TheInfoList

In
physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical scie ...

, a redshift is an increase in the
wavelength In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular su ...

, and corresponding decrease in the
frequency Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparen ...

and
photon energy Photon energy is the energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, i ...
, of
electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. ...

(such as
light Light or visible light is electromagnetic radiation within the portion of the electromagnetic spectrum that is visual perception, perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nan ...

). The opposite change, a decrease in wavelength and simultaneous increase in frequency and energy, is known as a negative redshift, or
blueshift A blueshift is any decrease in wavelength In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order ...

. The terms derive from the colours
red Red is the color at the long wavelength end of the visible spectrum of light, next to orange and opposite violet. It has a dominant wavelength Image:dominant wavelength.png, frame, Dominant/complementary wavelength example on the CIE color ...

and
blue Blue is one of the three primary colours of pigments in painting and traditional colour theory In the visual arts The visual arts are art forms such as painting Painting is the practice of applying paint Paint is any pig ...

which form the extremes of the
visible light spectrum File:Light Amplification by Stimulated Emission of Radiation.jpg, Laser beams with visible spectrum The visible spectrum is the portion of the electromagnetic spectrum that is visual perception, visible to the human eye. Electromagnetic radiation ...
. In
astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial objects and celestial event, phenomena. It uses mathematics, phys ...
and
cosmology Cosmology (from Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is appro ...
, the three main causes of electromagnetic redshift are # The radiation travels between objects which are moving apart (" relativistic" redshift, an example of the
relativistic Doppler effect The relativistic Doppler effect is the change in frequency Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is the indefinite continued sequence, progress of exi ...
) #The radiation travels towards an object in a weaker
gravitational potential In classical mechanics, the gravitational potential at a location is equal to the work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical w ...

, i.e. towards an object in less strongly
curved In mathematics, a curve (also called a curved line in older texts) is an object similar to a line (geometry), line, but that does not have to be Linearity, straight. Intuitively, a curve may be thought of as the trace left by a moving point (geo ...
(flatter)
spacetime In physics, spacetime is any mathematical model which fuses the three-dimensional space, three dimensions of space and the one dimension of time into a single four-dimensional manifold. Minkowski diagram, Spacetime diagrams can be used to visuali ...
(
gravitational redshift In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...
) #The radiation travels through expanding space (
cosmological redshift Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides ...
). The observation that all sufficiently distant light sources show redshift corresponding to their distance from Earth is known as
Hubble's law Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides ...
. Relativistic, gravitational, and cosmological redshifts can be understood under the umbrella of .
Gravitational wave Gravitational waves are disturbances in the curvature of spacetime In , spacetime is any which fuses the and the one of into a single . can be used to visualize effects, such as why different observers perceive differently where and wh ...
s, which also travel at
the speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. Its exact value is defined as (approximately ). It is exact because, by international agreement, a Metre#Speed ...
, are subject to the same redshift phenomena. Examples of strong redshifting are a
gamma ray A gamma ray, also known as gamma radiation (symbol γ or \gamma), is a penetrating form of electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, it ...
perceived as an
X-ray An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Moti ...

, or initially visible light perceived as
radio wave Radio waves are a type of electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space ...
s. Subtler redshifts are seen in the
spectroscopic Spectroscopy is the study of the interaction between matter and Electromagnetism, electromagnetic radiation as a function of the wavelength or frequency of the radiation. In simpler terms, spectroscopy is the precise study of color as generalize ...
observations of
astronomical Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies celestial objects and phenomena. It uses mathematics Mathematics (from Ancient Greek, Gr ...
objects, and are used in terrestrial technologies such as
Doppler radar A Doppler radar is a specialized radar Radar (radio detection and ranging) is a detection system that uses radio waves to determine the distance (''ranging''), angle, or velocity of objects. It can be used to detect aircraft, Marine radar, ...
and
radar gun A radar speed gun (also radar gun and speed gun) is a device used to measure the speed of moving objects. It is used in law-enforcement to measure the speed of moving vehicle A vehicle (from la, vehiculum) is a machine that transports peopl ...

s. Other physical processes exist that can lead to a shift in the frequency of electromagnetic radiation, including
scattering Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light Light or visible light is electromagnetic radiation within the portion of the electromagneti ...

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). 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 >1 for redshifts, <1 for blueshifts).

# History

The history of the subject began with the development in the 19th century of
wave In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular su ...

mechanics and the exploration of phenomena associated with the
Doppler effect The Doppler effect or Doppler shift (or simply Doppler, when in context) is the change in frequency Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is the ...

. The effect is named after
Christian Doppler Christian Andreas Doppler (; 29 November 1803 – 17 March 1853) was an Austrian mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics as ...

, who offered the first known physical explanation for the phenomenon in 1842. The hypothesis was tested and confirmed for
sound wave In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...

s by the
Dutch Dutch commonly refers to: * Something of, from, or related to the Netherlands * Dutch people () * Dutch language () *Dutch language , spoken in Belgium (also referred as ''flemish'') Dutch may also refer to:" Castle * Dutch Castle Places * ...

scientist Christophorus Buys Ballot in 1845. Doppler correctly predicted that the phenomenon should apply to all waves, and in particular suggested that the varying
color Color (American English American English (AmE, AE, AmEng, USEng, en-US), sometimes called United States English or U.S. English, is the set of varieties of the English language native to the United States. Currently, American Engli ...

s of
star A star is an astronomical object consisting of a luminous spheroid of plasma Plasma or plasm may refer to: Science * Plasma (physics), one of the four fundamental states of matter * Plasma (mineral) or heliotrope, a mineral aggregate * Quark ...

s could be attributed to their motion with respect to the Earth. Before this was verified, however, it was found that stellar colors were primarily due to a star's
temperature Temperature ( ) is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy Thermal radiation in visible light can be seen on this hot metalwork. Thermal energy refers to several distinct physical concept ...

, not motion. Only later was Doppler vindicated by verified redshift observations. The first Doppler redshift was described by French physicist
Hippolyte Fizeau Armand Hippolyte Louis Fizeau FRS FRSE MIF (23 September 181918 September 1896) was a French physicist A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branch ...

in 1848, who pointed to the shift in
spectral line A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light Light or visible light is electromagnetic radiation within the portion of the electromagnetic spect ...
s seen in stars as being due to the Doppler effect. The effect is sometimes called the "Doppler–Fizeau effect". In 1868, British astronomer
William Huggins Sir William Huggins (7 February 1824 – 12 May 1910) was an English astronomer best known for his pioneering work in astronomical spectroscopy together with his wife Margaret Lindsay Huggins. Biography William Huggins was born at Cornhill, ...

was the first to determine the velocity of a star moving away from the Earth by this method. In 1871, optical redshift was confirmed when the phenomenon was observed in
Fraunhofer lines (nm). Dips in intensity are observed as dark lines (absorption) at the wavelengths of the Fraunhofer lines, (e.g., the features G, F, b, E, B). The "spectrum of ''blue sky''" presents across 450 – 485 nm, the wavelengths of the color ''blue''. In ...

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 Aristarkh Apollonovich Belopolsky (Аристарх Аполлонович Белопольский) (), Moscow Moscow (, ; rus, links=no, Москва, r=Moskva, p=mɐˈskva, a=Москва.ogg) is the capital and largest city of Russia ...
verified optical redshift in the laboratory using a system of rotating mirrors. The earliest occurrence of the term ''red-shift'' in print (in this hyphenated form) appears to be by American astronomer Walter S. Adams in 1908, in which he mentions "Two methods of investigating that nature of the nebular red-shift". The word does not appear unhyphenated until about 1934 by
Willem de Sitter Willem de Sitter (6 May 1872 – 20 November 1934) was a Dutch mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quan ...

, perhaps indicating that up to that point its German equivalent, ''Rotverschiebung'', was more commonly used. Beginning with observations in 1912,
Vesto Slipher Vesto Melvin Slipher (; November 11, 1875 – November 8, 1969) was an American astronomer who performed the first measurements of radial velocities for galaxies. He was the first to discover that distant galaxies are redshifts, redshifted, thus pr ...
discovered that most
spiral galaxies Spiral galaxies form a galaxy morphological classification, class of galaxy originally described by Edwin Hubble in his 1936 work ''The Realm of the Nebulae''
, then mostly thought to be spiral nebulae, had considerable redshifts. Slipher first reports on his measurement in the inaugural volume of the ''
Lowell Observatory Lowell Observatory is an astronomical Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies celestial objects and phenomena. It uses mathematic ...

Bulletin''. Three years later, he wrote a review in the journal '' Popular Astronomy''. In it he states 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 In astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial objects and celestial event, phenomena. It uses ...

, all but three having observable "positive" (that is recessional) velocities. Subsequently,
Edwin Hubble Edwin Powell Hubble (November 20, 1889 – September 28, 1953) was an American astronomer. He played a crucial role in establishing the fields of extragalactic astronomy and observational cosmology. Hubble proved that many objects previously ...
discovered an approximate relationship between the redshifts of such "nebulae" and the
distance Distance is a numerical measurement Measurement is the quantification (science), quantification of variable and attribute (research), attributes of an object or event, which can be used to compare with other objects or events. The scope and ...

s to them with the formulation of his eponymous
Hubble's law Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides ...
. These observations corroborated
Alexander Friedmann Alexander Alexandrovich Friedmann (also spelled Friedman or Fridman ; russian: Алекса́ндр Алекса́ндрович Фри́дман) (June 16 .S. 4 1888 – September 16, 1925) was a Russian and Soviet The Soviet Union,. offi ...
's 1922 work, in which he derived the Friedmann–Lemaître equations. They are today considered strong evidence for an
expanding universe The expansion of the universe is the increase in distance Distance is a numerical measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other crite ...

and the
Big Bang The Big Bang theory A theory is a rational Rationality is the quality or state of being rational – that is, being based on or agreeable to reason Reason is the capacity of consciously making sense of things, applying logic ...

theory.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 (Reprint: )

# Measurement, characterization, and interpretation

The
spectrum A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum Continuum may refer to: * Continuum (measurement) Continuum theories or models expla ...
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 A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission (electromagnetic radiation), emission or absorption (electromagnetic radiation), absorption of light in a narrow frequency range, c ...
,
emission lines A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , ...
, 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 Hydrogen is the chemical element with the Symbol (chemistry), symbol H and atomic number 1. Hydrogen is the lightest element. At standard temperature and pressure, standard conditions hydrogen is a gas of diatomic molecules having the che ...

. 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. 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 In signal processing Signal processing is an electrical engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, elect ...

(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 In dimensional analysis In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantity, base quantities (such as length, mass, time, and electric cur ...
called . If represents wavelength and represents frequency (note, where is the
speed of light The speed of light in vacuum A vacuum is a space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called paramet ...
), then is defined by the equations: After is measured, the distinction between redshift and blueshift is simply a matter of whether is positive or negative. For example,
Doppler effect The Doppler effect or Doppler shift (or simply Doppler, when in context) is the change in frequency Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is the ...

blueshifts () are associated with objects approaching (moving closer to) the observer with the light shifting to greater
energies In physics, energy is the physical quantity, quantitative physical property, property that must be #Energy transfer, transferred to an Physical body, object in order to perform Work (thermodynamics), work on, or to heat, the object.The second ...

. Conversely, Doppler effect redshifts () 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 In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "P ...

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 ) is independent of the wavelength.See Binney and Merrifeld (1998), Carroll and Ostlie (1996), Kutner (2003) for applications in astronomy.

## Doppler effect

If a source of the light is moving away from an observer, then redshift () occurs; if the source moves towards the observer, then
blueshift A blueshift is any decrease in wavelength In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order ...

() occurs. This is true for all electromagnetic waves and is explained by the
Doppler effect The Doppler effect or Doppler shift (or simply Doppler, when in context) is the change in frequency Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is the ...

. Consequently, this type of redshift is called the ''Doppler redshift''. If the source moves away from the observer with
velocity The velocity of an object is the rate of change of its position with respect to a frame of reference In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical scie ...

, which is much less than the speed of light (), the redshift is given by :$z \approx \frac$     (since $\gamma \approx 1$) where is the
speed of light The speed of light in vacuum A vacuum is a space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called paramet ...
. 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 The relativistic Doppler effect is the change in frequency Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is the indefinite continued sequence, progress of exi ...
. In brief, objects moving close to the speed of light will experience deviations from the above formula due to the
time dilation In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular s ...

of
special relativity In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force ...
which can be corrected for by introducing the
Lorentz factor The Lorentz factor or Lorentz term is a quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assi ...

into the classical Doppler formula as follows (for motion solely in the line of sight): :$1 + z = \left\left(1 + \frac\right\right) \gamma.$ This phenomenon was first observed in a 1938 experiment performed by Herbert E. Ives and G.R. Stilwell, called the
Ives–Stilwell experiment The Ives–Stilwell experiment tested the contribution of relativistic time dilation to the Doppler effect, Doppler shift of light. The result was in agreement with the formula for the relativistic Doppler effect, transverse Doppler effect and was ...
. Since the Lorentz factor is dependent only on the
magnitude Magnitude may refer to: Mathematics *Euclidean vector, a quantity defined by both its magnitude and its direction *Magnitude (mathematics), the relative size of an object *Norm (mathematics), a term for the size or length of a vector *Order of ...
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 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: :$1+ z = \frac$ and for motion solely in the line of sight (), this equation reduces to: :$1 + z = \sqrt$ For the special case that the light is moving at
right angle In geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position ...

() to the direction of relative motion in the observer's frame, the relativistic redshift is known as the transverse redshift, and a redshift: :$1 + z = \frac$ 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.

## Expansion of space

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 The Milky Way is the galaxy A galaxy is a gravitation Gravity (), or gravitation, is a natural phenomenon by which all things with mass Mass is both a property Property (''latin: Res Privata'') in the Abstract and con ...

. 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 In the General relativity, general theory of relativity the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of Matter#In_general_relativity_and_cosmology, matter within it. Th ...
of
general relativity General relativity, also known as the general theory of relativity, is the geometric Geometry (from the grc, γεωμετρία; '' geo-'' "earth", '' -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathema ...
. The correlation between redshifts and distances is required by all such models that have a metric expansion of space. As a result, the wavelength of photons propagating through the expanding space is stretched, creating the
cosmological redshift Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides ...
. There is a distinction between a redshift in cosmological context as compared to that witnessed when nearby objects exhibit a
local Local may refer to: Geography and transportation * Local (train) In rail transport Rail transport (also known as train transport) is a means of transferring passengers and goods on wheeled vehicle A vehicle (from la, vehiculum) i ...
Doppler-effect redshift. Rather than cosmological redshifts being a consequence of the relative velocities that are subject to the laws of
special relativity In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force ...
(and thus subject to the rule that no two locally separated objects can have relative velocities with respect to each other faster than the speed of light), the photons instead increase in wavelength and redshift because of a global feature of the spacetime through which they are traveling. One interpretation of this effect is the idea that space itself is expanding. Due to the expansion increasing as distances increase, the distance between two remote galaxies can increase at more than 3 m/s, but this does not imply that the galaxies move faster than the speed of light at their present location (which is forbidden by
Lorentz covariance In relativistic physics In physics, relativistic mechanics refers to mechanics compatible with special relativity (SR) and general relativity (GR). It provides a non-quantum mechanics, quantum mechanical description of a system of particles, or ...
).

### Mathematical derivation

The observational consequences of this effect can be derived using the equations from
general relativity General relativity, also known as the general theory of relativity, is the geometric Geometry (from the grc, γεωμετρία; '' geo-'' "earth", '' -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathema ...
that describe a homogeneous and isotropic universe. To derive the redshift effect, use the
geodesic In geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position o ...

equation for a light wave, which is :$ds^2=0=-c^2dt^2+\frac$ where * is the
spacetime In physics, spacetime is any mathematical model which fuses the three-dimensional space, three dimensions of space and the one dimension of time into a single four-dimensional manifold. Minkowski diagram, Spacetime diagrams can be used to visuali ...
interval * is the time interval * is the spatial interval * is the speed of light * is the time-dependent cosmic
scale factor A scale factor is usually a decimal which scales Scale or scales may refer to: Mathematics * Scale (descriptive set theory)In the mathematical discipline of descriptive set theory, a scale is a certain kind of object defined on a set (mathemat ...
* is the
curvature In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities an ...

per unit area. For an observer observing the crest of a light wave at a position and time , the crest of the light wave was emitted at a time in the past and a distant position . Integrating over the path in both space and time that the light wave travels yields: :$c \int_^ \frac\; = \int_^ \frac\,.$ In general, the wavelength of light is not the same for the two positions and times considered due to the changing properties of the metric. When the wave was emitted, it had a wavelength . The next crest of the light wave was emitted at a time :$t=t_\mathrm+\lambda_\mathrm/c\,.$ The observer sees the next crest of the observed light wave with a wavelength to arrive at a time :$t=t_\mathrm+\lambda_\mathrm/c\,.$ Since the subsequent crest is again emitted from and is observed at , the following equation can be written: :$c \int_^ \frac\; = \int_^ \frac\,.$ The right-hand side of the two integral equations above are identical which means :$c \int_^ \frac\; = c \int_^ \frac\,$ Using the following manipulation: :$\begin 0 & = \int_^ \frac - \int_^ \frac \\ & = \int_^\frac+\int_^\frac- \int_^ \frac \\ & = \int_^\frac-\left\left(\int_^\frac+\int_^ \frac\right\right) \\ & = \int_^\frac-\int_^\frac \end$ we find that: :$\int_^ \frac\; = \int_^ \frac\,.$ For very small variations in time (over the period of one cycle of a light wave) the scale factor is essentially a constant ( today and previously). This yields :$\frac-\frac\; = \frac-\frac$ which can be rewritten as :$\frac=\frac\,.$ Using the definition of redshift provided above, the equation :$1+z = \frac$ is obtained. In an expanding universe such as the one we inhabit, the scale factor is monotonically increasing as time passes, thus, 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 Cosmic time, or cosmological time, is the time Time is the continued of and that occurs in an apparently succession from the , through the , into the . It is a component quantity of various s used to events, to compare the duration of ev ...
–redshift relation''. Denote a density ratio as : :$\Omega_0 = \frac \ ,$ with 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, , one finds: :$t\left(z\right) \approx \frac \ ,$ where is the present-day
Hubble constant Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology Physical cosmology is a branch of cosmology Cosmology (from Ancient Greek, Greek κόσμος, ''kosmos'' "world" and -λογία, ''-logia'' ...

, and is the redshift.

### Distinguishing between cosmological and local effects

For cosmological redshifts of additional Doppler redshifts and blueshifts due to the peculiar motions of the galaxies relative to one another cause a wide from the standard
Hubble Law Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provide ...
. The resulting situation can be illustrated by the Expanding Rubber Sheet Universe, a common cosmological analogy used to describe the expansion of space. If two objects are represented by ball bearings and spacetime by a stretching rubber sheet, the Doppler effect is caused by rolling the balls across the sheet to create peculiar motion. The cosmological redshift occurs when the ball bearings are stuck to the sheet and the sheet is stretched."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." The redshifts of galaxies include both a component related to
recessional velocity Recessional velocity is the rate at which an extragalactic astronomical Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies celestial objects and ...
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.. A pdf file can be found her

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 Steven Weinberg (; May 3, 1933 – July 23, 2021) was an American theoretical A theory is a rational Rationality is the quality or state of being rational – that is, being based on or agreeable to reason Reason is the capacity of con ...
clarified, "The increase of wavelength from emission to absorption of light does not depend on the rate of change of Robertson–Walker_scale_factor.html" ;"title="Scale factor (cosmology)">Robertson–Walker scale factor">Scale factor (cosmology)">Robertson–Walker scale factorat the times of emission or absorption, but on the increase of in the whole period from emission to absorption." Popular literature often uses the expression "Doppler redshift" instead of "cosmological redshift" to describe the redshift of galaxies dominated by the expansion of spacetime, but the cosmological redshift is not found using the relativistic Doppler equation which is instead characterized by
special relativity In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force ...
; thus is impossible while, in contrast, is possible for cosmological redshifts because the space which separates the objects (for example, a quasar from the Earth) can expand faster than the speed of light. More mathematically, the viewpoint that "distant galaxies are receding" and the viewpoint that "the space between galaxies is expanding" are related by changing
coordinate system In geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position o ...

s. Expressing this precisely requires working with the mathematics of the Friedmann–Robertson–Walker metric. 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

In the theory of
general relativity General relativity, also known as the general theory of relativity, is the geometric Geometry (from the grc, γεωμετρία; '' geo-'' "earth", '' -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathema ...
, there is time dilation within a gravitational well. This is known as the
gravitational redshift In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...
or ''Einstein Shift''. The theoretical derivation of this effect follows from the Schwarzschild solution of the
Einstein equations In the general theory of relativity General relativity, also known as the general theory of relativity, is the differential geometry, geometric scientific theory, theory of gravitation published by Albert Einstein in 1915 and is the current de ...
which yields the following formula for redshift associated with a photon traveling in the
gravitational field In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "P ...

of an uncharged, , spherically symmetric mass: :$1+z=\frac,$ where * is the
gravitational constant The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant), denoted by the capital letter , is an empirical Empirical evidence for a prop ...

, * is the
mass Mass is the quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value ...
of the object creating the gravitational field, * is the radial coordinate of the source (which is analogous to the classical distance from the center of the object, but is actually a Schwarzschild coordinate), and * is the
speed of light The speed of light in vacuum A vacuum is a space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called paramet ...
. This gravitational redshift result can be derived from the assumptions of
special relativity In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force ...
and the
equivalence principle In the theory A theory is a rational Rationality is the quality or state of being rational – that is, being based on or agreeable to reason Reason is the capacity of consciously making sense of things, applying logic Logic (fr ...
; 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 Image:JeffersonLeft.jpg, Jefferson laboratory at Harvard University. The experiment occurred in the left "tower". The attic was later extended in 2004. The Pound–Rebka experiment was an experiment in which gamma rays were emitted from the top of ...
. However, it is significant near a , and as an object approaches the
event horizon In astrophysics, an event horizon is a boundary beyond which events cannot affect an observer. The term was coined by Wolfgang Rindler Wolfgang Rindler (18 May 1924 – 8 February 2019) was a physicist working in the field of general relativity ...
the red shift becomes infinite. It is also the dominant cause of large angular-scale temperature fluctuations in the
cosmic microwave background The cosmic microwave background (CMB, CMBR), in Big Bang The Big Bang theory A theory is a rational Rationality is the quality or state of being rational – that is, being based on or agreeable to reason Reason is the capacity ...
Sachs–Wolfe effect The Sachs–Wolfe effect, named after Rainer K. Sachs and Arthur M. Wolfe, is a property of the cosmic microwave background radiation (CMB), in which photons from the CMB are Gravitational redshift, gravitationally redshifted, causing the CMB spect ...
).

# Observations in astronomy

The redshift observed in astronomy can be measured because the emission and
absorption Absorption may refer to: Chemistry and biology *Absorption (chemistry), diffusion of particles of gas or liquid into liquid or solid materials *Absorption (skin), a route by which substances enter the body through the skin *Absorption (pharmacolo ...
spectra for
atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of ato ...

s are distinctive and well known, calibrated from
spectroscopic Spectroscopy is the study of the interaction between matter and Electromagnetism, electromagnetic radiation as a function of the wavelength or frequency of the radiation. In simpler terms, spectroscopy is the precise study of color as generalize ...
experiments in
laboratories A laboratory (, ; colloquially lab) is a facility that provides controlled conditions in which scientific Science (from the Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-E ...
on Earth. When the redshift of various absorption and emission lines from a single astronomical object is measured, 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 A thermal column (or thermal) is a column of rising air The atmosphere of Earth is the layer of gas Gas is one of the four fundamental states of matter In physics Physics is the natural science that studies matter, its ...

or mechanical
motion Image:Leaving Yongsan Station.jpg, 300px, Motion involves a change in position In physics, motion is the phenomenon in which an object changes its position (mathematics), position over time. Motion is mathematically described in terms of Displacem ...

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 Tired light is a class of hypothetical redshift mechanisms that was proposed as an alternative explanation for the Hubble's law, redshift-distance relationship. These models have been proposed as alternatives to the models that require metric expa ...
are not generally considered plausible.When cosmological redshifts were first discovered,
Fritz Zwicky Fritz Zwicky (; ; February 14, 1898 – February 8, 1974) was a Swiss Swiss may refer to: * the adjectival form of Switzerland , french: Suisse(sse), it, svizzero/svizzera or , rm, Svizzer/Svizra , government_type = Federalism, ...
proposed an effect known as tired light. While usually considered for historical interests, it is sometimes, along with intrinsic redshift suggestions, utilized by nonstandard cosmologies. In 1981, H. J. Reboul summarised man
alternative redshift mechanisms
that had been discussed in the literature since the 1930s. In 2001, Geoffrey Burbidge remarked in
review
that the wider astronomical community has marginalized such discussions since the 1960s. Burbidge and Halton Arp, while investigating the mystery of Quasar#History of quasar observation, the nature of quasars, tried to develop alternative redshift mechanisms, and very few of their fellow scientists acknowledged let alone accepted their work. Moreover, pointed out that alternative theories are unable to account for timescale stretch observed in type Ia supernovae
Spectroscopy, as a measurement, is considerably more difficult than simple photometry (astronomy), photometry, which measures the brightness of astronomical objects through certain Optical filter, 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, observational error, errors for these sorts of measurements can range up to , 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 , it would be brightest in the infrared rather than at the yellow-green color associated with the peak of its Black body, blackbody spectrum, and the light intensity will be reduced in the filter by a factor of four, . 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 The Milky Way is the galaxy A galaxy is a gravitation Gravity (), or gravitation, is a natural phenomenon by which all things with mass Mass is both a property Property (''latin: Res Privata'') in the Abstract and con ...

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 velocity, velocities and parametrize the
mass Mass is the quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value ...
es of the orbiting
star A star is an astronomical object consisting of a luminous spheroid of plasma Plasma or plasm may refer to: Science * Plasma (physics), one of the four fundamental states of matter * Plasma (mineral) or heliotrope, a mineral aggregate * Quark ...

s in spectroscopic binaries, a method first employed in 1868 by British astronomer
William Huggins Sir William Huggins (7 February 1824 – 12 May 1910) was an English astronomer best known for his pioneering work in astronomical spectroscopy together with his wife Margaret Lindsay Huggins. Biography William Huggins was born at Cornhill, ...

. Similarly, small redshifts and blueshifts detected in the spectroscopic measurements of individual stars are one way astronomers have been able to Methods of detecting exoplanets#Radial velocity, diagnose and measure the presence and characteristics of Exoplanet, planetary systems around other stars and have even made very Rossiter–McLaughlin effect, detailed differential measurements of redshifts during Methods of detecting exoplanets, 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 Galaxy rotation curve, rotation of galaxies, and the dynamics (mechanics), dynamics of Accretion disk, accretion onto neutron stars and s which exhibit both Doppler and gravitational redshifts. Additionally, 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 velocity, 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 Galaxy, Andromeda. As a diagnostic tool, redshift measurements are one of the most important astronomical spectroscopy, spectroscopic measurements made in astronomy.

## Extragalactic observations

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 The cosmic microwave background (CMB, CMBR), in Big Bang The Big Bang theory A theory is a rational Rationality is the quality or state of being rational – that is, being based on or agreeable to reason Reason is the capacity ...
radiation; the Hubble's law#Redshift velocity, numerical value of its redshift is about ( 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 Big Bang theory A theory is a rational Rationality is the quality or state of being rational – that is, being based on or agreeable to reason Reason is the capacity of consciously making sense of things, applying logic ...

. The luminous point-like cores of quasars were the first "high-redshift" () 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 Edwin Powell Hubble (November 20, 1889 – September 28, 1953) was an American astronomer. He played a crucial role in establishing the fields of extragalactic astronomy and observational cosmology. Hubble proved that many objects previously ...
and has come to be known as
Hubble's law Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides ...
.
Vesto Slipher Vesto Melvin Slipher (; November 11, 1875 – November 8, 1969) was an American astronomer who performed the first measurements of radial velocities for galaxies. He was the first to discover that distant galaxies are redshifts, redshifted, thus pr ...
was the first to discover galactic redshifts, in about the year 1912, while Hubble correlated Slipher's measurements with distances he cosmic distance ladder, measured by other means to formulate his Law. In the widely accepted cosmological model based on
general relativity General relativity, also known as the general theory of relativity, is the geometric Geometry (from the grc, γεωμετρία; '' geo-'' "earth", '' -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathema ...
, redshift is mainly a result of the expansion of space: this means that the farther away a galaxy is from us, the more the space has expanded in the time since the light left that galaxy, so the more the light has been stretched, the more redshifted the light is, and so the faster it appears to be moving away from us. Hubble's law follows in part from the Copernican principle.Peebles (1993). Because it is usually not known how luminosity, luminous objects are, measuring the redshift is easier than more direct distance measurements, so redshift is sometimes in practice converted to a crude distance measurement using Hubble's law. Gravitational interactions of galaxies with each other and clusters cause a significant in the normal plot of the Hubble diagram. The peculiar velocity, peculiar velocities associated with galaxies superimpose a rough trace of the
mass Mass is the quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value ...
of virial theorem, virialized objects in the universe. This effect leads to such phenomena as nearby galaxies (such as the Andromeda Galaxy) exhibiting blueshifts as we fall towards a common 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, recent observations of the redshift-distance relationship using Type Ia supernovae have suggested that in comparatively recent times the expansion rate of the universe has Accelerating expansion of the universe, begun to accelerate.

## Highest redshifts

Currently, the objects with the highest known redshifts are galaxies and the objects producing gamma ray bursts. The most reliable redshifts are from
spectroscopic Spectroscopy is the study of the interaction between matter and Electromagnetism, electromagnetic radiation as a function of the wavelength or frequency of the radiation. In simpler terms, spectroscopy is the precise study of color as generalize ...
data, and the highest-confirmed spectroscopic redshift of a galaxy is that of GN-z11, with a redshift of , corresponding to 400 million years after the Big Bang. The previous record was held by UDFy-38135539 at a redshift of , corresponding to 600 million years after the Big Bang. Slightly less reliable are Lyman-break galaxy, Lyman-break redshifts, the highest of which is the lensed galaxy A1689-zD1 at a redshift and the next highest being . The most distant-observed gamma-ray burst with a spectroscopic redshift measurement was GRB 090423, which had a redshift of . The most distant-known quasar, ULAS J1342+0928, is at . The highest-known redshift radio galaxy (TGSS1530) is at a redshift and the highest-known redshift molecular material is the detection of emission from the CO molecule from the quasar SDSS J1148+5251 at . ''Extremely red objects'' (EROs) are Radio astronomy#Astronomical sources, astronomical sources of radiation that radiate energy in the red and near infrared part of the electromagnetic spectrum. These may be starburst galaxies that have a high redshift accompanied by reddening from intervening dust, or they could be highly redshifted elliptical galaxies with an older (and therefore redder) stellar population. Objects that are even redder than EROs are termed ''hyper extremely red objects'' (HEROs). The
cosmic microwave background The cosmic microwave background (CMB, CMBR), in Big Bang The Big Bang theory A theory is a rational Rationality is the quality or state of being rational – that is, being based on or agreeable to reason Reason is the capacity ...
has a redshift of , corresponding to an age of approximately 379,000 years after the Big Bang and a comoving 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 . 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 ) and the cosmic gravitational wave background emitted directly from inflation (cosmology), inflation at a redshift in excess of . In June 2015, astronomers reported evidence for Metallicity#Stars, Population III stars in the Cosmos Redshift 7 galaxy at . 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 Hydrogen is the chemical element with the Symbol (chemistry), symbol H and atomic number 1. Hydrogen is the lightest element. At standard temperature and pressure, standard conditions hydrogen is a gas of diatomic molecules having the che ...

that are needed for the later formation of planets and life as we know it.

## Redshift surveys

With advent of automated telescopes and improvements in astronomical spectroscopy, spectroscopes, a number of collaborations have been made to map the universe in redshift space. By combining redshift with angular position data, a redshift survey maps the 3D distribution of matter within a field of the sky. These observations are used to measure properties of the Observable universe, large-scale structure of the universe. The CfA2 Great Wall, 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 . 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 Wolf effect, coherence effects or the
scattering Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light Light or visible light is electromagnetic radiation within the portion of the electromagneti ...

of
electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. ...

whether from electric charge, charged elementary particles, from particulates, or from fluctuations of the index of refraction in a dielectric medium as occurs in the radio phenomenon of Whistler (radio), radio whistlers. While such phenomena are sometimes referred to as "redshifts" and "blueshifts", in astrophysics light-matter interactions that result in energy shifts in the radiation field are generally referred to as "reddening" rather than "redshifting" which, as a term, is normally reserved for the #Redshift formulae, effects discussed above. In many circumstances scattering causes radiation to redden because entropy results in the predominance of many low-energy photons over few high-energy ones (while conservation of energy, conserving total energy). Except possibly under carefully controlled conditions, scattering does not produce the same relative change in wavelength across the whole spectrum; that is, any calculated is generally a function (mathematics), function of wavelength. Furthermore, scattering from randomness, random matter, media generally occurs at many angles, and is a function of the scattering angle. If multiple scattering occurs, or the scattering particles have relative motion, then there is generally distortion of
spectral line A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light Light or visible light is electromagnetic radiation within the portion of the electromagnetic spect ...
s as well. In interstellar medium, interstellar astronomy, Visible spectrum, visible spectra can appear redder due to scattering processes in a phenomenon referred to as interstellar reddening—similarly Rayleigh scattering causes the Atmosphere of Earth, atmospheric reddening of the Sun seen in the sunrise or sunset and causes the rest of the sky to have a blue color. This phenomenon is distinct from red''shift''ing because the
spectroscopic Spectroscopy is the study of the interaction between matter and Electromagnetism, electromagnetic radiation as a function of the wavelength or frequency of the radiation. In simpler terms, spectroscopy is the precise study of color as generalize ...
lines are not shifted to other wavelengths in reddened objects and there is an additional extinction (astronomy), dimming and distortion associated with the phenomenon due to photons being scattered in and out of the Line-of-sight propagation, line of sight.

# Blueshift

The opposite of a redshift is a blueshift. A blueshift is any decrease in
wavelength In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular su ...

(increase in energy), with a corresponding increase in frequency, of an electromagnetic wave. In Light, visible light, this shifts a color towards the blue end of the spectrum.

## Doppler blueshift

Doppler effect, 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 Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial objects and celestial event, phenomena. It uses mathematics, phys ...
to determine relative motion: * The Andromeda Galaxy is moving toward our own
Milky Way The Milky Way is the galaxy A galaxy is a gravitation Gravity (), or gravitation, is a natural phenomenon by which all things with mass Mass is both a property Property (''latin: Res Privata'') in the Abstract and con ...

galaxy within the Local Group; thus, when observed from Earth, its light is undergoing a blueshift. * Components of a binary star 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 Tully–Fisher relation). * Blazars are known to propel relativistic jets toward us, emitting synchrotron radiation and bremsstrahlung that appears blueshifted. * Nearby stars such as Barnard's Star 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 Hubble's law, cosmological redshift to determine relative motion in the Metric expansion of space, expanding universe.

## Gravitational blueshift

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: It is a natural consequence of conservation of energy and mass–energy equivalence, and was confirmed experimentally in 1959 with the
Pound–Rebka experiment Image:JeffersonLeft.jpg, Jefferson laboratory at Harvard University. The experiment occurred in the left "tower". The attic was later extended in 2004. The Pound–Rebka experiment was an experiment in which gamma rays were emitted from the top of ...
. Gravitational blueshift contributes to
cosmic microwave background The cosmic microwave background (CMB, CMBR), in Big Bang The Big Bang theory A theory is a rational Rationality is the quality or state of being rational – that is, being based on or agreeable to reason Reason is the capacity ...
(CMB) anisotropy via the
Sachs–Wolfe effect The Sachs–Wolfe effect, named after Rainer K. Sachs and Arthur M. Wolfe, is a property of the cosmic microwave background radiation (CMB), in which photons from the CMB are Gravitational redshift, gravitationally redshifted, causing the CMB spect ...
: when a gravitational well evolves while a photon is passing, the amount of blueshift on approach will differ from the amount of
gravitational redshift In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...
as it leaves the region.

### Blue outliers

There are faraway active galaxies that show a blueshift in their Oxygen, [O III] emission Emission spectrum, 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 Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides ...
in the present
expanding universe The expansion of the universe is the increase in distance Distance is a numerical measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other crite ...

.

* Cosmic crystallography * Gravitational potential * Relativistic Doppler effect

# 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,
, ''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.)

## Books

* * * * * * * * * * * See also physical cosmology#Textbooks, physical cosmology textbooks for applications of the cosmological and gravitational redshifts.