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In
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
, a redshift is an increase in the
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
, and corresponding decrease in the
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
and
photon energy Photon energy is the energy carried by a single photon. The amount of energy is directly proportional to the photon's electromagnetic frequency and thus, equivalently, is inversely proportional to the wavelength. The higher the photon's frequency, ...
, of
electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic field, electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, inf ...
(such as
light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
). The opposite change, a decrease in wavelength and simultaneous increase in frequency and energy, is known as a negative redshift, or
blueshift 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 simultaneous increase in fr ...
. 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 of approximately 625–740 nanometres. It is a primary color in the RGB color model and a secondar ...
and
blue Blue is one of the three primary colours in the RYB colour model (traditional colour theory), as well as in the RGB (additive) colour model. It lies between violet and cyan on the spectrum of visible light. The eye perceives blue when obs ...
which form the extremes of the
visible light spectrum The visible spectrum is the portion of the electromagnetic spectrum that is visible to the human eye. Electromagnetic radiation in this range of wavelengths is called ''visible light'' or simply light. A typical human eye will respond to wav ...
. In
astronomy Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...
and
cosmology Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount (lexicographer), Thomas Blount's ''Glossographia'', and in 1731 taken up in ...
, 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 (and wavelength) of light, caused by the relative motion of the source and the observer (as in the classical Doppler effect), when taking into account effects described by the special rel ...
) #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 (energy transferred) per unit mass that would be needed to move an object to that location from a fixed reference location. It is analogous to the electric po ...
, 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, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that a ...
(flatter)
spacetime In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...
(
gravitational redshift In physics and general relativity, gravitational redshift (known as Einstein shift in older literature) is the phenomenon that electromagnetic waves or photons travelling out of a gravitational well (seem to) lose energy. This loss of energ ...
) #The radiation travels through expanding space (
cosmological redshift Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving a ...
). 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 that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving ...
. Relativistic, gravitational, and cosmological redshifts can be understood under the umbrella of frame transformation laws.
Gravitational wave Gravitational waves are waves of the intensity of gravity generated by the accelerated masses of an orbital binary system that propagate as waves outward from their source at the speed of light. They were first proposed by Oliver Heaviside in 1 ...
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. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit for ...
, 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 arising from the radioactive decay of atomic nuclei. It consists of the shortest wavelength electromagnetic waves, typically ...
perceived as an
X-ray An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10  picometers to 10  nanometers, corresponding to frequencies in the range 30&nb ...
, or initially visible light perceived as
radio wave Radio waves are a type of electromagnetic radiation with the longest wavelengths in the electromagnetic spectrum, typically with frequencies of 300 gigahertz (GHz) and below. At 300 GHz, the corresponding wavelength is 1 mm (short ...
s. Subtler redshifts are seen in the
spectroscopic Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter wav ...
observations of
astronomical Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, galaxies ...
objects, and are used in terrestrial technologies such as
Doppler radar A Doppler radar is a specialized radar that uses the Doppler effect to produce velocity data about objects at a distance. It does this by bouncing a microwave signal off a desired target and analyzing how the object's motion has altered the f ...
and
radar gun A radar speed gun (also radar gun and speed trap gun) is a device used to measure the speed of moving objects. It is used in law-enforcement to measure the speed of moving vehicles and is often used in professional spectator sport, for things su ...
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 or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including ...
and
optical effects Compositing is the process or technique of combining visual elements from separate sources into single images, often to create the illusion that all those elements are parts of the same scene. Live-action shooting for compositing is variously ca ...
; 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, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (res ...
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 of a wave in relation to an observer who is moving relative to the wave source. It is named after the Austrian physicist Christian Doppler, who d ...
. The effect is named after
Christian Doppler Christian Andreas Doppler ( (); 29 November 1803 – 17 March 1853) was an Austrian mathematician and physicist. He is celebrated for his principle – known as the Doppler effect – that the observed frequency of a wave depends on the relative ...
, who offered the first known physical explanation for the phenomenon in 1842. The hypothesis was tested and confirmed for
sound wave In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the ...
s by the
Dutch Dutch commonly refers to: * Something of, from, or related to the Netherlands * Dutch people () * Dutch language () Dutch may also refer to: Places * Dutch, West Virginia, a community in the United States * Pennsylvania Dutch Country People E ...
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) or colour (British English) is the visual perceptual property deriving from the spectrum of light interacting with the photoreceptor cells of the eyes. Color categories and physical specifications of color are associ ...
s of
star A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...
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 quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...
, 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, best known for measuring the speed of light in the namesake Fizeau experiment. Biography Fizeau was born in Paris to Louis and Beatrice Fiz ...
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 in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used to iden ...
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. Biography William Huggins was born at Cornhill, Middlesex, in ...
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 In physics and optics, the Fraunhofer lines are a set of spectral absorption lines named after the German physicist Joseph von Fraunhofer (1787–1826). The lines were originally observed as dark features (absorption lines) in the optical spectru ...
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 – 16 May 1934, Pulkovo (Saint Petersburg), Pulkovo, Leningrad Oblast, Leningrad) was a Russian astronomer. He was born in Moscow ...
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. 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 redshifted, thus providing th ...
discovered that most
spiral galaxies Spiral galaxies form a class of galaxy originally described by Edwin Hubble in his 1936 work ''The Realm of the Nebulae''spiral nebulae, had considerable redshifts. Slipher first reports on his measurement in the inaugural volume of the ''
Lowell Observatory Lowell Observatory is an astronomical observatory in Flagstaff, Arizona, United States. Lowell Observatory was established in 1894, placing it among the oldest observatories in the United States, and was designated a National Historic Landmark ...
Bulletin''. Three years later, he wrote a review in the journal ''
Popular Astronomy Amateur astronomy is a hobby where participants enjoy observing or imaging celestial objects in the sky using the unaided eye, binoculars, or telescopes. Even though scientific research may not be their primary goal, some amateur astronomers ...
''. 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 and navigation, the celestial sphere is an abstract sphere that has an arbitrarily large radius and is concentric to Earth. All objects in the sky can be conceived as being projected upon the inner surface of the celestial sphere, ...
, all but three having observable "positive" (that is recessional) velocities. Subsequently,
Edwin Hubble Edwin Powell Hubble (November 20, 1889 – September 28, 1953) was an Americans, American astronomer. He played a crucial role in establishing the fields of extragalactic astronomy and observational cosmology. Hubble proved that many objects ...
discovered an approximate relationship between the redshifts of such "nebulae" and the
distance Distance is a numerical or occasionally qualitative 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 criteria (e.g. "two counties over"). ...
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 that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving ...
. 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 physicist and mathematician ...
'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 between any two given gravitationally unbound parts of the observable universe with time. It is an intrinsic expansion whereby the scale of space itself changes. The universe does not exp ...
and the
Big Bang The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from the ...
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. The word was first used scientifically in optics to describe the rainbow of colors i ...
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, ...
,
emission lines A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used to iden ...
, 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 H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic, an ...
. 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 In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density. The term is used, with this or similar meanings, in many scientific and technical disciplines, ...
(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 A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...
called . If represents wavelength and represents frequency (note, where is 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. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
), 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 of a wave in relation to an observer who is moving relative to the wave source. It is named after the Austrian physicist Christian Doppler, who d ...
blueshifts () are associated with objects approaching (moving closer to) the observer with the light shifting to greater
energies In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat ...
. 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, a gravitational field is a model used to explain the influences that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational phenome ...
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 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 simultaneous increase in fr ...
() 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 of a wave in relation to an observer who is moving relative to the wave source. It is named after the Austrian physicist Christian Doppler, who d ...
. Consequently, this type of redshift is called the ''Doppler redshift''. If the source moves away from the observer with
velocity Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...
, 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, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
. 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 (and wavelength) of light, caused by the relative motion of the source and the observer (as in the classical Doppler effect), when taking into account effects described by the special rel ...
. In brief, objects moving close to the speed of light will experience deviations from the above formula due to the
time dilation In physics and relativity, time dilation is the difference in the elapsed time as measured by two clocks. It is either due to a relative velocity between them ( special relativistic "kinetic" time dilation) or to a difference in gravitational ...
of
special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The laws o ...
which can be corrected for by introducing the
Lorentz factor The Lorentz factor or Lorentz term is a quantity expressing how much the measurements of time, length, and other physical properties change for an object while that object is moving. The expression appears in several equations in special relativit ...
into the classical Doppler formula as follows (for motion solely in the line of sight): :1 + z = \left(1 + \frac\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 shift of light. The result was in agreement with the formula for the transverse Doppler effect and was the first direct, quantitative confirmatio ...
. 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 Projection, projections or projective may refer to: Physics * Projection (physics), the action/process of light, heat, or sound reflecting from a surface to another in a different direction * The display of images by a projector Optics, graphic ...
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 and trigonometry, a right angle is an angle of exactly 90 Degree (angle), degrees or radians corresponding to a quarter turn (geometry), turn. If a Line (mathematics)#Ray, ray is placed so that its endpoint is on a line and the ad ...
() 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 that includes our Solar System, with the name describing the galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars that cannot be individually distinguished by the naked eye ...
. 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 theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it. The equations were published by Einstein in 1915 in the form ...
of
general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
. 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 that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving a ...
. 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), a train serving local traffic demand * Local, Missouri, a community in the United States * Local government, a form of public administration, usually the lowest tier of administrat ...
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, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The laws o ...
(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, Lorentz symmetry or Lorentz invariance, named after the Dutch physicist Hendrik Lorentz, is an equivalence of observation or observational symmetry due to special relativity implying that the laws of physics stay the same ...
).


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 and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
that describe a homogeneous and isotropic universe. To derive the redshift effect, use the
geodesic In geometry, a geodesic () is a curve representing in some sense the shortest path ( arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection. ...
equation for a light wave, which is :ds^2=0=-c^2dt^2+\frac where * is the
spacetime In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...
interval * is the time interval * is the spatial interval * is the speed of light * is the time-dependent cosmic
scale factor In affine geometry, uniform scaling (or isotropic scaling) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a '' scale factor'' that is the same in all directions. The result of uniform scaling is similar ...
* is the
curvature In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane. For curves, the canonic ...
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(\int_^\frac+\int_^ \frac\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 In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order ...
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 coordinate commonly used in the Big Bang models of physical cosmology. Such time coordinate may be defined for a homogeneous, expanding universe so that the universe has the same density everywhere at ...
–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(z) \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 that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving ...
, 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 scatter from the standard
Hubble Law Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving a ...
. 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 object recedes (becomes more distant) from an observer as a result of the expansion of the universe. It can be measured by observing the wavelength shifts of spectral lines e ...
from expansion of the universe, and a component related to
peculiar motion Peculiar motion or peculiar velocity refers to the velocity of an object relative to a ''rest frame'' — usually a frame in which the average velocity of some objects is zero. Galactic astronomy In galactic astronomy, peculiar motion refers to ...
(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 Edward R. Harrison (8 January 1919 – 29 January 2007) "Physics Today Obituaries: Edward R. (Ted) Harrison", William M. Irvine, PhysicsToday.org, 2007-02-23, webpage: PToday-125 was a British astronomer and cosmologist, noted for his work ...
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 physicist and Nobel laureate in physics for his contributions with Abdus Salam and Sheldon Glashow to the unification of the weak force and electromagnetic interactio ...
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, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The laws o ...
; 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, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is sig ...
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 and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
, there is time dilation within a gravitational well. This is known as the
gravitational redshift In physics and general relativity, gravitational redshift (known as Einstein shift in older literature) is the phenomenon that electromagnetic waves or photons travelling out of a gravitational well (seem to) lose energy. This loss of energ ...
or ''Einstein Shift''. The theoretical derivation of this effect follows from the
Schwarzschild solution In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an exact solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumpti ...
of the
Einstein equations In the 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 within it. The equations were published by Einstein in 1915 in the form ...
which yields the following formula for redshift associated with a photon traveling in the
gravitational field In physics, a gravitational field is a model used to explain the influences that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational phenome ...
of an uncharged, nonrotating,
spherically symmetric In geometry, circular symmetry is a type of continuous symmetry for a planar object that can be rotated by any arbitrary angle and map onto itself. Rotational circular symmetry is isomorphic with the circle group in the complex plane, or the ...
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 physical constant involved in ...
, * is the
mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...
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, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
. This gravitational redshift result can be derived from the assumptions of
special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The laws o ...
and the
equivalence principle In the theory of general relativity, the equivalence principle is the equivalence of gravitational and inertial mass, and Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (suc ...
; the full theory of general relativity is not required. The effect is very small but measurable on Earth using the
Mössbauer effect The Mössbauer effect, or recoilless nuclear resonance fluorescence, is a physical phenomenon discovered by Rudolf Mössbauer in 1958. It involves the resonant and recoil-free emission and absorption of gamma radiation by atomic nuclei bound in a ...
and was first observed in the
Pound–Rebka experiment The Pound–Rebka experiment was an experiment in which gamma rays were emitted from the top of a tower and measured by a receiver at the bottom of the tower. The purpose of the experiment was to test Albert Einstein's theory of general relativit ...
. However, it is significant near a
black hole A black hole is a region of spacetime where gravitation, gravity is so strong that nothing, including light or other Electromagnetic radiation, electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts t ...
, and as an object approaches the
event horizon In astrophysics, an event horizon is a boundary beyond which events cannot affect an observer. Wolfgang Rindler coined the term in the 1950s. In 1784, John Michell proposed that gravity can be strong enough in the vicinity of massive compact obj ...
the red shift becomes infinite. It is also the dominant cause of large angular-scale temperature fluctuations in the
cosmic microwave background In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all spac ...
radiation (see
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 spec ...
).


Observations in astronomy

The redshift observed in astronomy can be measured because the emission and
absorption Absorption may refer to: Chemistry and biology * Absorption (biology), digestion **Absorption (small intestine) *Absorption (chemistry), diffusion of particles of gas or liquid into liquid or solid materials *Absorption (skin), a route by which ...
spectra for
atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, and ...
s are distinctive and well known, calibrated from
spectroscopic Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter wav ...
experiments in
laboratories A laboratory (; ; colloquially lab) is a facility that provides controlled conditions in which scientific or technological research, experiments, and measurement may be performed. Laboratory services are provided in a variety of settings: physicia ...
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 rising mass of buoyant air, a convective current in the atmosphere, that transfers heat energy vertically. Thermals are created by the uneven heating of Earth's surface from solar radiation, and are an example ...
or mechanical
motion In physics, motion is the phenomenon in which an object changes its position with respect to time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, speed and frame of reference to an observer and mea ...
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 redshift-distance relationship. These models have been proposed as alternatives to the models that require metric expansion of sp ...
are not generally considered plausible.When cosmological redshifts were first discovered,
Fritz Zwicky Fritz Zwicky (; ; February 14, 1898 – February 8, 1974) was a Swiss astronomer. He worked most of his life at the California Institute of Technology in the United States of America, where he made many important contributions in theoretical and ...
proposed an effect known as tired light. While usually considered for historical interests, it is sometimes, along with
intrinsic redshift A non-standard cosmology is any physical cosmological model of the universe that was, or still is, proposed as an alternative to the then-current standard model of cosmology. The term ''non-standard'' is applied to any theory that does not confo ...
suggestions, utilized by
nonstandard cosmologies A non-standard cosmology is any physical cosmological model of the universe that was, or still is, proposed as an alternative to the then-current standard model of cosmology. The term ''non-standard'' is applied to any theory that does not confo ...
. In 1981, H. J. Reboul summarised man
alternative redshift mechanisms
that had been discussed in the literature since the 1930s. In 2001,
Geoffrey Burbidge Geoffrey Ronald Burbidge Fellow of the Royal Society, FRS (24 September 1925 – 26 January 2010) was an English people, English astronomy professor and theoretical astrophysicist, most recently at the University of California, San Diego. He wa ...
remarked in
review
that the wider astronomical community has marginalized such discussions since the 1960s. Burbidge and
Halton Arp Halton Christian "Chip" Arp (March 21, 1927 – December 28, 2013) was an American astronomer. He was known for his 1966 ''Atlas of Peculiar Galaxies'', which (it was later theorized) catalogues many examples of interacting and merging galaxie ...
, while investigating the mystery of 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 A Type Ia supernova (read: "type one-A") is a type of supernova that occurs in binary systems (two stars orbiting one another) in which one of the stars is a white dwarf. The other star can be anything from a giant star to an even smaller white ...
 Spectroscopy, as a measurement, is considerably more difficult than simple
photometry Photometry can refer to: * Photometry (optics), the science of measurement of visible light in terms of its perceived brightness to human vision * Photometry (astronomy), the measurement of the flux or intensity of an astronomical object's electrom ...
, which measures the
brightness Brightness is an attribute of visual perception in which a source appears to be radiating or reflecting light. In other words, brightness is the perception elicited by the luminance of a visual target. The perception is not linear to luminance, ...
of astronomical objects through certain
filters Filter, filtering or filters may refer to: Science and technology Computing * Filter (higher-order function), in functional programming * Filter (software), a computer program to process a data stream * Filter (video), a software component tha ...
. When photometric data is all that is available (for example, the
Hubble Deep Field The Hubble Deep Field (HDF) is an image of a small region in the constellation Ursa Major, constructed from a series of observations by the Hubble Space Telescope. It covers an area about 2.6 arcminutes on a side, about one 24-millionth of the ...
and the
Hubble Ultra Deep Field The Hubble Ultra-Deep Field (HUDF) is a deep-field image of a small region of space in the constellation Fornax, containing an estimated 10,000 galaxies. The original data for the image was collected by the Hubble Space Telescope from Septemb ...
), astronomers rely on a technique for measuring
photometric redshift A photometric redshift is an estimate for the recession velocity of an astronomical object such as a galaxy or quasar, made without measuring its spectrum. The technique uses photometry (that is, the brightness of the object viewed through various ...
s. 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 , 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 Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from around ...
rather than at the yellow-green color associated with the peak of its
blackbody A black body or blackbody is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. The name "black body" is given because it absorbs all colors of light. A black body ...
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 K correction converts measurements of astronomical objects into their respective rest frames. The correction acts on that object's observed magnitude (or equivalently, its flux). Because astronomical observations often measure through a single fil ...
for more details on the photometric consequences of redshift.)


Local observations

In nearby objects (within our
Milky Way The Milky Way is the galaxy that includes our Solar System, with the name describing the galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars that cannot be individually distinguished by the naked eye ...
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 Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...
and parametrize the
mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...
es of the
orbit In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a p ...
ing
star A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...
s in
spectroscopic binaries A binary star is a system of two stars that are gravitationally bound to and in orbit around each other. Binary stars in the night sky that are seen as a single object to the naked eye are often resolved using a telescope as separate stars, in wh ...
, 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. Biography William Huggins was born at Cornhill, Middlesex, in ...
. 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 A planetary system is a set of gravitationally bound non- stellar objects in or out of orbit around a star or star system. Generally speaking, systems with one or more planets constitute a planetary system, although such systems may also cons ...
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 Helioseismology, a term coined by Douglas Gough, is the study of the structure and dynamics of the Sun through its oscillations. These are principally caused by sound waves that are continuously driven and damped by convection near the Sun's surfa ...
to determine the precise movements of the
photosphere The photosphere is a star's outer shell from which light is radiated. The term itself is derived from Ancient Greek roots, φῶς, φωτός/''phos, photos'' meaning "light" and σφαῖρα/''sphaira'' meaning "sphere", in reference to it ...
of the
Sun The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
. Redshifts have also been used to make the first measurements of the
rotation Rotation, or spin, is the circular movement of an object around a '' central axis''. A two-dimensional rotating object has only one possible central axis and can rotate in either a clockwise or counterclockwise direction. A three-dimensional ...
rates of
planet A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a you ...
s, velocities of
interstellar cloud An interstellar cloud is generally an accumulation of gas, plasma, and dust in our and other galaxies. Put differently, an interstellar cloud is a denser-than-average region of the interstellar medium, the matter and radiation that exists in t ...
s, the rotation of galaxies, and the dynamics of
accretion Accretion may refer to: Science * Accretion (astrophysics), the formation of planets and other bodies by collection of material through gravity * Accretion (meteorology), the process by which water vapor in clouds forms water droplets around nucl ...
onto
neutron star A neutron star is the collapsed core of a massive supergiant star, which had a total mass of between 10 and 25 solar masses, possibly more if the star was especially metal-rich. Except for black holes and some hypothetical objects (e.g. white ...
s and
black hole A black hole is a region of spacetime where gravitation, gravity is so strong that nothing, including light or other Electromagnetic radiation, electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts t ...
s which exhibit both Doppler and gravitational redshifts. Additionally, the
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...
s of various emitting and absorbing objects can be obtained by measuring
Doppler broadening In atomic physics, Doppler broadening is broadening of spectral lines due to the Doppler effect caused by a distribution of velocities of atoms or molecules. Different velocities of the emitting (or absorbing) particles result in different Dopp ...
—effectively redshifts and blueshifts over a single emission or absorption line. By measuring the broadening and shifts of the 21-centimeter
hydrogen line The hydrogen line, 21 centimeter line, or H I line is the electromagnetic radiation spectral line that is created by a change in the energy state of neutral hydrogen atoms. This electromagnetic radiation has a precise frequency of , w ...
in different directions, astronomers have been able to measure the recessional velocities of
interstellar gas In astronomy, the interstellar medium is the matter and radiation that exist in the space between the star systems in a galaxy. This matter includes gas in ionic, atomic, and molecular form, as well as dust and cosmic rays. It fills interstellar s ...
, which in turn reveals the
rotation curve The rotation curve of a disc galaxy (also called a velocity curve) is a plot of the orbital speeds of visible stars or gas in that galaxy versus their radial distance from that galaxy's centre. It is typically rendered graphically as a plot, and ...
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 most distant objects exhibit larger redshifts corresponding to the
Hubble flow Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving a ...
of the
universe The universe is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and energy. The Big Bang theory is the prevailing cosmological description of the development of the universe. Acc ...
. The largest-observed redshift, corresponding to the greatest distance and furthest back in time, is that of the
cosmic microwave background In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all spac ...
radiation; the 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 event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from the ...
. The luminous point-like cores of
quasar A quasar is an extremely Luminosity, luminous active galactic nucleus (AGN). It is pronounced , and sometimes known as a quasi-stellar object, abbreviated QSO. This emission from a galaxy nucleus is powered by a supermassive black hole with a m ...
s 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 The Local Group is the galaxy group that includes the Milky Way. It has a total diameter of roughly , and a total mass of the order of . It consists of two collections of galaxies in a "dumbbell" shape: the Milky Way and its satellites form ...
and the nearby
Virgo Cluster The Virgo Cluster is a large cluster of galaxies whose center is 53.8 ± 0.3 Mly (16.5 ± 0.1 Mpc) away in the constellation Virgo. Comprising approximately 1,300 (and possibly up to 2,000) member galaxies, the cluster forms the heart of the lar ...
, but within a thousand mega
parsec The parsec (symbol: pc) is a unit of length used to measure the large distances to astronomical objects outside the Solar System, approximately equal to or (au), i.e. . The parsec unit is obtained by the use of parallax and trigonometry, and ...
s 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 Americans, American astronomer. He played a crucial role in establishing the fields of extragalactic astronomy and observational cosmology. Hubble proved that many objects ...
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 that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving ...
.
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 redshifted, thus providing th ...
was the first to discover galactic redshifts, in about the year 1912, while Hubble correlated Slipher's measurements with distances he 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 and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
, 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 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.
Gravitation In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stron ...
al 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 Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...
of virialized objects in the universe. This effect leads to such phenomena as nearby galaxies (such as the
Andromeda Galaxy The Andromeda Galaxy (IPA: ), also known as Messier 31, M31, or NGC 224 and originally the Andromeda Nebula, is a barred spiral galaxy with the diameter of about approximately from Earth and the nearest large galaxy to the Milky Way. The gala ...
) exhibiting blueshifts as we fall towards a common
barycenter In astronomy, the barycenter (or barycentre; ) is the center of mass of two or more bodies that orbit one another and is the point about which the bodies orbit. A barycenter is a dynamical point, not a physical object. It is an important conc ...
, 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 In astrophysics and physical cosmology the mass-to-light ratio, normally designated with the Greek letter upsilon, , is the quotient between the total mass of a spatial volume (typically on the scales of a galaxy or a cluster) and its luminosity. T ...
(the ratio of a galaxy's mass in solar masses to its brightness in solar luminosities), an important tool for measuring
dark matter Dark matter is a hypothetical form of matter thought to account for approximately 85% of the matter in the universe. Dark matter is called "dark" because it does not appear to interact with the electromagnetic field, which means it does not ab ...
. 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 supernova A Type Ia supernova (read: "type one-A") is a type of supernova that occurs in binary systems (two stars orbiting one another) in which one of the stars is a white dwarf. The other star can be anything from a giant star to an even smaller white ...
e have suggested that in comparatively recent times the expansion rate of the universe has 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 field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter wav ...
data, and the highest-confirmed spectroscopic redshift of a galaxy is that of
GN-z11 GN-z11 is a high-redshift galaxy found in the constellation Ursa Major. It is one of the farthest known galaxies from Earth ever discovered. The 2015 discovery was published in a 2016 paper headed by Pascal Oesch and Gabriel Brammer (Cosmic Dawn ...
, with a redshift of , corresponding to 400 million years after the Big Bang. The previous record was held by
UDFy-38135539 UDFy-38135539 (also known as "HUDF.YD3") is the Hubble Ultra Deep Field (UDF) identifier for a galaxy which was calculated to have a light travel time of 13.1 billion years with a present proper distance of around 30 billion light-years. ...
at a redshift of , 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 and the next highest being . The most distant-observed
gamma-ray burst In gamma-ray astronomy, gamma-ray bursts (GRBs) are immensely energetic explosions that have been observed in distant galaxies. They are the most energetic and luminous electromagnetic events since the Big Bang. Bursts can last from ten milli ...
with a spectroscopic redshift measurement was
GRB 090423 GRB 090423 was a gamma-ray burst (GRB) detected by the Swift Gamma-Ray Burst Mission on April 23, 2009 at 07:55:19 UTC whose afterglow was detected in the infrared and enabled astronomers to determine that its redshift is ''z'' = 8.2, ...
, which had a redshift of . The most distant-known quasar,
ULAS J1342+0928 ULAS J1342+0928 is the second-most distant known quasar detected and contains the second-most distant and oldest known supermassive black hole, at a reported redshift of z = 7.54. The ULAS J1342+0928 quasar is located in the Boötes, Boötes con ...
, 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 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 In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all spac ...
has a redshift of , 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 During 1944, Walter Baade categorized groups of stars within the Milky Way into stellar populations. In the abstract of the article by Baade, he recognizes that Jan Oort originally conceived this type of classification in 1926: Baade noticed th ...
, 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 The cosmic neutrino background (CNB or CB) is the universe's background particle radiation composed of neutrinos. They are sometimes known as relic neutrinos. The CB is a relic of the Big Bang; while the cosmic microwave background radiation (CM ...
from about two seconds after the Big Bang (and a redshift in excess of ) and the cosmic
gravitational wave background The gravitational wave background (also GWB and stochastic background) is a random gravitational-wave signal potentially detectable by gravitational wave detection experiments. Since the background is supposed to be statistically random, it has ...
emitted directly from
inflation In economics, inflation is an increase in the general price level of goods and services in an economy. When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation corresponds to a reductio ...
at a redshift in excess of . In June 2015, astronomers reported evidence for
Population III stars During 1944, Walter Baade categorized groups of stars within the Milky Way into stellar populations. In the abstract of the article by Baade, he recognizes that Jan Oort originally conceived this type of classification in 1926: Baade noticed th ...
in the
Cosmos Redshift 7 Cosmos Redshift 7 (also known as COSMOS Redshift 7, Galaxy Cosmos Redshift 7, Galaxy CR7 or CR7) is a high-redshift Lyman-alpha emitter galaxy. At a redshift z = 6.6, the galaxy is observed as it was about 800 million years after the Big Bang, ...
galaxy A galaxy is a system of stars, stellar remnants, interstellar gas, dust, dark matter, bound together by gravity. The word is derived from the Greek ' (), literally 'milky', a reference to the Milky Way galaxy that contains the Solar System. ...
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 element A chemical element is a species of atoms that have a given number of protons in their nuclei, including the pure substance consisting only of that species. Unlike chemical compounds, chemical elements cannot be broken down into simpler sub ...
s heavier than
hydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic, an ...
that are needed for the later formation of
planet A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a you ...
s 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
quasar A quasar is an extremely Luminosity, luminous active galactic nucleus (AGN). It is pronounced , and sometimes known as a quasi-stellar object, abbreviated QSO. This emission from a galaxy nucleus is powered by a supermassive black hole with a m ...
s 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 or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including ...
of
electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic field, electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, inf ...
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 in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used to iden ...
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 field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter wav ...
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, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
(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 () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...
to determine relative motion: * The
Andromeda Galaxy The Andromeda Galaxy (IPA: ), also known as Messier 31, M31, or NGC 224 and originally the Andromeda Nebula, is a barred spiral galaxy with the diameter of about approximately from Earth and the nearest large galaxy to the Milky Way. The gala ...
is moving toward our own
Milky Way The Milky Way is the galaxy that includes our Solar System, with the name describing the galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars that cannot be individually distinguished by the naked eye ...
galaxy A galaxy is a system of stars, stellar remnants, interstellar gas, dust, dark matter, bound together by gravity. The word is derived from the Greek ' (), literally 'milky', a reference to the Milky Way galaxy that contains the Solar System. ...
within the
Local Group The Local Group is the galaxy group that includes the Milky Way. It has a total diameter of roughly , and a total mass of the order of . It consists of two collections of galaxies in a "dumbbell" shape: the Milky Way and its satellites form ...
; 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 The Pound–Rebka experiment was an experiment in which gamma rays were emitted from the top of a tower and measured by a receiver at the bottom of the tower. The purpose of the experiment was to test Albert Einstein's theory of general relativit ...
. Gravitational blueshift contributes to
cosmic microwave background In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all spac ...
(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 spec ...
: 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 and general relativity, gravitational redshift (known as Einstein shift in older literature) is the phenomenon that electromagnetic waves or photons travelling out of a gravitational well (seem to) lose energy. This loss of energ ...
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 A quasar is an extremely Luminosity, luminous active galactic nucleus (AGN). It is pronounced , and sometimes known as a quasi-stellar object, abbreviated QSO. This emission from a galaxy nucleus is powered by a supermassive black hole with a m ...
, 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 that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving a ...
in the present
expanding universe The expansion of the universe is the increase in distance between any two given gravitationally unbound parts of the observable universe with time. It is an intrinsic expansion whereby the scale of space itself changes. The universe does not exp ...
.


See also

* Cosmic crystallography * Gravitational potential * Relativistic Doppler effect


References


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.)


Books

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


External links


Ned Wright's Cosmology tutorial





Animated GIF of Cosmological Redshift
by Wayne Hu * {{Cosmology topics Astronomical spectroscopy Doppler effects Effects of gravitation Physical cosmology Physical quantities Concepts in astronomy