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{{short description|Change of wavelength in photons during travel}}
] of ]s in the ] of a supercluster of distant galaxies (right), as compared to that of the Sun (left).]]
{{About|the astronomical phenomenon||}}
:''This article is about the optical phenomenon. For the photochemical usage, see ]. For other uses of the phrase "Red Shift", see ].''
] in the ] of a ] of distant galaxies (right), as compared to absorption lines in the visible spectrum of the ] (left). Arrows indicate redshift. Wavelength increases up towards the red and beyond (frequency decreases).]]
{{General relativity sidebar}}
{{Physical cosmology}}
{{Special relativity sidebar}}
In ], a '''redshift''' is an increase in the ], and corresponding decrease in the ] and ], of ] (such as ]). The opposite change, a decrease in wavelength and increase in frequency and energy, is known as a ], or negative redshift. The terms derive from the colours ] and ] which form the extremes of the ]. The main causes of electromagnetic redshift in ] and ] are the relative motions of radiation sources, which give rise to the ], and gravitational potentials, which ] escaping radiation. All sufficiently distant light sources show ] corresponding to recession speeds proportional to their distances from Earth, a fact known as ] that implies the ].


All redshifts can be understood under the umbrella of ]. ]s, which also travel at ], are subject to the same redshift phenomena.<ref>{{cite journal | title=Detectability of primordial black hole binaries at high redshift | last=Ding | first=Qianhang | journal=Physical Review D | volume=104 | issue=4 | at=id. 043527 | date=August 2021 | doi=10.1103/PhysRevD.104.043527 | arxiv=2011.13643 | bibcode=2021PhRvD.104d3527D }}</ref> The value of a redshift is often denoted by the letter {{math|''z''}}, corresponding to the fractional change in wavelength (positive for redshifts, negative for blueshifts), and by the wavelength ratio {{math|1 + ''z''}} (which is greater than 1 for redshifts and less than 1 for blueshifts).
In ] and ], '''redshift''' is an observed increase in the ] of ] received by a detector compared to that ] by the source. For ], ] is the ] with the longest wavelength, so colors experiencing redshift shift towards the red part of the ]. The phenomenon goes by the same name even if it occurs at non-optical wavelengths (in fact, longer-wavelength radiation "redshifts" ''away'' from red). The corresponding shift to shorter wavelengths is called ].


Examples of strong redshifting are a ] perceived as an ], or initially visible light perceived as ]s. Subtler redshifts are seen in the ] observations of ] objects, and are used in terrestrial technologies such as ] and ]s.
] redshift occurs, for example, when a light source moves away from an observer in an analogous but not equivalent fashion to a ] of ] from a receding object. Redshift is used as a diagnostic in ] astrophysics to determine information about the ] and ] of distant objects. Most famously, redshifts are observed in the spectra from distant ], ], and ] to increase proportionally with the ] to the object. Astronomers consider this to be one of the major forms of evidence that ], supporting the ] model.


Other physical processes exist that can lead to a shift in the frequency of electromagnetic radiation, including ] and ]; however, the resulting changes are distinguishable from (astronomical) redshift and are not generally referred to as such (see section on ]).
== The relative change in wavelength ''z'' ==


==History==
A redshift (or blueshift) may be characterized by the difference between the observed and emitted wavelengths. In astronomy it is customary to refer to the ''relative'' change in wavelength, a ] quantity called ''z'' and defined by the equation
The history of the subject began in the 19th century, with the development of classical ] mechanics and the exploration of phenomena which are associated with the ]. The effect is named after the ] mathematician, ], who offered the first known physical explanation for the phenomenon in 1842.<ref>
{{cite book
|last=Doppler | first=Christian
|date=1846
|title=Beiträge zur fixsternenkunde
|location=Prague |publisher=G. Haase Söhne
|bibcode=1846befi.book.....D
|volume=69
}}</ref> In 1845, the hypothesis was tested and confirmed for ]s by the ] scientist ].<ref>
{{cite book
|last=Maulik | first=Dev
|chapter=Doppler Sonography: A Brief History
|chapter-url=https://books.google.com/books?id=HedeGJms0n4C&q=%22Ballot%22&pg=PA3
|editor1-last=Maulik | editor1-first=Dev
|editor2-last=Zalud | editor2-first=Ivica
|date=2005
|title=Doppler Ultrasound in Obstetrics And Gynecology
|url= https://www.springer.com/west/home/medicine/gynecology?SGWID=4-10066-22-46625046-0
|isbn=978-3-540-23088-5
|publisher=Springer
}}</ref> Doppler correctly predicted that the phenomenon would apply to all waves and, in particular, suggested that the varying ]s of ]s could be attributed to their motion with respect to the Earth.<ref>
{{cite web
|last1=O'Connor | first1=John J.
|last2=Robertson | first2=Edmund F.
|date=1998
|url=http://www-history.mcs.st-andrews.ac.uk/Biographies/Doppler.html
|title=Christian Andreas Doppler
|work=]
|publisher=]
}}</ref> Before this was verified, it was found that stellar colors were primarily due to a star's ], not motion. Only later was Doppler vindicated by verified redshift observations.{{cn|date=March 2023}}


The Doppler redshift was first described by French physicist ] in 1848, who noted the shift in ]s seen in stars as being due to the Doppler effect. The effect is sometimes called the "Doppler–Fizeau effect". In 1868, British astronomer ] was the first to determine the velocity of a star moving away from the Earth by the method.<ref name=Huggins>
:<math>z = \frac{\lambda_{\mathrm{observed}} - \lambda_{\mathrm{emitted}}}{\lambda_{\mathrm{emitted}}},</math>
{{cite journal
|last=Huggins | first=William
|date=1868
|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
|journal=]
|volume= 158 |pages=529–564
|bibcode=1868RSPT..158..529H
|doi=10.1098/rstl.1868.0022
}}</ref> In 1871, optical redshift was confirmed when the phenomenon was observed in ], using solar rotation, about 0.1 Å in the red.<ref>
{{cite journal
|last=Reber | first=G.
|date=1995
|title=Intergalactic Plasma
|journal=]
|volume=227
|issue=1–2 |pages=93–96
|doi=10.1007/BF00678069
|bibcode=1995Ap&SS.227...93R
|s2cid=30000639
}}</ref> 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 |date=1961|publisher=Dover|page=451|isbn=978-0-486-65994-7}}</ref> In 1901, ] verified optical redshift in the laboratory using a system of rotating mirrors.<ref>
{{cite journal
|last=Bélopolsky | first=A.
|date=1901
|bibcode=1901ApJ....13...15B
|title=On an Apparatus for the Laboratory Demonstration of the Doppler-Fizeau Principle
|journal=]
|volume=13 |page=15
|doi=10.1086/140786
|doi-access=free
}}</ref>


] used the term "red-shift" as early as 1923,<ref>{{Cite book |last=Eddington |first=Arthur Stanley |url=https://books.google.com/books?id=errkj2WXGzIC&pg=PA164 |title=The Mathematical Theory of Relativity |date=1923 |publisher=The University Press |page=164 |language=en |author-link=Arthur Eddington}}</ref><ref>{{Cite OED|term=redshift|id=160477|access-date=2023-03-17}}</ref> although the word does not appear unhyphenated until about 1934, when ] used it.<ref>
where <math>\lambda</math> is the wavelength of electromagnetic radiation.
{{cite journal
|last=de Sitter | first=W.
|date=1934
|title=On distance, magnitude, and related quantities in an expanding universe
|journal=]
|volume=7 |page=205
|bibcode=1934BAN.....7..205D
|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
}}</ref>


Beginning with observations in 1912, ] discovered that most ], then mostly thought to be ], had considerable redshifts. Slipher first reported on his measurement in the inaugural volume of the ''] Bulletin''.<ref>
One advantage of using ''z'' is that it is independent of the wavelength observed for Doppler-like redshifts (]), which is the most common usage of the term redshift.
{{cite journal
|last=Slipher | first=Vesto
|date=1912
|title=The radial velocity of the Andromeda Nebula
|journal=]
|volume=1 |issue=8
|pages=2.56–2.57
|bibcode=1913LowOB...2...56S
|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
}}</ref> Three years later, he wrote a review in the journal '']''.<ref>
{{cite journal
|last=Slipher | first=Vesto
|title=Spectrographic Observations of Nebulae
|journal=]
|volume=23 |pages=21–24 |date=1915
|bibcode=1915PA.....23...21S
}}</ref> In it he stated that "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>
{{cite journal |last=Slipher | first=Vesto |date=1915 |title=Spectrographic Observations of Nebulae |journal=] |volume=23 |page=22 |bibcode=1915PA.....23...21S}}</ref>


Slipher reported the velocities for 15 spiral nebulae spread across the entire ], all but three having observable "positive" (that is recessional) velocities. Subsequently, ] discovered an approximate relationship between the redshifts of such "nebulae", and the ]s to them, with the formulation of his eponymous ].<ref>
The increase in wavelength of a photon subjected to a redshift corresponds to a decrease in its ],
{{cite journal
|doi=10.1073/pnas.15.3.168
|last=Hubble |first=Edwin
|date=1929
|bibcode=1929PNAS...15..168H
|title=A Relation between Distance and Radial Velocity among Extra-Galactic Nebulae
|journal=]
|volume=15 |issue=3 |pages=168–173
|pmid=16577160
|pmc=522427
|doi-access=free
}}</ref> ] worked on those observations with Hubble.<ref>{{Cite web|url=https://imagine.gsfc.nasa.gov/educators/programs/cosmictimes/online_edition/1929/expanding.html|title=Universe is Expanding|date=2017-12-08|access-date=2023-09-06}}</ref> These observations corroborated ]'s 1922 work, in which he derived the ].<ref>{{cite journal
|last=Friedman |first=A. A.
|date=1922
|title=Über die Krümmung des Raumes
|journal=]
|volume=10
|issue=1 |pages=377–386
|doi=10.1007/BF01332580
|bibcode = 1922ZPhy...10..377F |s2cid=125190902
}} English translation in {{cite journal |title=On the Curvature of Space|doi=10.1023/A:1026751225741 |last=Friedman |first=A. |date=1999 |journal=] |volume=31 |issue=12 |pages=1991–2000 |bibcode=1999GReGr..31.1991F|s2cid=122950995 }})</ref> They are now considered to be strong evidence for an ] and the ] 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
|last=Eddington |first=Arthur | author-link=Arthur Eddington
|date=1933
|title=The Expanding Universe: Astronomy's 'Great Debate', 1900–1931
|url=https://archive.org/details/in.ernet.dli.2015.220736
|publisher=]
}} (Reprint: {{ISBN|978-0-521-34976-5}})</ref>


==Measurement, characterization, and interpretation==
:<math>z = \frac{f_{\mathrm{emitted}} - f_{\mathrm{observed}}}{f_{\mathrm{observed}}},</math>
], 2012<ref>{{cite news|title=Hubble census finds galaxies at redshifts 9 to 12|url=https://esahubble.org/news/heic1219/|access-date=13 December 2012|newspaper=ESA/Hubble Press Release}}</ref> ]]


The ] of light that comes from a source (see idealized spectrum illustration top-right) can be measured. To determine the redshift, one searches for features in the spectrum such as ], ], or other variations in light intensity<!--Don't link to disambiguation page-->. 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 ] in space is ].
where <math>f</math> is the frequency of electromagnetic radiation.


The spectrum of originally featureless light shone through hydrogen will show a ] 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.
Sometimes it is preferable to use the form


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 traveling 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 ] (random fluctuations in a spectrum).<ref>See, for example, this 25 May 2004 from ]'s ] ] that is researching ]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>
:<math>1+z = \frac{\lambda_{\mathrm{observed}}}{\lambda_{\mathrm{emitted}}} = \frac{f_{\mathrm{emitted}}}{f_{\mathrm{observed}}}.</math>


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 ] called {{math|''z''}}. If {{math|''λ''}} represents wavelength and {{math|''f''}} represents frequency (note, {{math|''λf'' {{=}} ''c''}} where {{math|''c''}} is the ]), then {{math|''z''}} is defined by the equations:<ref>For a tutorial on how to define and interpret large redshift measurements, see:<br />{{cite web
== Redshift mechanisms ==
| title=Extragalactic Redshifts
| first=John
| last=Huchra
| publisher=Harvard-Smithsonian Center for Astrophysics
| website=NASA/IPAC Extragalactic Database
| url=http://ned.ipac.caltech.edu/help/zdef.html
| access-date=2023-03-16
| archive-date=2013-12-22
| archive-url=https://web.archive.org/web/20131222052715/http://ned.ipac.caltech.edu/help/zdef.html
}}</ref>


{| class="wikitable" style="margin:auto;"
A single ] propagated through a ] can redshift in three distinct ways. Each of these mechanisms produces a Doppler-like redshift, meaning that ''z'' is independent of wavelength. These mechanisms are all due to ], ], or ] between one ] and another.
|+ '''Calculation of redshift, <math>z</math>'''
! '''Based on wavelength''' !! '''Based on frequency'''
|- align=center
| <math>z = \frac{\lambda_{\mathrm{obsv}} - \lambda_{\mathrm{emit}}}{\lambda_{\mathrm{emit}}}</math>
| <math>z = \frac{f_{\mathrm{emit}} - f_{\mathrm{obsv}}}{f_{\mathrm{obsv}}}</math>
|- align=center
| <math>1+z = \frac{\lambda_{\mathrm{obsv}}}{\lambda_{\mathrm{emit}}}</math>
| <math>1+z = \frac{f_{\mathrm{emit}}}{f_{\mathrm{obsv}}}</math>
|}


After {{math|''z''}} is measured, the distinction between redshift and blueshift is simply a matter of whether {{math|''z''}} is positive or negative. For example, ] blueshifts ({{math|''z'' < 0}}) are associated with objects approaching (moving closer to) the observer with the light shifting to greater ]. Conversely, Doppler effect redshifts ({{math|''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 ] as observed from within a stronger gravitational field, while gravitational redshifting implies the opposite conditions.
=== Doppler effect ===


== Redshift formulae ==
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 ] (''z'' < 0) occurs. This is true for all electromagnetic waves and is explained by the ]. Consequently, this type of redshift is also called the ''Doppler redshift''. If the source moves away from the observer with ] ''v'', then, ignoring relativistic effects, the redshift is given by
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 {{math|''z''}}) is independent of the wavelength.<ref name="basicastronomy">See Binney and Merrifeld (1998), Carroll and Ostlie (1996), Kutner (2003) for applications in astronomy.</ref>


{| class="wikitable" style="max-width:1000px;"
:<math>z \approx \frac{v}{c}</math>
|+ '''Redshift summary'''
! Redshift type !! Geometry !! Formula<ref>Where z = redshift; v<sub>||</sub> = ] parallel to line-of-sight (positive if moving away from receiver); c = ]; ''γ'' = ]; ''a'' = ]; G = ]; M = object ]; r = ], g<sub>tt</sub> = t,t component of the ]</ref>
|-
| ]|| ]<br />(flat spacetime) ||
For motion completely in the radial or<br />line-of-sight direction:


:<math>1 + z = \gamma \left(1 + \frac{v_{\parallel}}{c}\right) = \sqrt{\frac{1+\frac{v_{\parallel}}{c}}{1-\frac{v_{\parallel}}{c}}}</math>
where ''c'' is the ]. For a more complete discussion on the origin of the frequency shift, see the article on the ]. In the classical Doppler effect, the frequency of the source is not modified, but the recessional motion causes the illusion of a lower frequency.
:<math>z \approx \frac{v_{\parallel}}{c}</math> &ensp;for&nbsp;small <math>v_{\parallel}</math>


<br />
=== Expansion of space ===
For motion completely in the transverse direction:


:<math>1 + z=\frac{1}{\sqrt{1-\frac{v_\perp^2}{c^2}}}</math>
An effect very similar to the Doppler effect is caused by the ] predicted by the current models of ]. Again, the properties of the source are not modified, but the photons will be stretched as the space through which it is traveling expands, which increases the wavelength. This effect is predicted by ] as an observable manifestation of the time-dependent cosmic ] (<math>a</math>) in the following way:
:<math>z \approx \frac{1}{2} \left( \frac{v_{\perp}}{c} \right)^2</math> &ensp;for&nbsp;small <math>v_{\perp}</math>


|-
:<math>1+z = \frac{a_{\mathrm{now}}}{a_{\mathrm{then}}}.</math>
| ]|| ]<br />(expanding Big Bang universe) ||
:<math>1 + z = \frac{a_{\mathrm{now}}}{a_{\mathrm{then}}}</math>


]:
This type of redshift is also called the '']'' or ''Hubble redshift''. If the Universe were contracting instead of expanding, we would see distant galaxies blueshifted by an amount proportional to their distance instead of redshifted. This is relevant to the old conundrum known as ]: if the Universe were static and filled with a uniform distribution of stars, then every line of sight in the sky would end on a star, and the sky would be uniformly bright. (In fact, if the Universe were ''infinitely'' large, then by this reasoning, the entire sky would be as bright as the surface of a star.) However, the night sky is largely dark. Since the ], astronomers and other thinkers have proposed many possible ways to resolve this paradox, of which the currently accepted standard depends upon the ] theory. If the universe has existed for only a finite amount of time, as this theory holds, then only the light of finitely many stars has had a chance to reach us yet, and the paradox breaks down. Alternatively, if the universe is expanding and distant stars are receding from us (also a key prediction of the theory), then their light is redshifted which diminishes their brightness, again resolving the paradox. Either effect alone would resolve the paradox, but according to the Big Bang theory, both effects contribute (the finite duration of the Universe's history being usually judged the more important of the two). The darkness of the night sky, then, provides confirmation for the Big Bang. {{ref|Chase}}


:<math>z \approx \frac{H_0 D}{c}</math> &ensp;for <math>D \ll \frac{c}{H_0}</math>
While this redshift of distant galaxies closely resembles what would be seen if distant galaxies simply had recessional velocities, in ] stretching of spacetime is different from the physical movement of the source. These galaxies are not believed to be receding; instead, the intervening space is believed to be stretching, which is subtly different. Nevertheless, astronomers (especially professional ones) sometimes refer to "recession velocity" in the context of the redshifting of distant galaxies from the expansion of the Universe, even though it is only an apparent recession. More mathematically, the viewpoint that "distant galaxies are receding" and the viewpoint that "the space between galaxies is expanding" are related by changing ]s. Expressing this precisely requires working with the mathematics of the ]. {{ref|Weiss}}


|-
=== Relativistic effects ===
| ]|| any ] ||
:<math>1 + z = \sqrt{\frac{g_{tt}(\text{receiver})}{g_{tt}(\text{source})}}</math>
For the ]:


:<math>1 + z = \sqrt{\frac{1 - \frac{r_S}{r_{\text{receiver}}}}{1 - \frac{r_S}{r_{\text{source} }}}} = \sqrt{\frac{1 - \frac{2GM}{ c^2 r_{\text{receiver}}}}{1 - \frac{2GM}{ c^2 r_{\text{source} }}}} </math>
In a third class of redshifts, the frequency of the source is lowered by relativistic effects. One possibility is the ] of ], which introduces the ] <math>\gamma</math> into the classical Doppler formula,

:<math>z \approx \frac{1}{2} \left( \frac{r_S}{r_\text{source}} - \frac{r_S}{r_\text{receiver}} \right)</math> &ensp;for <math>r \gg r_S</math>

In terms of ]:

:<math>z \approx \frac{1}{2} \left(\frac{v_\text{e}}{c}\right)_\text{source}^2 - \frac{1}{2} \left(\frac{v_\text{e}}{c}\right)_\text{receiver}^2 </math>
for <math>v_\text{e} \ll c</math>

|}

===Doppler effect===
{{Main|Doppler effect|Relativistic Doppler effect}}
], yellow (~575 ] wavelength) ball appears greenish (blueshift to ~565 nm wavelength) approaching observer, turns ] (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 5,200 ], or about 32 times faster than the speed record for the ].]]
]

If a source of the light is moving away from an observer, then redshift ({{math|''z'' > 0}}) occurs; if the source moves towards the observer, then ] ({{math|''z'' < 0}}) occurs. This is true for all electromagnetic waves and is explained by the ]. Consequently, this type of redshift is called the ''Doppler redshift''. If the source moves away from the observer with ] {{math|''v''}}, which is much less than the speed of light ({{math|''v'' ≪ ''c''}}), the redshift is given by

:<math>z \approx \frac{v}{c}</math> &nbsp; &nbsp; (since <math>\gamma \approx 1</math>)

where {{math|''c''}} is the ]. In the classical Doppler effect, the frequency of the source is not modified, but the recessional motion causes the illusion of a lower frequency.

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 ]. In brief, objects moving close to the speed of light will experience deviations from the above formula due to the ] of ] which can be corrected for by introducing the ] {{math|''γ''}} into the classical Doppler formula as follows (for motion solely in the line of sight):


:<math>1 + z = \left(1 + \frac{v}{c}\right) \gamma.</math> :<math>1 + z = \left(1 + \frac{v}{c}\right) \gamma.</math>


which was first observed in a 1938 experiment performed by Herbert E. Ives and G.R. Stilwell, called the Ives-Stilwell experiment {{ref|Ives}}. This phenomenon was first observed in a 1938 experiment performed by Herbert E. Ives and G.R. Stilwell, called the ].<ref>{{cite journal | last1 = Ives | first1 = H. | last2 = Stilwell | first2 = G. | year = 1938 | title = An Experimental study of the rate of a moving atomic clock | journal = Journal of the Optical Society of America | volume = 28 | issue = 7| pages = 215–226 | doi=10.1364/josa.28.000215 | bibcode = 1938JOSA...28..215I}}</ref>
For the special case that the source is moving at right angles to the detector, the relativistic redshift is known as the ].


Since the Lorentz factor is dependent only on the ] 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 ] of the movement of the source into the ] which yields different results for different orientations. If {{math|''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|date=2008|publisher=World Scientific|page=120|isbn=978-981-277-160-5}}</ref> (zero angle is directly away from the observer), the full form for the relativistic Doppler effect becomes:
] due to a ].]]


:<math>1+ z = \frac{1 + v \cos (\theta)/c}{\sqrt{1-v^2/c^2}}</math>
In the theory of ], there is also time dilation within a gravitational well. This is known as the ] or ''Einstein Shift''. The effect is very small but measurable on Earth using the ] and was first observed in the ] {{ref|Poundrebka}}. However, it is significant near a ], and as an object approaches the ], the red shift becomes infinite. It is also the dominant cause of large angular-scale temperature fluctuations in the ] (see ]). In the 1970s, science historians discovered a letter dated 1784 from ], a natural philosopher and geologist, to scientist ], in which he considers the effect of a heavenly object massive enough to prevent light from escaping (see ]), and using a prism to measure the gravitational weakening of starlight due to the surface gravity of the source. This letter has been considered to be the first prediction of gravitational redshift {{ref|Michell}}.


and for motion solely in the line of sight ({{math|''θ'' {{=}} 0°}}), this equation reduces to:


:<math>1 + z = \sqrt{\frac{1+v/c}{1-v/c}}</math>
=== Coherent interactions with matter ===
{{verify}}
A coherent interaction of ligh beams with matter is an interaction in which the relation between any molecule and the local field is the same. Refraction is the best known coherent interaction, but many coherent interactions are used in laser technology to multiply, combine, shift frequencies. The problem is that getting the coherence requires a relation between the wave vectors which is not easily fulfilled: except for refraction, tricks are needed, such as the use of two indices of refraction in a crystal.


For the special case that the light is moving at ] ({{math|''θ'' {{=}} 90°}}) to the direction of relative motion in the observer's frame,<ref>{{cite book|last=Ditchburn|first=R. |title=Light|date=1961|publisher=Dover|page=329|isbn=978-0-12-218101-6}}</ref> the relativistic redshift is known as the ], and a redshift:
The CREIL effect is a coherent interaction between ordinary, time-incoherent light beams refracted by a matter for which the light pulses are "ultrashort", that is "shorter than all relevant time constants" , the collisional time and a Raman type resonance. In astrophysics, neutral atomic hydrogen in the states 2P or 2S works, maybe H2+ has a secondary role.


:<math>1 + z = \frac{1}{\sqrt{1-v^2/c^2}}</math>
The increase of entropy of the set of beams interacting in a CREIL effect produces a decrease of the frequency of the beams whose temperature (deduced from Planck's law) is high (redshift), while the frequencies of cold beams are increased (blueshifts). The refracting medium is only temporarily excited (to a non-stationary state).


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>
The CREIL effect may be considered as a set of simultaneous coherent Raman scatterings such that, each incident beam and the corresponding scattered beams interfere locally into a single emergent beam. It is the origin of the acronym CREIL : space-Coherent Raman Effect on time-Incoherent Light. Evidently, the sum of the exchanges of energy with matter is zero.
See " {{Webarchive|url=https://web.archive.org/web/20060827063802/http://www.physics.uq.edu.au/people/ross/phys2100/doppler.htm |date=2006-08-27 }} " at the University of Queensland
</ref>


===Cosmic expansion===
Using the CREIL effect is powerful: look for excited (2P, 2S) hydrogen, you find anomalous frequency shifts. This hydrogen is produced usually:
{{Main|Expansion of the universe}}
In the earlier part of the twentieth century, Slipher, Wirtz and others made the first measurements of the redshifts and blueshifts of galaxies beyond the ]. They initially interpreted these redshifts and blueshifts as being due to random motions, but later Lemaître (1927) and Hubble (1929), using previous data, discovered a roughly linear correlation between the increasing redshifts of, and distances to, galaxies. Lemaître realized that these observations could be explained by a mechanism of producing redshifts seen in Friedmann's solutions to ] of ]. The correlation between redshifts and distances arises in all expanding models.<ref name=Eddington/>


This ] is commonly attributed to stretching of the wavelengths of photons propagating through the expanding space. This interpretation can be misleading, however; expanding space is only a choice of ] and thus cannot have physical consequences. The cosmological redshift is more naturally interpreted as a Doppler shift arising due to the recession of distant objects.<ref name="Hogg">{{cite journal |author=Bunn |first1=E. F. |last2=Hogg |first2=D. W. |year=2009 |title=The kinematic origin of the cosmological redshift |journal=American Journal of Physics |volume=77 |issue=8 |pages=688–694 |arxiv=0808.1081 |bibcode=2009AmJPh..77..688B |doi=10.1119/1.3129103 |s2cid=1365918}}</ref>
-a) thermally (100 000 K) if the pressure is high enough to forbid a full ionization,


The observational consequences of this effect can be derived using ] from ] that describe a ]. The cosmological redshift can thus be written as a function of {{math|''a''}}, the time-dependent cosmic ]:
-b) at 10 000 K by a Lyman α pumping (2P)


:<math>1+z = \frac{a_\mathrm{now}}{a_\mathrm{then}}</math>
-c) by a cooling of a plasma of hydrogen (mainly metastable 2S).


In an expanding universe such as the one we inhabit, the scale factor is ] as time passes, thus, {{math|''z''}} is positive and distant galaxies appear redshifted.
Case a) explains the very different shift between the sharp emission lines of the quasars and the other lines.


Using a model of the expansion of the universe, redshift can be related to the age of an observed object, the so-called '']–redshift relation''. Denote a density ratio as {{math|Ω<sub>0</sub>}}:
Case c) explains the "anomalous acceleration" of the Pioneer 10 and 11 probes which reach, beyond 5 UA a region where the solar wind cools, producing hydrogen atoms able to transfer energy from the solar light to the radiowaves. It explains that the anisotropy of the microwave background is bound to the ecliplic by blueshift beyond 5 UA, as the wind is.


:<math>\Omega_0 = \frac {\rho}{ \rho_\text{crit}} \ , </math>
Case b) is the most common case; for instance, the light from the quasars pumps hydrogen to the 2P state, producing the "proximity effect", the "very red objects".


with {{math|''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 cubic meter of space.<ref Name=Weinberg>{{cite book |first=Steven | last=Weinberg |edition=2nd |title=The First Three Minutes: A Modern View of the Origin of the Universe | page=34 |isbn=9780-465-02437-7 |date=1993 |publisher=Basic Books|title-link=The First Three Minutes: A Modern View of the Origin of the Universe }}</ref> At large redshifts, {{math| ''1 + z'' > Ω<sub>0</sub><sup>−1</sup>}}, one finds:
Case b) is at the origin of a nonlinear effect: suppose a far UV continuous spectrum propagates in neutral atomic hydrogen in its ground state. The Ly α pumping produces 2P hydrogen which redshifts the spectrum, renewing the energy at the Ly α frequency, so that the redshift is permanent, the spectral lines of the gas are written with the width of the redshift, wide and weak, invisible. Suppose that an absorption line was written previously in the spectrum; when it is shifted to the Ly α frequency, the redshift stops, all lines are strongly written. But the states populated by the Ly β, γ, δ,... absorptions decay to the 2S, 2P states, so that the redshift restart. The written Ly β and Ly γ come to the Ly α frequency for redshifts z = 3*0.062 and 4*0.062 respectively, so that the frequently observed periodicity z = 0.062 appears.


:<math> t(z) \approx \frac {2}{3 H_0 {\Omega_0}^{1/2} } z^{-3/2}\ , </math>
The CREIL allows a full interpretation of the spectrum of the quasars, which appear as micro-quasars surrounded by hydrogen while they leave the galaxy where they are born.


where {{math|''H''<sub>0</sub>}} is the present-day ], and {{math|''z''}} is the redshift.<ref name="Bergström">{{cite book |title=Cosmology and Particle Astrophysics |url=https://books.google.com/books?id=CQYu_sutWAoC&pg=PA77 |page=77, Eq.4.79 |isbn=978-3-540-32924-4 |publisher=Springer |edition=2nd|date=2006|first1 = Lars |last1=Bergström|first2 = Ariel |last2=Goobar|author-link1=Lars Bergström (physicist) |author-link2=Ariel Goobar }}</ref><ref name = Longair>{{cite book |title=Galaxy Formation |first=M. S. |last=Longair |url=https://books.google.com/books?id=2ARuLT-tk5EC&pg=PA161 |page=161 |isbn=978-3-540-63785-1 |publisher=Springer |date=1998}}</ref>
== Observations in astronomy ==


There are several websites for calculating various times and distances from redshift, as the precise calculations require numerical integrals for most values of the parameters.<ref name="UCLA-2015">{{cite web |author=Staff |title=UCLA Cosmological Calculator |url=http://www.astro.ucla.edu/~wright/ACC.html |date=2015 |work=] |access-date=6 August 2022 }} Light travel distance was calculated from redshift value using the UCLA Cosmological Calculator, with parameters values as of 2015: H<sub>0</sub>=67.74 and Omega<sub>M</sub>=0.3089 (see Table/Planck2015 at "]" )</ref><ref name="UCLA-2018">{{cite web |author=Staff |title=UCLA Cosmological Calculator |url=http://www.astro.ucla.edu/~wright/ACC.html |date=2018 |work=] |access-date=6 August 2022 }} Light travel distance was calculated from redshift value using the UCLA Cosmological Calculator, with parameters values as of 2018: H<sub>0</sub>=67.4 and Omega<sub>M</sub>=0.315 (see Table/Planck2018 at "]" )</ref><ref name="ICRAR-2022">{{cite web |author=Staff |title=ICRAR Cosmology Calculator |url=https://cosmocalc.icrar.org/ |date=2022 |work=] |access-date=6 August 2022 }} ICRAR Cosmology Calculator - Set H<sub>0</sub>=67.4 and Omega<sub>M</sub>=0.315 (see Table/Planck2018 at "]")</ref><ref name="KEMP-2022">{{cite web |last=Kempner |first=Joshua |title=KEMPNER Cosmology Calculator |url=https://www.kempner.net/cosmic.php |date=2022 |work=Kempner.net |access-date=6 August 2022 }} KEMP Cosmology Calculator - Set H<sub>0</sub>=67.4, Omega<sub>M</sub>=0.315, and Omega<sub>Λ</sub>=0.6847 (see Table/Planck2018 at "]")</ref>
The redshift observed in astronomy can be measured because the ] and ] spectra for ] are distinctive and well known, calibrated from ] in ] 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. (See ]) Furthermore, distant objects are not blurred, and the lines are not broadened more than can be explained by thermal or 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 (for example, ] and other suggestions from ]) are not generally considered plausible.


====Distinguishing between cosmological and local effects====
=== Local observations ===
For cosmological redshifts of {{math|''z'' < 0.01}} additional Doppler redshifts and blueshifts due to the ] of the galaxies relative to one another cause a wide ] from the standard ].<ref>Measurements of the peculiar velocities out to 5 ] using the ] were reported in 2003 by {{cite journal
| title=Local galaxy flows within 5 Mpc
| last1=Karachentsev | first1=I. D. | last2=Makarov | first2=D. I.
| last3=Sharina | first3=M. E. | last4=Dolphin | first4=A. E.
| last5=Grebel | first5=E. K. | last6=Geisler | first6=D.
| last7=Guhathakurta | first7=P. | last8=Hodge | first8=P. W.
| last9=Karachentseva | first9=V. E. | last10=Sarajedini | first10=A.
| last11=Seitzer | first11=P. | display-authors=1
| journal=]
| volume=398 | issue=2 | pages=479–491 | year=2003
| doi=10.1051/0004-6361:20021566 | bibcode=2003A&A...398..479K
| s2cid=26822121 | arxiv=astro-ph/0211011
}}</ref> The resulting situation can be illustrated by the ], a common cosmological analogy used to describe the expansion of the universe. 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 | first1=Theo | last1=Koupelis | first2=Karl F. | last2=Kuhn |edition=5th |url=https://archive.org/details/inquestofunivers00koup |url-access=registration |page= |publisher=Jones & Bartlett Publishers |date=2007 |isbn=978-0-7637-4387-1}}</ref><ref name=Lewis>{{cite journal | quote=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. |title=Cosmological Radar Ranging in an Expanding Universe |arxiv=0805.2197 |journal=] | first1=Geraint F. | last1=Lewis |date=2008 |pages=960–964 |issue=3 |volume=388 |doi=10.1111/j.1365-2966.2008.13477.x |bibcode=2008MNRAS.388..960L|display-authors=4|last2=Francis |first2=Matthew J. |last3=Barnes |first3=Luke A. |last4=Kwan |first4=Juliana |last5=James |first5=J. Berian |doi-access=free |s2cid=15147382 }}</ref><ref name=Chodorowski>{{Cite journal | first=Michal | last=Chodorowski |title=Is space really expanding? A counterexample |date=2007 |arxiv=astro-ph/0601171 |journal=Concepts Phys |volume=4 |issue=1 |pages=17–34|bibcode = 2007ONCP....4...15C |doi = 10.2478/v10005-007-0002-2 |s2cid=15931627 }}</ref>


The redshifts of galaxies include both a component related to ] from expansion of the universe, and a component related to ] (Doppler shift).<ref>{{cite journal
In nearby objects (within our ] ]) observed redshifts are almost always related to the ] velocities associated with the objects being observed. Observations of such redshifts and blueshifts have enabled astronomers to measure ] and parametrize the ]es of the ]ing ]s in ], a method first employed in ] by British astronomer ]. Similarly, small redshifts and blueshifts detected in the spectroscopic measurements of individual stars are one way astronomers have been able to ] the presence and characteristics of ] around other stars. Measurements of redshifts to fine detail are also used in ] to determine the precise movements of the ] of the ]. Redshifts have also been used to measure the velocity of gas of ], the ], and the ] of ] onto ]s and ]s which exhibit both Doppler and gravitational redshifts. Additionally, the ]s of various emitting and absorbing objects can be obtained by measuring ] — effectively redshifts and blueshifts over a single emission or absorption line. By measuring the broadening and shifts of the 21-centimeter ] in different directions, astronomers have been able to measure the recessional velocities of ], which in turn reveals the ] of our ]. Similar measurements have also been performed on other galaxies, such as ]. As a diagnostic tool, measuring redshifts is one of the most important ] made in astronomy.
| title=A comparison between the Doppler and cosmological redshifts
| last=Bedran | first=M. L. | year=2002
| journal=American Journal of Physics
| volume=70 | issue=4 | pages=406–408
| doi=10.1119/1.1446856 | bibcode=2002AmJPh..70..406B
| url=http://www.df.uba.ar/users/sgil/physics_paper_doc/papers_phys/cosmo/doppler_redshift.pdf
| access-date=2023-03-16
}}</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 |last=Harrison |first=Edward |date=1992 |title=The redshift-distance and velocity-distance laws |journal=Astrophysical Journal, Part 1 |volume=403 |pages=28–31 |bibcode=1993ApJ...403...28H |doi=10.1086/172179 |doi-access=free}}. A pdf file can be found here .</ref> Describing the cosmological expansion origin of redshift, cosmologist ] 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=302}}.</ref> ] clarified, "The increase of wavelength from emission to absorption of light does not depend on the rate of change of {{math|''a''(''t'')}} ]] at the times of emission or absorption, but on the increase of {{math|''a''(''t'')}} in the whole period from emission to absorption."<ref name=Weinberg_Cosmology>{{cite book |url=https://books.google.com/books?id=48C-ym2EmZkC&pg=PA11 |first=Steven | last=Weinberg |title=Cosmology |publisher=Oxford University Press |page=11 |date=2008 |isbn=978-0-19-852682-7}}</ref>


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 ]. Otherwise, redshifts combine as
=== Extragalactic observations ===
{{Cosmology}}
The most distant objects exhibit larger redshifts corresponding to the ] of the universe. The largest observed redshift, corresponding to the greatest distance and furthest back in time, is that of the ]; the numerical value of its redshift is about ''z'' = 1089 (''z'' = 0 corresponds to present time), and it shows the state of the Universe about 13.7 billion years ago, and 379,000 years after the initial moments of the ].


:<math>1+z=(1+z_{\mathrm{Doppler}})(1+z_{\mathrm{expansion}})</math>
The luminous point-like cores of ] (]) were the first "high-redshift" (<math>z > 0.1</math>) objects discovered before the improvement of telescopes allowed for the discovery of extended-source high-redshift ]. Currently, the highest measured quasar redshift is <math>z=6.4</math>{{ref|sloan}}, with the highest confirmed galaxy redshift being <math>z=7.0</math>{{ref|egami}} while as-yet unconfirmed reports from a ] observed in a distant ] may indicate a galaxy with a redshift of <math>z=10</math>{{ref|pello}}.
which yields solutions where certain objects that "recede" are blueshifted and other objects that "approach" are redshifted. For more on this bizarre result see: {{cite journal
| last1=Davis | first1=T. M. | last2=Lineweaver | first2=C. H. | last3=Webb | first3=J. K.
| title=Solutions to the tethered galaxy problem in an expanding universe and the observation of receding blueshifted objects
| journal=American Journal of Physics
| volume=71 | issue=4 | pages=358–364
| date=April 2003 | doi=10.1119/1.1528916
| arxiv=astro-ph/0104349 | bibcode=2003AmJPh..71..358D | s2cid=3219383 }}</ref>


===Gravitational redshift===
For galaxies more distant than the ] and the nearby ], but within a thousand ] or so, the redshift is approximately ] to the galaxy's distance. This correlation was first observed by ] and has come to be known as ]. ] was the first to discover galactic redshifts, in about the year ], while Hubble correlated Slipher's measurements with distances he ] to formulate his Law. In the widely accepted cosmological model based on ], 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. ] follows in part from the ]. Measuring the redshift is often easier than more direct distance measurements, so redshift is sometimes in practice converted to a crude distance measurement using ].
{{Main|Gravitational redshift}}
In the theory of ], there is time dilation within a gravitational well. This is known as the ] or ''Einstein Shift''.<ref>{{cite journal | last=Chant | first=C. A. | bibcode = 1930JRASC..24..390C | title = Notes and Queries (Telescopes and Observatory Equipment – The Einstein Shift of Solar Lines) | date = 1930 | journal = ] | volume = 24 | page = 390 }}</ref> The theoretical derivation of this effect follows from the ] of the ] which yields the following formula for redshift associated with a photon traveling in the ] of an ], ], ] mass:


:<math>1+z=\frac{1}{\sqrt{1-\frac{2GM}{rc^2}}},</math>
] of galaxies with each other and clusters cause a significant ] in the normal plot of the Hubble diagram. The ] associated with galaxies superimpose a rough trace of the ] of ] in the universe. This effect leads to such phenomena as nearby galaxies (such as the ]) exhibiting blueshifts as we fall towards a common ], and redshift maps of clusters showing a ] effect due to the spread of peculiar velocities in a roughly spherical distribution. 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 ].


where
For more distant galaxies, the relationship between current distance and observed redshift becomes more complex. When one sees a distant galaxy, one is seeing the galaxy as it was sometime in the past, when the expansion rate of the Universe was different from what it is now. At these early times, we expect differences in the expansion rate for at least two reasons:
* {{math|''G''}} is the ],
* {{math|''M''}} is the ] of the object creating the gravitational field,
* {{math|''r''}} is the radial coordinate of the source (which is analogous to the classical distance from the center of the object, but is actually a ]), and
* {{math|''c''}} is the ].


This gravitational redshift result can be derived from the assumptions of ] and the ]; the full theory of general relativity is not required.<ref>{{cite journal | last = Einstein | first = A. | author-link = Albert Einstein | date = 1907 | title = Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen | journal = Jahrbuch der Radioaktivität und Elektronik | volume = 4 | pages = 411–462 | bibcode=1908JRE.....4..411E}} See p. 458 ''The influence of a gravitational field on clocks''</ref>
#The gravitational attraction between galaxies has been acting to slow down the expansion of the Universe since then.
#The possible existence of a ] may be changing the expansion rate of the Universe.


The effect is very small but measurable on Earth using the ] and was first observed in the ].<ref>{{cite journal | doi = 10.1103/PhysRevLett.4.337 | title = Apparent Weight of Photons | date = 1960 | last1 = Pound | first1 = R. | last2 = Rebka | first2 = G. | journal = Physical Review Letters | volume = 4 | issue = 7 | pages = 337–341 | bibcode=1960PhRvL...4..337P| doi-access = free }}. This paper was the first measurement.</ref> However, it is significant near a ], and as an object approaches the ] the red shift becomes infinite. It is also the dominant cause of large angular-scale temperature fluctuations in the ] radiation (see ]).<ref>{{cite journal | last1=Sachs | first1=R. K. | author-link=Rainer K. Sachs | last2=Wolfe | first2=A. M. | author-link2=Arthur M. Wolfe | date=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>
Recent observations have suggested the expansion of the Universe is not slowing down, as expected from the first point, but accelerating (see ]). It is widely, though not quite universally, believed that this is because there is a form of the ] due to a ] dubbed ]. Such a ] also implies that the ] is not a ], but instead will continue to exist foreseeably (though most physical processes within the Universe will still come to an ]).


==Observations in astronomy==
The expanding Universe is a central prediction of the ] theory. If extrapolated back in time, the theory predicts a "singularity", a point in time when the Universe had infinite density. The theory of ], on which the ] theory is based, breaks down at this point. It is believed that a yet unknown theory of ] would take over before the density becomes infinite.
] of extragalactic observations by their redshift up to z=20.<ref name="Pilipenko">S.V. Pilipenko (2013-2021) arxiv:1303.5961, including upon which the citing charts and formulae are based.</ref> There are websites for calculating many such physical measures from redshift.<ref name="UCLA-2015"/><ref name="UCLA-2018"/><ref name="ICRAR-2022"/><ref name="KEMP-2022"/>]]


The redshift observed in astronomy can be measured because the ] and ] spectra for ]s are distinctive and well known, calibrated from ] experiments in ] on Earth. When the redshift of various absorption and emission lines from a single astronomical object is measured, {{math|''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 ] or mechanical ] 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 ] are not generally considered plausible.<ref name=reboul>When cosmological redshifts were first discovered, ] proposed an effect known as tired light. While usually considered for historical interests, it is sometimes, along with ] suggestions, utilized by ]. In 1981, H. J. Reboul summarised many that had been discussed in the literature since the 1930s. In 2001, ] remarked in a that the wider astronomical community has marginalized such discussions since the 1960s. Burbidge and ], while investigating the mystery of ], tried to develop alternative redshift mechanisms, and very few of their fellow scientists acknowledged let alone accepted their work. Moreover, {{cite journal | title=Timescale Stretch Parameterization of Type Ia Supernova B-Band Lightcurves | first1=G. | last1=Goldhaber | first2=D. E. | last2=Groom | first3=A. | last3=Kim | first4=G. | last4=Aldering | first5=P. | last5=Astier | first6=A. | last6=Conley | first7=S. E. | last7=Deustua | first8=R. | last8=Ellis | first9=S. | last9=Fabbro | first10=A. S. | last10=Fruchter | first11=A. | last11=Goobar | first12=I. | last12=Hook | first13=M. | last13=Irwin | first14=M. | last14=Kim | first15=R. A. | last15=Knop | first16=C. | last16=Lidman | first17=R. | last17=McMahon | first18=P. E. | last18=Nugent | first19=R. | last19=Pain | first20=N. | last20=Panagia | first21=C. R. | last21=Pennypacker | first22=S. | last22=Perlmutter | first23=P. | last23=Ruiz-Lapuente | first24=B. | last24=Schaefe | first25=N. A. | last25=Walton | first26=T. | last26=York | display-authors=1 | year=2001 | journal=Astrophysical Journal | volume=558 | issue=1 | pages=359–386 | doi=10.1086/322460 | arxiv=astro-ph/0104382 | bibcode=2001ApJ...558..359G | s2cid=17237531| doi-access=free }} pointed out that alternative theories are unable to account for timescale stretch observed in ]</ref>
====Redshift surveys====
{{main|redshift survey}}


Spectroscopy, as a measurement, is considerably more difficult than simple ], which measures the ] of astronomical objects through certain ].<ref>For a review of the subject of photometry, consider: {{cite book | last=Budding | first=E. | title=Introduction to Astronomical Photometry | publisher=Cambridge University Press | date=September 24, 1993 | isbn=0-521-41867-4 }}</ref> When photometric data is all that is available (for example, the ] and the ]), astronomers rely on a technique for measuring ]s.<ref>The technique was first described by: {{cite conference | last=Baum | first=W. A. | year=1962 | editor-first=G. C. | editor-last=McVittie | title=Problems of extra-galactic research | page=390 | conference=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, ] for these sorts of measurements can range up to {{math|δ''z'' {{=}} 0.5}}, and are much less reliable than spectroscopic determinations.<ref>{{cite journal | last1=Bolzonella | first1=M. | last2=Miralles | first2=J.-M. | last3=Pelló | first3=R. | title=Photometric redshifts based on standard SED fitting procedures | journal=Astronomy and Astrophysics | volume=363 | pages=476–492 | year=2000 | arxiv=astro-ph/0003380 | bibcode=2000A&A...363..476B }}</ref>
]
With the advent of automated ]s and improvements in ], 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 ] of the universe. The ], a vast ] of galaxies over 500 million ]s wide, provides a dramatic example of a large-scale structure that redshift surveys can detect.


However, photometry does at least allow a qualitative characterization of a redshift. For example, if a Sun-like spectrum had a redshift of {{math|''z'' {{=}} 1}}, it would be brightest in the ](1000nm) rather than at the blue-green(500nm) color associated with the peak of its ] spectrum, and the light intensity will be reduced in the filter by a factor of four, {{math|(1 + ''z''){{sup|2}}}}. Both the photon count rate and the photon energy are redshifted. (See ] 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 ] collaboration can be found at: {{cite arXiv | title=The K correction | last1=Hogg | first1=David W. | last2=Baldry | first2=Ivan K. | last3=Blanton | first3=Michael R. | last4=Eisenstein | first4=Daniel J. | display-authors=1 | date=October 2002 | eprint=astro-ph/0210394}}</ref>
The first redshift survey was the ], started in ] with the initial data collection completed in ]. More recently, the ] determined the large-scale structure of one section of the Universe, measuring ''z''-values for over 220,000 galaxies; data collection was completed in 2002, and the final data set was released ] 2003. (In addition to mapping large-scale patterns of galaxies, 2dF also established an upper limit on ] mass.) Another notable investigation, the ] (SDSS), is ongoing ] and aims to obtain measurements on around 100 million objects. SDSS has recorded redshifts for galaxies as high as 0.4, and has been involved in the detection of ]s beyond ''z'' = 6. The ] uses the ] with the new "DEIMOS" ]; 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 complement to SDSS and 2dF.


===Local observations===
== "Reddening" due to physical optics and radiative transfer==
In nearby objects (within our ] galaxy) observed redshifts are almost always related to the ] velocities associated with the objects being observed. Observations of such redshifts and blueshifts have enabled astronomers to measure ] and parametrize the ]es of the ]ing ]s in ], a method first employed in 1868 by British astronomer ].<ref name=Huggins/> Similarly, small redshifts and blueshifts detected in the spectroscopic measurements of individual stars are one way astronomers have been able to ] the presence and characteristics of ] around other stars and have even made very ] of redshifts during ] to determine precise orbital parameters.<ref>The ] 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 |last1=Ge |first1=Jian |last2=Van Eyken |first2=Julian |last3=Mahadevan |first3=Suvrath |author3-link=Suvrath Mahadevan |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 |last10=Henry |first10=Gregory W. |last11=Schneider |first11=Donald P. |last12=Ramsey |first12=Lawrence W. |last13=Wittenmyer |first13=Robert A. |last14=Endl |first14=Michael |last15=Cochran |first15=William D. |display-authors=4 |date=2006 |title=The First Extrasolar Planet Discovered with a New-Generation High-Throughput Doppler Instrument |journal=The Astrophysical Journal |volume=648 |issue=1 |pages=683–695 |arxiv=astro-ph/0605247 |bibcode=2006ApJ...648..683G |doi=10.1086/505699 |s2cid=13879217 |last16=Ford |first16=Eric B. |last17=Martin |first17=Eduardo L. |last18=Israelian |first18=Garik |last19=Valenti |first19=Jeff |last20=Montes |first20=David}}</ref>


Finely detailed measurements of redshifts are used in ] to determine the precise movements of the ] of the ].<ref>{{cite journal | doi = 10.1007/BF00243557 | title = Solar and stellar seismology | date = 1988 | last1 = Libbrecht | first1 = Keng | journal = Space Science Reviews | volume = 47 | issue = 3–4 |bibcode=1988SSRv...47..275L | pages=275–301| s2cid = 120897051 | url = https://authors.library.caltech.edu/104214/1/1988SSRv___47__275L.pdf }}</ref> Redshifts have also been used to make the first measurements of the ] rates of ]s,<ref>In 1871 ] measured the rotation rate of ]. ] was working on such measurements when he turned his attention to spiral nebulae.</ref> velocities of ]s,<ref>An early review by ] on the subject: {{cite journal | title=The formation of galaxies and the origin of the high-velocity hydrogen | journal=] | volume=7 | page=381 | date=1970 | bibcode=1970A&A.....7..381O | last= Oort | first= J. H. }}</ref> the ],<ref name="basicastronomy" /> and the ] of ] onto ]s and ]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=Publications of the Astronomical Society of Japan | volume=41 | issue=4 | date=1989 | pages=763–778 }}</ref> The ]s of various emitting and absorbing objects can be obtained by measuring ]—effectively redshifts and blueshifts over a single emission or absorption line.<ref>{{cite book | last1=Rybicki | first1=G. B. | first2=A. R. | last2=Lightman | title=Radiative Processes in Astrophysics | publisher=John Wiley & Sons | year=1979 | page=288 | isbn=0-471-82759-2 }}</ref> By measuring the broadening and shifts of the 21-centimeter ] in different directions, astronomers have been able to measure the ] of ], which in turn reveals the ] of our Milky Way.<ref name=basicastronomy/> Similar measurements have been performed on other galaxies, such as ].<ref name=basicastronomy/> As a diagnostic tool, redshift measurements are one of the most important ] made in astronomy.
The interaction between light and matter summarized in the subject of ] and ] 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 ] (see ]) or due to the ] of ] whether from ] ]s, from particulates, or from fluctuations in a ]. While such phenomena are sometimes referred to as "redshifts" and "blueshifts", the electromagnetic interaction of the photons with intervening matter distinguishes these phenomena from the reference-frame effects. 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 ].


===Extragalactic observations===
In many circumstances scattering causes radiation to redden because ] results in the predominance of many low ] photons over few high energy ones (while ]). 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 ] of wavelength. Furthermore, scattering from ] ] generally occurs at many ]s, and ''z'' is also a function of the scattering angle. If multiple scattering occurs, or the scattering particles have relative motion, then there is generally distortion of ]s as well.
]


The most distant objects exhibit larger redshifts corresponding to the ] of the ]. The largest-observed redshift, corresponding to the greatest distance and furthest back in time, is that of the ] radiation; the ] is about {{math|''z'' {{=}} 1089}} ({{math|''z'' {{=}} 0}} corresponds to present time), and it shows the state of the universe about 13.8 billion years ago,<ref>{{cite web
In ], ] can appear ] due to scattering processes in a phenomenon referred to as ] — the same effect that causes the ] reddening of the ] seen in the ] or ] and causes the rest of the ] to have a ] ]. This phenomenon is distinct from red''shift''ing because the ] are not shifted to other wavelengths in reddened objects and there is an additional ] and distortion associated with the phenomenon due to photons being scattered in and out of the ].
| title=Cosmic Detectives
| url=http://www.esa.int/Our_Activities/Space_Science/Cosmic_detectives
| publisher=The European Space Agency (ESA)
| date=2013-04-02
| access-date=2013-04-25
}}</ref> and 379,000 years after the initial moments of the ].<ref>An accurate measurement of the cosmic microwave background was achieved by the ] experiment. The final published temperature of 2.73 K was reported in this paper: {{cite journal | last1=Fixsen | first1=D. J. | last2=Cheng | first2=E. S. | last3=Cottingham | first3=D. A. | last4=Eplee | first4=R. E. Jr. | last5=Isaacman | first5=R. B. | last6=Mather | first6=J. C. | last7=Meyer | first7=S. S. | last8=Noerdlinger | first8=P. D. | last9=Shafer | first9=R. A. | last10=Weiss | first10=R. | last11=Wright | first11=E. L. | last12=Bennett | first12=C. L. | last13=Boggess | first13=N. W. | author-link13 = Nancy Boggess|last14=Kelsall | first14=T. | last15=Moseley | first15=S. H. | last16=Silverberg | first16=R. F. | last17=Smoot | first17=G. F. | last18=Wilkinson | first18=D. T. | date=January 1994 | title=Cosmic microwave background dipole spectrum measured by the COBE FIRAS instrument | journal=Astrophysical Journal | volume=420 | page=445 | doi=10.1086/173575 | bibcode=1994ApJ...420..445F }}. The most accurate measurement as of 2006 was achieved by the ] experiment.</ref>


The luminous point-like cores of ]s were the first "high-redshift" ({{math|''z'' > 0.1}}) objects discovered before the improvement of telescopes allowed for the discovery of other high-redshift galaxies.{{cn|date=March 2023}}
''For a list of scattering processes, see ].''


For galaxies more distant than the ] and the nearby ], but within a thousand mega]s or so, the redshift is approximately proportional to the galaxy's distance. This correlation was first observed by ] and has come to be known as ]. ] was the first to discover galactic redshifts, in about 1912, while Hubble correlated Slipher's measurements with distances he ] to formulate his Law.<ref name="Peebles-1993"/> Hubble's law follows in part from the ].<ref name="Peebles-1993">Peebles (1993).</ref> Because it is usually not known how ] 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.{{cn|date=March 2023}}
== References ==
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===Citations===
# {{note|Chase}} S. I. Chase, Olbers' Paradox, in the Physics FAQ; see also ], ''Far as Human Eye Could See'' (Doubleday, 1987), ISBN 0-385-23514-3
# {{note|Weiss}} M. Weiss, What Causes the Hubble Redshift?, entry in the Physics ] (1994), available via ]'s
# {{note|Ives}} H. Ives and G. Stilwell, An Experimental study of the rate of a moving atomic clock , J. Opt. Soc. Am. 28, 215-226 (1938)
# {{note|Poundrebka}} R. V. Pound and G. A. Rebka Jr., Apparent weight of photons, ''Phys. Rev. Lett.'' '''4''', 337 (1960). This paper was the first measurement.
# {{note|Michell}} J. Michell, Phil. Trans. Roy. Soc., 74 (1784) 35-57.
# {{note|sloan}} Fan, Xiahoui et al., A Survey of z>5.7 Quasars in the Sloan Digital Sky Survey. II. Discovery of Three Additional Quasars at z>6, '']'' (2003), v. 125, Issue 4, pp. 1649-1659 .
# {{note|egami}} Egami, E., et al., Spitzer and Hubble Space Telescope Constraints on the Physical Properties of the z~7 Galaxy Strongly Lensed by A2218, '']'' (2005), v. 618, Issue 1, pp. L5-L8 .
# {{note|pello}} Pelló, R., Schaerer, D., Richard, J., Le Borgne, J.-F., & Kneib, J.P., ISAAC/VLT observations of a lensed galaxy at z = 10.0, '']'' (2004), 416, L35 .


]al interactions of galaxies with each other and clusters cause a significant ] in the normal plot of the Hubble diagram. The ] associated with galaxies superimpose a rough trace of the ] of ] in the universe. This effect leads to such phenomena as nearby galaxies (such as the ]) exhibiting blueshifts as we fall towards a common ], and redshift maps of clusters showing a ] 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 ] (the ratio of a galaxy's mass in solar masses to its brightness in solar luminosities), an important tool for measuring ].<ref>{{cite book | first1=James | last1=Binney | first2=Scott | last2=Treimane | title=Galactic dynamics|publisher=Princeton University Press | isbn=978-0-691-08445-9 | date=1994 }}</ref>{{Page needed|date=March 2023}}
===Book references===

* {{cite book | author=Carroll, Bradley W. and Dale A. Ostlie| title=An Introduction to Modern Astrophysics| publisher=Addison-Wesley Publishing Company, Inc.| year=1996| id=ISBN 0201547309}}
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.{{cn|date=March 2023}}
* {{cite book | author=Kutner, Marc | title=Astronomy: A Physical Perspective | publisher=Cambridge University Press | year=2003 | id=ISBN 0521529271}}

While it was long believed that the expansion rate has been continuously decreasing since the Big Bang, observations beginning in 1988 of the redshift-distance relationship using ]e have suggested that in comparatively recent times the expansion rate of the universe has ].<ref>{{cite web|url=https://www.nobelprize.org/uploads/2019/05/popular-physicsprize2011.pdf |title=The Nobel Prize in Physics 2011: Information for the Public |website=nobelprize.org |access-date=2023-06-13}}</ref>

===Highest redshifts===
{{see also|List of the most distant astronomical objects#List of most distant objects by type{{!}}List of most distant objects by type}}
] and ] for the Planck 2018 cosmology parameters, from redshift 0 to 15, with distance (blue solid line) on the left axis, and time (orange dashed line) on the right. Note that the time that has passed (in giga years) from a given redshift until now is not the same as the distance (in giga light years) light would have traveled from that redshift, due to the expansion of the universe over the intervening period.]]

Currently, the objects with the highest known redshifts are galaxies and the objects producing gamma ray bursts.{{cn|date=August 2024}} The most reliable redshifts are from ] data,{{cn|date=August 2024}} and the highest-confirmed spectroscopic redshift of a galaxy is that of ] with a redshift of {{math|''z'' {{=}} 14.32}}, corresponding to 290 million years after the Big Bang.<ref>{{Cite journal |last1=Carniani |first1=Stefano |last2=Hainline |first2=Kevin |last3=D’Eugenio |first3=Francesco |last4=Eisenstein |first4=Daniel J. |last5=Jakobsen |first5=Peter |last6=Witstok |first6=Joris |last7=Johnson |first7=Benjamin D. |last8=Chevallard |first8=Jacopo |last9=Maiolino |first9=Roberto |last10=Helton |first10=Jakob M. |last11=Willott |first11=Chris |last12=Robertson |first12=Brant |last13=Alberts |first13=Stacey |last14=Arribas |first14=Santiago |last15=Baker |first15=William M. |date=2024-07-29 |title=Spectroscopic confirmation of two luminous galaxies at a redshift of 14 |journal=Nature |volume=633 |issue=8029 |language=en |pages=318–322 |doi=10.1038/s41586-024-07860-9 |issn=1476-4687|doi-access=free |pmid=39074505 |pmc=11390484 }}</ref> The previous record was held by ],<ref>{{cite journal
| title=A Remarkably Luminous Galaxy at z=11.1 Measured with Hubble Space Telescope Grism Spectroscopy
| last1=Oesch | first1=P. A. | last2=Brammer | first2=G.
| last3=van Dokkum | first3=P. G. | last4=Illingworth | first4=G. D.
| last5=Bouwens | first5=R. J. | last6=Labbé | first6=I.
| last7=Franx | first7=M. | last8=Momcheva | first8=I.
| last9=Ashby | first9=M. L. N. | last10=Fazio | first10=G. G.
| last11=Gonzalez | first11=V. | last12=Holden | first12=B.
| last13=Magee | first13=D. | last14=Skelton | first14=R. E.
| last15=Smit | first15=R. | last16=Spitler | first16=L. R.
| last17=Trenti | first17=M. | last18=Willner | first18=S. P.
| display-authors=1 | journal=The Astrophysical Journal
| date=March 1, 2016 | volume=819 | issue=2 | page=129
| arxiv=1603.00461 | doi=10.3847/0004-637X/819/2/129
| bibcode=2016ApJ...819..129O | s2cid=119262750
| doi-access=free }}</ref> with a redshift of {{math|''z'' {{=}} 11.1}}, corresponding to 400 million years after the Big Bang, and by ]<ref>
{{cite journal
| display-authors=4 | first1=M. D. | last1=Lehnert
| last2=Nesvadba | first2=N. P. | last3=Cuby | first3=J. G.
| last4=Swinbank | first4=A. M. | last5=Morris | first5=S.
| last6=Clément | first6=B. | last7=Evans | first7=C. J.
| last8=Bremer | first8=M. N. | last9=Basa | first9=S.
| title=Spectroscopic Confirmation of a galaxy at redshift z = 8.6
| journal=Nature | year=2010
| volume=467 | issue=7318 | pages=940–942
| doi=10.1038/nature09462 | pmid=20962840
| bibcode=2010Natur.467..940L | arxiv=1010.4312
| s2cid=4414781
}}</ref> at a redshift of {{math|''z'' {{=}} 8.6}}, corresponding to 600 million years after the Big Bang.

Slightly less reliable are ] redshifts, the highest of which is the lensed galaxy A1689-zD1 at a redshift {{math|''z'' {{=}} 7.5}}<ref>{{Cite journal|last1=Watson|first1=Darach|last2=Christensen|first2=Lise|last3=Knudsen|first3=Kirsten Kraiberg|last4=Richard|first4=Johan|last5=Gallazzi|first5=Anna|last6=Michałowski|first6=Michał Jerzy|title=A dusty, normal galaxy in the epoch of reionization|journal=Nature|volume=519|issue=7543|pages=327–330|doi=10.1038/nature14164|arxiv = 1503.00002 |bibcode = 2015Natur.519..327W|pmid=25731171|year=2015|s2cid=2514879}}</ref><ref>{{cite journal
| title=Discovery of a Very Bright Strongly Lensed Galaxy Candidate at z ~ 7.6
| first1=L. D. | last1=Bradley | first2=R. J. | last2=Bouwens
| first3=H. C. | last3=Ford | first4=G. D. | last4=Illingworth
| first5=M. J. | last5=Jee | first6=N. | last6=Benítez
| first7=T. J. | last7=Broadhurst | first8=M. | last8=Franx
| first9=B. L. | last9=Frye | first10=L. | last10=Infante
| display-authors=1 | journal=]
| volume=678 | issue=2 | pages=647–654 | year=2008
| bibcode=2008ApJ...678..647B | s2cid=15574239
| doi=10.1086/533519 | arxiv=0802.2506
}}</ref> and the next highest being {{math|''z'' {{=}} 7.0}}.<ref>{{cite journal
| display-authors=1 | first1=E. | last1=Egami
| first2=J.-P. | last2=Kneib | first3=G. H. | last3=Rieke
| first4=R. S. | last4=Ellis | first5=J. | last5=Richard
| first6=J. | last6=Rigby | first7=C. | last7=Papovich
| first8=D. | last8=Stark | first9=M. R. | last9=Santos
| first10=J.-S. | last10=Huang | first11=H. | last11=Dole
| first12=E. Le | last12=Floc'H | first13=P. G. | last13=Pérez-González
| title=Spitzer and Hubble Space Telescope Constraints on the Physical Properties of the z~7 Galaxy Strongly Lensed by A2218
| journal=]
| volume=618 | issue=1 | pages=L5–L8 | year=2005
| bibcode=2005ApJ...618L...5E | doi=10.1086/427550
| arxiv=astro-ph/0411117 | s2cid=15920310 }}</ref> The most distant-observed ] with a spectroscopic redshift measurement was ], which had a redshift of {{math|''z'' {{=}} 8.2}}.<ref>{{cite journal
| title=GRB 090423 reveals an exploding star at the epoch of re-ionization
| last1=Salvaterra | first1=R. | first2=M. Della | last2=Valle
| last3=Campana | first3=S. |author-link3=Sergio Campana (astrophysicist)| last4=Chincarini | first4=G.
| last5=Covino | first5=S. | last6=d'Avanzo | first6=P.
| last7=Fernández-Soto | first7=A. | last8=Guidorzi | first8=C.
| last9=Mannucci | first9=F. | last10=Margutti | first10=R.
| last11=Thöne | first11=C. C. | last12=Antonelli | first12=L. A.
| last13=Barthelmy | first13=S. D. | last14=De Pasquale | first14=M.
| last15=d'Elia | first15=V. | last16=Fiore | first16=F.
| last17=Fugazza | first17=D. | last18=Hunt | first18=L. K.
| last19=Maiorano | first19=E. | last20=Marinoni | first20=S.
| last21=Marshall | first21=F. E. | last22=Molinari | first22=E.
| last23=Nousek | first23=J. | last24=Pian | first24=E.
| last25=Racusin | first25=J. L. | last26=Stella | first26=L.
| last27=Amati | first27=L. | last28=Andreuzzi | first28=G.
| last29=Cusumano | first29=G. | last30=Fenimore | first30=E. E.
| display-authors=4 | journal=]
| volume=461 | issue=7268 | pages=1258–60
| doi=10.1038/nature08445 | date=2009 | pmid=19865166
| s2cid=205218263 | bibcode=2009Natur.461.1258S |arxiv=0906.1578
}}</ref> The most distant-known quasar, ], is at {{math|''z'' {{=}} 7.54}}.<ref>{{cite web|url=https://news.mit.edu/2017/scientists-observe-supermassive-black-hole-infant-universe-1206|title=Scientists observe supermassive black hole in infant universe|website=MIT News |publisher=Massachusetts Institute of Technology |date=2017-12-06 |first=Jennifer |last=Chu}}</ref><ref name="Nature-2018-01">{{cite journal |last1=Bañados |first1=Eduardo |last2=Venemans |first2=Bram P. |last3=Mazzucchelli |first3=Chiara |last4=Farina |first4=Emanuele P. |last5=Walter |first5=Fabian |last6=Wang |first6=Feige |last7=Decarli |first7=Roberto |last8=Stern |first8=Daniel |last9=Fan |first9=Xiaohui |last10=Davies |first10=Frederick B. |last11=Hennawi |first11=Joseph F. |last12=Simcoe |first12=Robert A. |last13=Turner |first13=Monica L. |last14=Rix |first14=Hans-Walter |last15=Yang |first15=Jinyi |last16=Kelson |first16=Daniel D. |last17=Rudie |first17=Gwen C. |last18=Winters |first18=Jan Martin |title=An 800-million-solar-mass black hole in a significantly neutral Universe at a redshift of 7.5 |journal=Nature |date=January 2018 |volume=553 |issue=7689 |pages=473–476 |doi=10.1038/nature25180 |pmid=29211709 |arxiv=1712.01860 |bibcode=2018Natur.553..473B |s2cid=205263326 }}</ref> The highest-known redshift radio galaxy (TGSS1530) is at a redshift {{math|''z'' {{=}} 5.72}}<ref>{{cite journal|last1=Saxena|first1=A.|date=2018|title=Discovery of a radio galaxy at z = 5.72|journal=Monthly Notices of the Royal Astronomical Society|volume=480|issue=2|pages=2733–2742|arxiv=1806.01191|bibcode=2018MNRAS.480.2733S|doi=10.1093/mnras/sty1996|doi-access=free |s2cid=118830412}}</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}}.<ref>{{cite journal | doi = 10.1038/nature01821 | title = Molecular gas in the host galaxy of a quasar at redshift z = 6.42 | date = 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. | last10 = Menten | first10 = Karl M. | journal = Nature | volume = 424 | issue = 6947 | pages = 406–8 | pmid = 12879063 |bibcode=2003Natur.424..406W|arxiv = astro-ph/0307410 |s2cid = 4419009| display-authors = 4 }}</ref>

''Extremely red objects'' (EROs) are ] 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>
{{cite journal
| display-authors=4
| author=Smail, Ian
| author2=Owen, F. N.
| author3=Morrison, G. E.
| author4=Keel, W. C.
| author5=Ivison, R. J.
| author6=Ledlow, M. J.
| journal=The Astrophysical Journal | volume=581 | issue=2
| pages=844–864 | doi=10.1086/344440 | bibcode=2002ApJ...581..844S
| title=The Diversity of Extremely Red Objects
| date=2002
|arxiv = astro-ph/0208434 | s2cid=51737034
}}</ref> Objects that are even redder than EROs are termed ''hyper extremely red objects'' (HEROs).<ref>
{{cite journal
| display-authors=4
| author=Totani, Tomonori
| author2=Yoshii, Yuzuru
| author3=Iwamuro, Fumihide
| author4=Maihara, Toshinori
| author5=Motohara, Kentaro
| title=Hyper Extremely Red Objects in the Subaru Deep Field: Evidence for Primordial Elliptical Galaxies in the Dusty Starburst Phase
| journal=The Astrophysical Journal | volume=558 | issue=2
| date=2001 | pages=L87–L91 | doi=10.1086/323619
| bibcode=2001ApJ...558L..87T
|arxiv = astro-ph/0108145 | s2cid=119511017
}}</ref>

The ] has a redshift of {{math|z {{=}} 1089}}, corresponding to an age of approximately 379,000 years after the Big Bang and a ] of more than 46 billion light-years.<ref name="ly93">
{{cite journal | last1 = Lineweaver | first1 = Charles | first2=Tamara M. | last2=Davis | date = 2005 | title = Misconceptions about the Big Bang | journal = Scientific American | volume = 292 | issue = 3 | pages = 36–45 | doi = 10.1038/scientificamerican0305-36 | bibcode = 2005SciAm.292c..36L }}</ref> The yet-to-be-observed first light from the oldest ], 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}}.<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|date=2006|last1=Naoz|first1=S.|last2=Noter|first2=S.|last3=Barkana|first3=R.|journal=Monthly Notices of the Royal Astronomical Society: Letters|volume=373|issue = 1 |pages=L98–L102 |doi-access = free |s2cid = 14454275 }}</ref> Other high-redshift events predicted by physics but not presently observable are the ] from about two seconds after the Big Bang (and a redshift in excess of {{math|''z'' > 10{{sup|10}}}})<ref>{{cite journal|bibcode=2006PhR...429..307L|arxiv = astro-ph/0603494 |doi = 10.1016/j.physrep.2006.04.001|title=Massive neutrinos and cosmology|date=2006|last1=Lesgourgues|first1=J|last2=Pastor|first2=S|journal=Physics Reports|volume=429|issue=6|pages=307–379 |s2cid = 5955312 }}</ref> and the cosmic ] emitted directly from ] at a redshift in excess of {{math|''z'' > 10{{sup|25}}}}.<ref>{{cite journal|bibcode=2005PhyU...48.1235G|arxiv = gr-qc/0504018 |doi = 10.1070/PU2005v048n12ABEH005795|title=Relic gravitational waves and cosmology|date=2005|last1=Grishchuk|first1=Leonid P|journal=Physics-Uspekhi|volume=48|issue=12|pages=1235–1247 |s2cid = 11957123 }}</ref>

In June 2015, astronomers reported evidence for ] in the ] ] at {{math|''z'' {{=}} 6.60}}. Such stars are likely to have existed in the very early universe (i.e., at high redshift), and may have started the production of ]s heavier than ] that are needed for the later formation of ]s and ] as we know it.<ref name="AJ-20150604">{{cite journal |last1=Sobral |first1=David |last2=Matthee |first2=Jorryt |last3=Darvish |first3=Behnam |last4=Schaerer |first4=Daniel |last5=Mobasher |first5=Bahram |last6=Röttgering |first6=Huub J. A. |last7=Santos |first7=Sérgio |last8=Hemmati |first8=Shoubaneh |title=Evidence For POPIII-Like Stellar Populations In The Most Luminous LYMAN-α Emitters At The Epoch Of Re-Ionisation: Spectroscopic Confirmation |date=4 June 2015 |journal=] |doi=10.1088/0004-637x/808/2/139 |bibcode=2015ApJ...808..139S |volume=808 |issue=2 |page=139|arxiv=1504.01734|s2cid=18471887 }}</ref><ref name="NYT-20150617">{{cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |title=Astronomers Report Finding Earliest Stars That Enriched Cosmos |url=https://www.nytimes.com/2015/06/18/science/space/astronomers-report-finding-earliest-stars-that-enriched-cosmos.html |date=17 June 2015 |work=] |access-date=17 June 2015 }}</ref>

===Redshift surveys===
]
{{Main|Redshift survey}}
With advent of automated ]s and improvements in ], 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 ] of the universe. The ], a vast ] of galaxies over 500 million ]s wide, provides a dramatic example of a large-scale structure that redshift surveys can detect.<ref>{{cite journal | title=Mapping the Universe | first1=M. J. | last1=Geller | first2=J. P. | last2=Huchra | journal=Science | volume=246 | issue=4932 | pages=897–903 | year=1989 | doi=10.1126/science.246.4932.897 | pmid=17812575 | bibcode=1989Sci...246..897G | s2cid=31328798 }}</ref>

The first redshift survey was the ], started in 1977 with the initial data collection completed in 1982.<ref>See the CfA website for more details: {{cite web
| title=The CfA Redshift Survey
| first=John P. | last=Huchra | author-link=John Huchra
| publisher=Harvard & Smithsonian Center for Astrophysics
| url=https://lweb.cfa.harvard.edu/~dfabricant/huchra/zcat/
| access-date=2023-03-20
}}</ref> More recently, the ] 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 ] was released 30 June 2003.<ref>{{cite journal
|title=The 2dF galaxy redshift survey: Power-spectrum analysis of the final dataset and cosmological implications
| first1=Shaun | last1=Cole | author-link=Shaun Cole
| last2=Percival | first2=Will J. | last3=Peacock | first3=John A.
| last4=Norberg | first4=Peder | last5=Baugh | first5=Carlton M.
| last6=Frenk | first6=Carlos S. | last7=Baldry | first7=Ivan
| last8=Bland-Hawthorn | first8=Joss | last9=Bridges | first9=Terry
| last10=Cannon | first10=Russell | last11=Colless | first11=Matthew
| last12=Collins | first12=Chris | last13=Couch | first13=Warrick
| last14=Cross | first14=Nicholas J. G. | last15=Dalton | first15=Gavin
| last16=Eke | first16=Vincent R. | last17=De Propris | first17=Roberto
| last18=Driver | first18=Simon P. | last19=Efstathiou | first19=George
| last20=Ellis | first20=Richard S. | last21=Glazebrook | first21=Karl
| last22=Jackson | first22=Carole | last23=Jenkins | first23=Adrian
| last24=Lahav | first24=Ofer | last25=Lewis | first25=Ian
| last26=Lumsden | first26=Stuart | last27=Maddox | first27=Steve
| last28=Madgwick | first28=Darren | last29=Peterson | first29=Bruce A.
| last30=Sutherland | first30=Will | last31=Taylor | first31=Keith
| journal=Monthly Notices of the Royal Astronomical Society
| volume=362 | issue=2 | pages=505–34 | date=2005
| bibcode=2005MNRAS.362..505C | arxiv=astro-ph/0501174
| doi=10.1111/j.1365-2966.2005.09318.x
| doi-access=free | s2cid=6906627| display-authors=4
}} {{Webarchive|url=https://web.archive.org/web/20070205010241/http://msowww.anu.edu.au/2dFGRS/ |date=2007-02-05 }}</ref> The ] (SDSS), is ongoing as of 2013 and aims to measure the redshifts of around 3 million objects.<ref>{{cite web | url=https://www.sdss3.org/ | access-date=2023-03-20 | title=SDSS-III | website=www.sdss3.org }}</ref> SDSS has recorded redshifts for galaxies as high as 0.8, and has been involved in the detection of ]s beyond {{math|''z'' {{=}} 6}}. The ] uses the ] with the new "DEIMOS" ]; 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| first1=Marc | last1=Davis | author2=DEEP2 collaboration |date=2002 | conference=Conference on Astronomical Telescopes and Instrumentation, Waikoloa, Hawaii, 22–28 Aug 2002 | arxiv=astro-ph/0209419 | bibcode=2003SPIE.4834..161D | doi=10.1117/12.457897 }}</ref>

==Effects from physical optics or radiative transfer==
The interactions and phenomena summarized in the subjects of ] and ] 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 by a transformation between reference frames. Such shifts can be from such physical phenomena as ] or the ] of ] whether from ] ]s, from ], or from fluctuations of the ] in a ] medium as occurs in the radio phenomenon of ].<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 ].<ref name=basicastronomy/>

In many circumstances scattering causes radiation to redden because ] results in the predominance of many low-] photons over few high-energy ones (while ]).<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 {{math|''z''}} is generally a ] of wavelength. Furthermore, scattering from ] ] generally occurs at many ]s, and {{math|''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 ]s as well.<ref name=basicastronomy/>

In ], ] can appear redder due to scattering processes in a phenomenon referred to as ]<ref name=basicastronomy/>—similarly ] causes the ] 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 ] lines are not shifted to other wavelengths in reddened objects and there is an additional ] and distortion associated with the phenomenon due to photons being scattered in and out of the ].{{cn|date=March 2023}}

==Blueshift==
{{redirect|Blueshift|the term as used in photochemistry|hypsochromic shift|the political phenomenon|blue shift (politics)|other uses of "blueshift" or "blue shift"}}
The opposite of a redshift is a '''blueshift'''. A blueshift is any decrease in ] (increase in ]), with a corresponding increase in frequency, of an ]. In ], this shifts a color towards the blue end of the spectrum.

=== Doppler blueshift ===
]
] blueshift is caused by movement of a source towards the observer. The term applies to any decrease in wavelength and increase in frequency caused by relative motion, even outside the ]. Only objects moving at near-] toward the observer are noticeably bluer to the ], but the wavelength of any reflected or emitted photon or other particle is shortened in the direction of travel.<ref>{{cite book|title=In Quest of the Universe | first1=Karl F. | last1=Kuhn | first2=Theo | last2=Koupelis |year= 2004|publisher=]|isbn=978-0-7637-0810-8|pages=122–3}}</ref>

Doppler blueshift is used in ] to determine relative motion:
* The ] is moving toward our own ] ] within the ]; thus, when observed from Earth, its light is undergoing a blueshift.<ref>{{cite book |last=Woodhouse |first=Chris |chapter=M31 (Andromeda Galaxy) |date=2017-12-04 |title=The Astrophotography Manual |pages=308–313 |edition=2nd |publisher=Routledge |language=en |doi=10.4324/9781315159225-42 |isbn=978-1-315-15922-5}}</ref>
* Components of a ] system will be blueshifted when moving towards Earth
* When observing spiral galaxies, the side spinning toward us will have a slight blueshift ''relative to'' the side spinning away from us (see ]).
* ]s are known to propel ]s toward us, emitting ] and ] that appears blueshifted.{{cn|date=March 2023}}
* Nearby stars such as ] are moving toward us, resulting in a very small blueshift.
* Doppler blueshift of distant objects with a high ''z'' can be subtracted from the much larger ] to determine relative motion in the ].<ref name="Aoki2005">{{cite journal | title = The Largest Blueshifts of the Emission Line in Two Narrow-Line Quasars | journal = Astrophysical Journal | date = January 2005 | first1=Kentaro | last1=Aoki | first2=Toshihiro | last2=Kawaguchi | first3=Kouji | last3=Ohta | volume = 618 | issue = 2 | pages = 601–608 |arxiv = astro-ph/0409546 |bibcode = 2005ApJ...618..601A |doi = 10.1086/426075 | s2cid = 17680991 }}</ref>

=== Gravitational blueshift ===
] (protons, electrons, photons, etc.) falling into a ] become more energetic and undergo observer-independent blueshifting.]]
Unlike the ''relative'' Doppler blueshift, caused by movement of a source towards the observer and thus dependent on the received angle of the photon, gravitational blueshift is ''absolute'' and does not depend on the received angle of the photon:
{{Blockquote|Photons climbing out of a gravitating object become less energetic. This loss of energy is known as a "redshifting", as photons in the visible spectrum would appear more red. Similarly, photons falling into a gravitational field become more energetic and exhibit a blueshifting. ... Note that the magnitude of the redshifting (blueshifting) effect is not a function of the emitted angle or the received angle of the photon—it depends only on how far radially the photon had to climb out of (fall into) the potential well.<ref name=R.N_1>{{cite web| first=R. J. | last=Nemiroff| title=Gravitational Principles and Mathematics| url=http://antwrp.gsfc.nasa.gov/htmltest/gifcity/nslens_math.html| date=1993| publisher=]}}</ref><ref name=R.N_2>{{cite journal| first=R. J. | last=Nemiroff| title=Visual distortions near a neutron star and black hole| date=1993| journal=American Journal of Physics| volume=61| issue=7| pages=619–632| bibcode=1993AmJPh..61..619N| doi=10.1119/1.17224| arxiv=astro-ph/9312003v1| s2cid=16640860}}</ref>}}

It is a natural consequence of ] and ], and was confirmed experimentally in 1959 with the ]. Gravitational blueshift contributes to ] (CMB) anisotropy via the ]: when a gravitational well evolves while a photon is passing, the amount of blueshift on approach will differ from the amount of ] as it leaves the region.<ref name="Bonometto2002">{{cite book | last1 = Bonometto | first1 = Silvio | last2 = Gorini | first2 = Vittorio | last3 = Moschella | first3 = Ugo | title = Modern Cosmology | publisher = ] | date = 2002 | isbn = 978-0-7503-0810-6 }}</ref>

==== Blue outliers ====
There are faraway ] that show a blueshift in their ]] emission ]. One of the largest blueshifts is found in the narrow-line ], ], which has a relative velocity of -1150&nbsp;km/s.<ref name="Aoki2005" /> These types of galaxies are called "blue outliers".<ref name="Aoki2005" />

===Cosmological blueshift===
In a hypothetical universe undergoing a runaway ] contraction, a cosmological blueshift would be observed, with galaxies further away being increasingly blueshifted—the exact opposite of the actually observed ] in the present ].{{cn|date=March 2023}}

==See also==
* ]
* ]

==References==
{{Reflist|30em}}

==Sources==
===Articles===
* 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.)
* Lineweaver, Charles H. and Tamara M. Davis, "", '']'', 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.)

===Books===
* {{cite book | last=Nussbaumer|first=Harry|author2=Lydia Bieri |author2-link=Lydia Bieri|title=Discovering the Expanding Universe|publisher=Cambridge University Press|date=2009|isbn=978-0-521-51484-2}}
* {{cite book | last=Binney|first=James|author2=Michael Merrifeld |title=Galactic Astronomy|publisher=Princeton University Press|date=1998|isbn=978-0-691-02565-0}}
* {{cite book | author=Carroll, Bradley W. | author2=Dale A. Ostlie | name-list-style=amp| title=An Introduction to Modern Astrophysics| publisher=Addison-Wesley Publishing Company, Inc.| date=1996| isbn=978-0-201-54730-6}}
* {{cite book | author=Feynman, Richard | author2=Leighton, Robert | author3=Sands, Matthew | title=Feynman Lectures on Physics. Vol. 1 | publisher=Addison-Wesley | date=1989 | isbn=978-0-201-51003-4| title-link=The Feynman Lectures on Physics }}
* {{cite book | last = Grøn | first = Øyvind |author-link=Øyvind Grøn|author2=Hervik, Sigbjørn | title = Einstein's General Theory of Relativity | location = New York | publisher = Springer | date = 2007 | isbn = 978-0-387-69199-2}}
* {{cite book |last=Harrison |first=Edward |date=2000 |title=Cosmology: The Science of the Universe |edition=2nd |publisher=Cambridge University Press |isbn=978-0-521-66148-5}}
* {{cite book | author=Kutner, Marc | title=Astronomy: A Physical Perspective | url=https://archive.org/details/astronomyphysica00kutn | url-access=registration | publisher=Cambridge University Press | date=2003 | isbn=978-0-521-52927-3}}
* {{cite book | last = Misner | first = Charles | author2 = Thorne, Kip S. | author3 = Wheeler, John Archibald | title = Gravitation | location = San Francisco | publisher = W. H. Freeman | date = 1973 | isbn = 978-0-7167-0344-0}}
* {{cite book | first = P. J. E. | last = Peebles | title = Principles of Physical Cosmology | publisher = Princeton University Press | date = 1993 | isbn = 978-0-691-01933-8 | url = https://archive.org/details/principlesofphys00pjep }}
* {{cite book | title=Spacetime Physics: Introduction to Special Relativity | edition=2nd | publisher=W.H. Freeman | date=1992 | isbn=978-0-7167-2327-1 | last1=Taylor | first1=Edwin F. | last2=Wheeler | first2=John Archibald | author-link2=John Archibald Wheeler | url=https://archive.org/details/spacetimephysics00edwi_0 }}
* {{cite book | first = Steven | last = Weinberg | title = Gravitation and Cosmology | publisher = John Wiley | date = 1971 | isbn = 978-0-471-92567-5 | url = https://archive.org/details/gravitationcosmo00stev_0 }}
* See also ] for applications of the cosmological and gravitational redshifts.


==External links== ==External links==
{{Commons|redshift}} {{Commons|Redshift}}
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*
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{{wiktionary}}
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*
]
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* by Wayne Hu
* {{cite web|last1=Merrifield|first1=Michael|last2=Hill|first2=Richard|title=Z Redshift|url=http://www.sixtysymbols.com/videos/redshift.htm|work=SIXTψ SYMBΦLS|date=2009|publisher=] for the ]}}


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Latest revision as of 23:29, 19 December 2024

Change of wavelength in photons during travel This article is about the astronomical phenomenon. For other uses, see Redshift (disambiguation).
Absorption lines in the visible spectrum of a supercluster of distant galaxies (right), as compared to absorption lines in the visible spectrum of the Sun (left). Arrows indicate redshift. Wavelength increases up towards the red and beyond (frequency decreases).
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In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation (such as light). The opposite change, a decrease in wavelength and increase in frequency and energy, is known as a blueshift, or negative redshift. The terms derive from the colours red and blue which form the extremes of the visible light spectrum. The main causes of electromagnetic redshift in astronomy and cosmology are the relative motions of radiation sources, which give rise to the relativistic Doppler effect, and gravitational potentials, which gravitationally redshift escaping radiation. All sufficiently distant light sources show cosmological redshift corresponding to recession speeds proportional to their distances from Earth, a fact known as Hubble's law that implies the universe is expanding.

All redshifts can be understood under the umbrella of frame transformation laws. Gravitational waves, which also travel at the speed of light, are subject to the same redshift phenomena. The value of a redshift is often denoted by the letter z, corresponding to the fractional change in wavelength (positive for redshifts, negative for blueshifts), and by the wavelength ratio 1 + z (which is greater than 1 for redshifts and less than 1 for blueshifts).

Examples of strong redshifting are a gamma ray perceived as an X-ray, or initially visible light perceived as radio waves. Subtler redshifts are seen in the spectroscopic observations of astronomical objects, and are used in terrestrial technologies such as Doppler radar and radar guns.

Other physical processes exist that can lead to a shift in the frequency of electromagnetic radiation, including scattering and optical effects; however, the resulting changes are distinguishable from (astronomical) redshift and are not generally referred to as such (see section on physical optics and radiative transfer).

History

The history of the subject began in the 19th century, with the development of classical wave mechanics and the exploration of phenomena which are associated with the Doppler effect. The effect is named after the Austrian mathematician, Christian Doppler, who offered the first known physical explanation for the phenomenon in 1842. In 1845, the hypothesis was tested and confirmed for sound waves by the Dutch scientist Christophorus Buys Ballot. Doppler correctly predicted that the phenomenon would apply to all waves and, in particular, suggested that the varying colors of stars could be attributed to their motion with respect to the Earth. Before this was verified, it was found that stellar colors were primarily due to a star's temperature, not motion. Only later was Doppler vindicated by verified redshift observations.

The Doppler redshift was first described by French physicist Hippolyte Fizeau in 1848, who noted the shift in spectral lines 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 the method. In 1871, optical redshift was confirmed when the phenomenon was observed in Fraunhofer lines, using solar rotation, about 0.1 Å in the red. 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. In 1901, Aristarkh Belopolsky verified optical redshift in the laboratory using a system of rotating mirrors.

Arthur Eddington used the term "red-shift" as early as 1923, although the word does not appear unhyphenated until about 1934, when Willem de Sitter used it.

Beginning with observations in 1912, Vesto Slipher discovered that most spiral galaxies, then mostly thought to be spiral nebulae, had considerable redshifts. Slipher first reported on his measurement in the inaugural volume of the Lowell Observatory Bulletin. Three years later, he wrote a review in the journal Popular Astronomy. In it he stated that "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."

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 distances to them, with the formulation of his eponymous Hubble's law. Milton Humason worked on those observations with Hubble. These observations corroborated Alexander Friedmann's 1922 work, in which he derived the Friedmann–Lemaître equations. They are now considered to be strong evidence for an expanding universe and the Big Bang theory.

Measurement, characterization, and interpretation

High-redshift galaxy candidates in the Hubble Ultra Deep Field, 2012

The spectrum of light that comes from a source (see idealized spectrum illustration top-right) can be measured. To determine the redshift, one searches for features in the spectrum such as absorption lines, emission lines, or other variations in light intensity. 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 atomic element in space is hydrogen.

The spectrum of originally featureless light shone through hydrogen will show a 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 traveling 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).

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:

Calculation of redshift, z {\displaystyle z}
Based on wavelength Based on frequency
z = λ o b s v λ e m i t λ e m i t {\displaystyle z={\frac {\lambda _{\mathrm {obsv} }-\lambda _{\mathrm {emit} }}{\lambda _{\mathrm {emit} }}}} z = f e m i t f o b s v f o b s v {\displaystyle z={\frac {f_{\mathrm {emit} }-f_{\mathrm {obsv} }}{f_{\mathrm {obsv} }}}}
1 + z = λ o b s v λ e m i t {\displaystyle 1+z={\frac {\lambda _{\mathrm {obsv} }}{\lambda _{\mathrm {emit} }}}} 1 + z = f e m i t f o b s v {\displaystyle 1+z={\frac {f_{\mathrm {emit} }}{f_{\mathrm {obsv} }}}}

After z is measured, the distinction between redshift and blueshift is simply a matter of whether z is positive or negative. For example, Doppler effect blueshifts (z < 0) are associated with objects approaching (moving closer to) the observer with the light shifting to greater 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.

Redshift formulae

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.

Redshift summary
Redshift type Geometry Formula
Relativistic Doppler Minkowski space
(flat spacetime)

For motion completely in the radial or
line-of-sight direction:

1 + z = γ ( 1 + v c ) = 1 + v c 1 v c {\displaystyle 1+z=\gamma \left(1+{\frac {v_{\parallel }}{c}}\right)={\sqrt {\frac {1+{\frac {v_{\parallel }}{c}}}{1-{\frac {v_{\parallel }}{c}}}}}}
z v c {\displaystyle z\approx {\frac {v_{\parallel }}{c}}}  for small v {\displaystyle v_{\parallel }}


For motion completely in the transverse direction:

1 + z = 1 1 v 2 c 2 {\displaystyle 1+z={\frac {1}{\sqrt {1-{\frac {v_{\perp }^{2}}{c^{2}}}}}}}
z 1 2 ( v c ) 2 {\displaystyle z\approx {\frac {1}{2}}\left({\frac {v_{\perp }}{c}}\right)^{2}}  for small v {\displaystyle v_{\perp }}
Cosmological redshift FLRW spacetime
(expanding Big Bang universe)
1 + z = a n o w a t h e n {\displaystyle 1+z={\frac {a_{\mathrm {now} }}{a_{\mathrm {then} }}}}

Hubble's law:

z H 0 D c {\displaystyle z\approx {\frac {H_{0}D}{c}}}  for D c H 0 {\displaystyle D\ll {\frac {c}{H_{0}}}}
Gravitational redshift any stationary spacetime
1 + z = g t t ( receiver ) g t t ( source ) {\displaystyle 1+z={\sqrt {\frac {g_{tt}({\text{receiver}})}{g_{tt}({\text{source}})}}}}

For the Schwarzschild geometry:

1 + z = 1 r S r receiver 1 r S r source = 1 2 G M c 2 r receiver 1 2 G M c 2 r source {\displaystyle 1+z={\sqrt {\frac {1-{\frac {r_{S}}{r_{\text{receiver}}}}}{1-{\frac {r_{S}}{r_{\text{source}}}}}}}={\sqrt {\frac {1-{\frac {2GM}{c^{2}r_{\text{receiver}}}}}{1-{\frac {2GM}{c^{2}r_{\text{source}}}}}}}}
z 1 2 ( r S r source r S r receiver ) {\displaystyle z\approx {\frac {1}{2}}\left({\frac {r_{S}}{r_{\text{source}}}}-{\frac {r_{S}}{r_{\text{receiver}}}}\right)}  for r r S {\displaystyle r\gg r_{S}}

In terms of escape velocity:

z 1 2 ( v e c ) source 2 1 2 ( v e c ) receiver 2 {\displaystyle z\approx {\frac {1}{2}}\left({\frac {v_{\text{e}}}{c}}\right)_{\text{source}}^{2}-{\frac {1}{2}}\left({\frac {v_{\text{e}}}{c}}\right)_{\text{receiver}}^{2}}

for v e c {\displaystyle v_{\text{e}}\ll c}

Doppler effect

Main articles: Doppler effect and Relativistic Doppler effect
Doppler effect, yellow (~575 nm wavelength) ball appears greenish (blueshift to ~565 nm wavelength) approaching observer, turns 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 5,200 km/s, or about 32 times faster than the speed record for the fastest space probe.
Redshift and blueshift

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 (vc), the redshift is given by

z v c {\displaystyle z\approx {\frac {v}{c}}}     (since γ 1 {\displaystyle \gamma \approx 1} )

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.

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 (for motion solely in the line of sight):

1 + z = ( 1 + v c ) γ . {\displaystyle 1+z=\left(1+{\frac {v}{c}}\right)\gamma .}

This phenomenon was first observed in a 1938 experiment performed by Herbert E. Ives and G.R. Stilwell, called the Ives–Stilwell experiment.

Since the Lorentz factor is dependent only on the 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 projection of the movement of the source into the 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 (zero angle is directly away from the observer), the full form for the relativistic Doppler effect becomes:

1 + z = 1 + v cos ( θ ) / c 1 v 2 / c 2 {\displaystyle 1+z={\frac {1+v\cos(\theta )/c}{\sqrt {1-v^{2}/c^{2}}}}}

and for motion solely in the line of sight (θ = 0°), this equation reduces to:

1 + z = 1 + v / c 1 v / c {\displaystyle 1+z={\sqrt {\frac {1+v/c}{1-v/c}}}}

For the special case that the light is moving at right angle (θ = 90°) to the direction of relative motion in the observer's frame, the relativistic redshift is known as the transverse redshift, and a redshift:

1 + z = 1 1 v 2 / c 2 {\displaystyle 1+z={\frac {1}{\sqrt {1-v^{2}/c^{2}}}}}

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.

Cosmic expansion

Main article: Expansion of the universe

In the earlier part of the twentieth century, Slipher, Wirtz 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 being due to random motions, but later Lemaître (1927) and Hubble (1929), using previous data, discovered a roughly linear correlation between the increasing redshifts of, and distances to, galaxies. Lemaître realized that these observations could be explained by a mechanism of producing redshifts seen in Friedmann's solutions to Einstein's equations of general relativity. The correlation between redshifts and distances arises in all expanding models.

This cosmological redshift is commonly attributed to stretching of the wavelengths of photons propagating through the expanding space. This interpretation can be misleading, however; expanding space is only a choice of coordinates and thus cannot have physical consequences. The cosmological redshift is more naturally interpreted as a Doppler shift arising due to the recession of distant objects.

The observational consequences of this effect can be derived using the equations from general relativity that describe a homogeneous and isotropic universe. The cosmological redshift can thus be written as a function of a, the time-dependent cosmic scale factor:

1 + z = a n o w a t h e n {\displaystyle 1+z={\frac {a_{\mathrm {now} }}{a_{\mathrm {then} }}}}

In an expanding universe such as the one we inhabit, the scale factor is 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 Ω0:

Ω 0 = ρ ρ crit   , {\displaystyle \Omega _{0}={\frac {\rho }{\rho _{\text{crit}}}}\ ,}

with ρcrit the critical density demarcating a universe that eventually crunches from one that simply expands. This density is about three hydrogen atoms per cubic meter of space. At large redshifts, 1 + z > Ω0, one finds:

t ( z ) 2 3 H 0 Ω 0 1 / 2 z 3 / 2   , {\displaystyle t(z)\approx {\frac {2}{3H_{0}{\Omega _{0}}^{1/2}}}z^{-3/2}\ ,}

where H0 is the present-day Hubble constant, and z is the redshift.

There are several websites for calculating various times and distances from redshift, as the precise calculations require numerical integrals for most values of the parameters.

Distinguishing between cosmological and local effects

For cosmological redshifts of z < 0.01 additional Doppler redshifts and blueshifts due to the peculiar motions of the galaxies relative to one another cause a wide scatter from the standard Hubble Law. The resulting situation can be illustrated by the Expanding Rubber Sheet Universe, a common cosmological analogy used to describe the expansion of the universe. 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.

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). 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. 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..." Steven Weinberg clarified, "The increase of wavelength from emission to absorption of light does not depend on the rate of change of a(t) at the times of emission or absorption, but on the increase of a(t) in the whole period from emission to absorption."

If the universe were contracting instead of expanding, we would see distant galaxies blueshifted by an amount proportional to their distance instead of redshifted.

Gravitational redshift

Main article: 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. The theoretical derivation of this effect follows from the Schwarzschild solution of the Einstein equations which yields the following formula for redshift associated with a photon traveling in the gravitational field of an uncharged, nonrotating, spherically symmetric mass:

1 + z = 1 1 2 G M r c 2 , {\displaystyle 1+z={\frac {1}{\sqrt {1-{\frac {2GM}{rc^{2}}}}}},}

where

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.

The effect is very small but measurable on Earth using the Mössbauer effect and was first observed in the Pound–Rebka experiment. 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).

Observations in astronomy

The lookback time of extragalactic observations by their redshift up to z=20. There are websites for calculating many such physical measures from redshift.

The redshift observed in astronomy can be measured because the emission and absorption spectra for atoms are distinctive and well known, calibrated from spectroscopic experiments in 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 or 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.

Spectroscopy, as a measurement, is considerably more difficult than simple photometry, which measures the brightness of astronomical objects through certain filters. 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 redshifts. Due to the broad wavelength ranges in photometric filters and the necessary assumptions about the nature of the spectrum at the light-source, errors for these sorts of measurements can range up to δz = 0.5, and are much less reliable than spectroscopic determinations.

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(1000nm) rather than at the blue-green(500nm) color associated with the peak of its blackbody spectrum, and the light intensity will be reduced in the filter by a factor of four, (1 + z). Both the photon count rate and the photon energy are redshifted. (See K correction for more details on the photometric consequences of redshift.)

Local observations

In nearby objects (within our Milky Way galaxy) observed redshifts are almost always related to the line-of-sight velocities associated with the objects being observed. Observations of such redshifts and blueshifts have enabled astronomers to measure velocities and parametrize the masses of the orbiting stars in spectroscopic binaries, a method first employed in 1868 by British astronomer William Huggins. Similarly, small redshifts and blueshifts detected in the spectroscopic measurements of individual stars are one way astronomers have been able to diagnose and measure the presence and characteristics of planetary systems around other stars and have even made very detailed differential measurements of redshifts during planetary transits to determine precise orbital parameters.

Finely detailed measurements of redshifts are used in helioseismology to determine the precise movements of the photosphere of the Sun. Redshifts have also been used to make the first measurements of the rotation rates of planets, velocities of interstellar clouds, the rotation of galaxies, and the dynamics of accretion onto neutron stars and black holes which exhibit both Doppler and gravitational redshifts. The temperatures of various emitting and absorbing objects can be obtained by measuring Doppler broadening—effectively redshifts and blueshifts over a single emission or absorption line. By measuring the broadening and shifts of the 21-centimeter hydrogen line in different directions, astronomers have been able to measure the recessional velocities of interstellar gas, which in turn reveals the rotation curve of our Milky Way. Similar measurements have been performed on other galaxies, such as Andromeda. As a diagnostic tool, redshift measurements are one of the most important spectroscopic measurements made in astronomy.

Extragalactic observations

The age of the universe versus redshift from z=5 to 20.

The most distant objects exhibit larger redshifts corresponding to the 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 z = 1089 (z = 0 corresponds to present time), and it shows the state of the universe about 13.8 billion years ago, and 379,000 years after the initial moments of the Big Bang.

The luminous point-like cores of quasars were the first "high-redshift" (z > 0.1) objects discovered before the improvement of telescopes allowed for the discovery of other high-redshift galaxies.

For galaxies more distant than the Local Group and the nearby Virgo Cluster, but within a thousand 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 1912, while Hubble correlated Slipher's measurements with distances he measured by other means to formulate his Law. Hubble's law follows in part from the Copernican principle. Because it is usually not known how 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.

Gravitational interactions of galaxies with each other and clusters cause a significant scatter in the normal plot of the Hubble diagram. The peculiar velocities associated with galaxies superimpose a rough trace of the mass of 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 barycenter, and redshift maps of clusters showing a fingers of god effect due to the scatter of peculiar velocities in a roughly spherical distribution. 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.

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.

While it was long believed that the expansion rate has been continuously decreasing since the Big Bang, observations beginning in 1988 of the redshift-distance relationship using Type Ia supernovae have suggested that in comparatively recent times the expansion rate of the universe has begun to accelerate.

Highest redshifts

See also: List of most distant objects by type
Comoving distance and lookback time for the Planck 2018 cosmology parameters, from redshift 0 to 15, with distance (blue solid line) on the left axis, and time (orange dashed line) on the right. Note that the time that has passed (in giga years) from a given redshift until now is not the same as the distance (in giga light years) light would have traveled from that redshift, due to the expansion of the universe over the intervening period.

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 JADES-GS-z14-0 with a redshift of z = 14.32, corresponding to 290 million years after the Big Bang. The previous record was held by GN-z11, with a redshift of z = 11.1, corresponding to 400 million years after the Big Bang, and by UDFy-38135539 at a redshift of z = 8.6, corresponding to 600 million years after the Big Bang.

Slightly less reliable are Lyman-break redshifts, the highest of which is the lensed galaxy A1689-zD1 at a redshift z = 7.5 and the next highest being z = 7.0. The most distant-observed gamma-ray burst with a spectroscopic redshift measurement was GRB 090423, which had a redshift of z = 8.2. The most distant-known quasar, ULAS J1342+0928, is at z = 7.54. The highest-known redshift radio galaxy (TGSS1530) is at a redshift z = 5.72 and the highest-known redshift molecular material is the detection of emission from the CO molecule from the quasar SDSS J1148+5251 at z = 6.42.

Extremely red objects (EROs) are 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. Objects that are even redder than EROs are termed hyper extremely red objects (HEROs).

The cosmic microwave background has a redshift of z = 1089, corresponding to an age of approximately 379,000 years after the Big Bang and a proper distance of more than 46 billion light-years. 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 20 < z < 100. 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 z > 10) and the cosmic gravitational wave background emitted directly from inflation at a redshift in excess of z > 10.

In June 2015, astronomers reported evidence for Population III stars in the Cosmos Redshift 7 galaxy at z = 6.60. Such stars are likely to have existed in the very early universe (i.e., at high redshift), and may have started the production of chemical elements heavier than hydrogen that are needed for the later formation of planets and life as we know it.

Redshift surveys

Rendering of the 2dFGRS data
Main article: Redshift survey

With advent of automated telescopes and improvements in 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 universe. The Great Wall, a vast supercluster of galaxies over 500 million light-years wide, provides a dramatic example of a large-scale structure that redshift surveys can detect.

The first redshift survey was the CfA Redshift Survey, started in 1977 with the initial data collection completed in 1982. 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. The Sloan Digital Sky Survey (SDSS), is ongoing as of 2013 and aims to measure the redshifts of around 3 million objects. SDSS has recorded redshifts for galaxies as high as 0.8, and has been involved in the detection of quasars 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.

Effects from physical optics or radiative transfer

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 by a transformation between reference frames. Such shifts can be from such physical phenomena as coherence effects or the scattering of electromagnetic radiation whether from charged elementary particles, from particulates, or from fluctuations of the index of refraction in a dielectric medium as occurs in the radio phenomenon of radio whistlers. 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 effects discussed above.

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 conserving total energy). 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 of wavelength. Furthermore, scattering from random media generally occurs at many angles, 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 lines as well.

In interstellar astronomy, visible spectra can appear redder due to scattering processes in a phenomenon referred to as interstellar reddening—similarly Rayleigh scattering causes the 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 redshifting because the spectroscopic lines are not shifted to other wavelengths in reddened objects and there is an additional dimming and distortion associated with the phenomenon due to photons being scattered in and out of the line of sight.

Blueshift

"Blueshift" redirects here. For the term as used in photochemistry, see hypsochromic shift. For the political phenomenon, see blue shift (politics). For other uses of "blueshift" or "blue shift", see Blueshift (disambiguation).

The opposite of a redshift is a blueshift. A blueshift is any decrease in wavelength (increase in energy), with a corresponding increase in frequency, of an electromagnetic wave. In visible light, this shifts a color towards the blue end of the spectrum.

Doppler blueshift

Doppler redshift and blueshift

Doppler blueshift is caused by movement of a source towards the observer. The term applies to any decrease in wavelength and increase in frequency caused by relative motion, even outside the visible spectrum. Only objects moving at near-relativistic speeds toward the observer are noticeably bluer to the naked eye, but the wavelength of any reflected or emitted photon or other particle is shortened in the direction of travel.

Doppler blueshift is used in astronomy to determine relative motion:

Gravitational blueshift

Matter waves (protons, electrons, photons, etc.) falling into a gravity well become more energetic and undergo observer-independent blueshifting.

Unlike the relative Doppler blueshift, caused by movement of a source towards the observer and thus dependent on the received angle of the photon, gravitational blueshift is absolute and does not depend on the received angle of the photon:

Photons climbing out of a gravitating object become less energetic. This loss of energy is known as a "redshifting", as photons in the visible spectrum would appear more red. Similarly, photons falling into a gravitational field become more energetic and exhibit a blueshifting. ... Note that the magnitude of the redshifting (blueshifting) effect is not a function of the emitted angle or the received angle of the photon—it depends only on how far radially the photon had to climb out of (fall into) the potential well.

It is a natural consequence of conservation of energy and mass–energy equivalence, and was confirmed experimentally in 1959 with the Pound–Rebka experiment. Gravitational blueshift contributes to cosmic microwave background (CMB) anisotropy via the Sachs–Wolfe effect: when a gravitational well evolves while a photon is passing, the amount of blueshift on approach will differ from the amount of gravitational redshift as it leaves the region.

Blue outliers

There are faraway active galaxies that show a blueshift in their emission lines. One of the largest blueshifts is found in the narrow-line quasar, PG 1543+489, which has a relative velocity of -1150 km/s. These types of galaxies are called "blue outliers".

Cosmological blueshift

In a hypothetical universe undergoing a runaway Big Crunch contraction, a cosmological blueshift would be observed, with galaxies further away being increasingly blueshifted—the exact opposite of the actually observed cosmological redshift in the present expanding universe.

See also

References

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  34. ^ Staff (2022). "ICRAR Cosmology Calculator". International Centre for Radio Astronomy Research. Retrieved 6 August 2022. ICRAR Cosmology Calculator - Set H0=67.4 and OmegaM=0.315 (see Table/Planck2018 at "Lambda-CDM model#Parameters")
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  36. Measurements of the peculiar velocities out to 5 Mpc using the Hubble Space Telescope were reported in 2003 by Karachentsev, I. D.; et al. (2003). "Local galaxy flows within 5 Mpc". Astronomy and Astrophysics. 398 (2): 479–491. arXiv:astro-ph/0211011. Bibcode:2003A&A...398..479K. doi:10.1051/0004-6361:20021566. S2CID 26822121.
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  38. Lewis, Geraint F.; Francis, Matthew J.; Barnes, Luke A.; Kwan, Juliana; et al. (2008). "Cosmological Radar Ranging in an Expanding Universe". Monthly Notices of the Royal Astronomical Society. 388 (3): 960–964. arXiv:0805.2197. Bibcode:2008MNRAS.388..960L. doi:10.1111/j.1365-2966.2008.13477.x. S2CID 15147382. 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.
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  44. This is only true in a universe where there are no peculiar velocities. Otherwise, redshifts combine as
    1 + z = ( 1 + z D o p p l e r ) ( 1 + z e x p a n s i o n ) {\displaystyle 1+z=(1+z_{\mathrm {Doppler} })(1+z_{\mathrm {expansion} })}
    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.; Webb, J. K. (April 2003). "Solutions to the tethered galaxy problem in an expanding universe and the observation of receding blueshifted objects". American Journal of Physics. 71 (4): 358–364. arXiv:astro-ph/0104349. Bibcode:2003AmJPh..71..358D. doi:10.1119/1.1528916. S2CID 3219383.
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Sources

Articles

  • 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.)
  • Lineweaver, Charles H. and Tamara M. Davis, "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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