}
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| * See also [[physical cosmology#Textbooks|physical cosmology textbooks]] for applications of the cosmological and gravitational redshifts.
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| ==External links==
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| {{Commons|Redshift}}
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| * [http://www.astro.ucla.edu/~wright/doppler.htm Ned Wright's Cosmology tutorial]
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| * [http://coolcosmos.ipac.caltech.edu/cosmic_classroom/cosmic_reference/redshift.html Cosmic reference guide entry on redshift]
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| * [http://www.asterism.org/tutorials/tut29-1.htm Mike Luciuk's Astronomical Redshift tutorial]
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| * [http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/Images/hu_animexp.gif Animated GIF of Cosmological Redshift] by Wayne Hu
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| * {{cite web|last1=Merrifield|first1=Michael|last2=Hill|first2=Richard|title=Z Redshift|url=http://www.sixtysymbols.com/videos/redshift.htm|work=SIXTψ SYMBΦLS|year=2009|publisher=[[Brady Haran]] for the [[University of Nottingham]]}}
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| {{featured article}}
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| [[Category:Astronomical spectroscopy]]
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| [[Category:Doppler effects]]
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| [[Category:Physical cosmology]]
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| [[Category:Physical quantities]]
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| {{Link GA|zh}}
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| {{Link FA|ro}}
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