In physics, a redshift is an increase in the wavelength, or equivalently, a decrease in the frequency, of electromagnetic radiation (such as light). The opposite change, a decrease in wavelength and increase in frequency and energy, is known as a blueshift.
Three forms of redshift occur in astronomy and cosmology: Doppler redshifts due to the relative motions of radiation sources, gravitational redshift as radiation escapes from gravitational potentials, and cosmological redshifts caused by the universe expanding. The value of a redshift is often denoted by the letter , corresponding to the fractional change in wavelength (positive for redshifts, negative for blueshifts), and by the wavelength ratio (which is greater than 1 for redshifts and less than 1 for blueshifts). Automated astronomical redshift surveys are an important tool for learning about the large-scale structure of the universe. Redshift and blueshift can also be related to photon energy and, via Planck's law, to a corresponding blackbody temperature.
Examples of strong redshifting are a gamma ray perceived as an X-ray, or initially visible light perceived as radio waves. The initial 3000 kelvin (K) radiation from the Big Bang has redshifted far down to become the 3K cosmic microwave background. Subtler redshifts are seen in the spectroscopic observations of astronomical objects, and are used in terrestrial technologies such as Doppler radar and radar guns. Gravitational waves, which also travel at the speed of light, are subject to the same redshift phenomena.
Other physical processes exist that can lead to a shift in the frequency of electromagnetic radiation, including scattering and optical effects; however, the resulting changes are distinguishable from (astronomical) redshift and are not generally referred to as such.
History
The history of the subject began in the 19th century, with the development of classical wave mechanics and the exploration of phenomena which are associated with the Doppler effect. The effect is named after the Austrian mathematician Christian Doppler, who offered the first known physical explanation for the phenomenon in 1842. In 1845, the hypothesis was tested and confirmed for sound waves by the Dutch scientist Christophorus Buys Ballot. Doppler correctly predicted that the phenomenon would apply to all waves and, in particular, suggested that the varying colors of stars could be attributed to their motion with respect to the Earth.
Unaware of Doppler's work, French physicist Hippolyte Fizeau suggested in 1848 that a shift in spectral lines from stars might be used to measure their motion relative to Earth. In 1850, François-Napoléon-Marie Moigno analysed both Doppler's and Fizeau's ideas in a publication read by both James Clerk Maxwell and William Huggins, who initially stuck to the idea that the color of stars related to their chemistry, however by 1868, Huggins was the first to determine the velocity of a star moving away from the Earth by the analysis of spectral shifts.
In 1871, optical redshift was confirmed when the phenomenon was observed in Fraunhofer lines, using solar rotation, about 0.1 Å in the red. In 1887, Hermann Carl Vogel and Julius Scheiner discovered the "annual Doppler effect", the yearly change in the Doppler shift of stars located near the ecliptic, due to the orbital velocity of the Earth. In 1901, Aristarkh Belopolsky verified optical redshift in the laboratory using a system of rotating mirrors.
Beginning with observations in 1912, Vesto Slipher discovered that the Andromeda Galaxy had a blue shift, indicating that it was moving towards the Earth. Slipher first reported his measurement in the inaugural volume of the Lowell Observatory Bulletin. Three years later, he wrote a review in the journal Popular Astronomy. In it he stated that "the early discovery that the great Andromeda spiral had the quite exceptional velocity of –300 km[/s] showed the means then available, capable of investigating not only the spectra of the spirals but their velocities as well." Slipher reported the velocities for 15 spiral nebulae spread across the entire celestial sphere, all but three having observable "positive" (that is recessional) velocities.
Until 1923 the nature of the nebulae was unclear. By that year Edwin Hubble had established that these were galaxies and worked out a procedure to measure distance based on the period-luminosity relation of variable Cepheids stars. This made it possible to test a prediction by Willem de Sitter in 1917 that redshift would be correlated with distance. In 1929 Hubble combined his distance estimates with redshift data from Slipher's reports and measurements by Milton Humason to report an approximate relationship between the redshift and distance, a result now called Hubble's law.
Theories relating to the redshift-distance relation also evolved during the 1920s. The solution to the equations of general relativity described by de Sitter contained no matter, but in 1922 Alexander Friedmann derived dynamic solutions, now called the Friedmann equations, based on frictionless fluid models. English translation in ) Independently Georges Lemaître derived similar equations in 1927 and his analysis became widely known around the time of Hubble's key publication.
By early 1930 the combination of the redshift measurements and theoretical models established a major breakthrough in the new science of cosmology: the universe had a history and its expansion could be investigated with physical models backed up with observational astronomy.
When cosmological redshifts were first discovered, Fritz Zwicky proposed an effect known as tired light. However this model has largely been ruled out by timescale stretch observations in type Ia supernovae.
Arthur Eddington used the term "red shift" as early as 1923, which is the oldest example of the term reported by the Oxford English Dictionary. Willem de Sitter used the single-word version redshift in 1934.
In the 1960s the discovery of quasars, which appear as very blue point sources and thus were initially thought to be unusual stars, led to the idea that they were as bright as they were because they were closer than their redshift data indicated. A flurry of theoretical and observational work concluded that these objects were very powerful but distant astronomical objects.
Physical origins Redshifts are differences between two wavelength measurements and wavelengths are a property of both the photons and the measuring equipment. Thus redshifts characterise differences between two measurement locations. These differences are commonly organised in three groups, attributed to relative motion between the source and the observer, to the expansion of the universe, and to gravity. The following sections explain these groups.
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 () occurs. This is true for all electromagnetic waves and is explained by the Doppler effect. Consequently, this type of redshift is called the Doppler redshift. If the source moves away from the observer with velocity , which is much less than the speed of light (), the redshift is given by
where is the speed of light (since ). In the classical Doppler effect, the frequency of the source is not modified, but the recessional motion causes the illusion of a lower frequency.
A more complete treatment of the Doppler redshift requires considering relativistic effects associated with motion of sources close to the speed of light. A complete derivation of the effect can be found in the article on the relativistic Doppler effect. In brief, objects moving close to the speed of light will experience deviations from the above formula due to the time dilation of special relativity which can be corrected for by introducing the Lorentz factor into the classical Doppler formula as follows (for motion solely in the line of sight):
This phenomenon was first observed in a 1938 experiment performed by Herbert E. Ives and G. R. Stilwell, called the Ives–Stilwell experiment.
Since the Lorentz factor is dependent only on the magnitude of the velocity, this causes the redshift associated with the relativistic correction to be independent of the orientation of the source movement. In contrast, the classical part of the formula is dependent on the projection of the movement of the source into the line-of-sight which yields different results for different orientations. If 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:
and for motion solely in the line of sight (), this equation reduces to:
For the special case that the light is moving at right angle () to the direction of relative motion in the observer's frame, the relativistic redshift is known as the transverse redshift, and a redshift:
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."Photons, Relativity, Doppler shift". . University of Queensland.
Cosmological
The observations of increasing redshifts from more and more distant galaxies can be modelled assuming a homogeneous and isotropic universe combined with general relativity. This cosmological redshift can be written as a function of , the time-dependent cosmic scale factor:
The scale factor is monotonically increasing as time passes. Thus is positive, close to zero for local stars, and increasing for distant galaxies that appear redshifted.
Using a Friedmann–Robertson–Walker model of the expansion of the universe, redshift can be related to the age of an observed object, the so-called cosmic time–redshift relation. Denote a density ratio as :
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:
where is age of the object after the big bang, is the present-day Hubble constant, and is the redshift. For these large redshifts, the age of the universe, , is small, meaning that the light was emitted when the universe was young.
The cosmological redshift is commonly attributed to stretching of the wavelengths of photons due to the stretching of space. This interpretation can be misleading. As required by general relativity, the cosmological expansion of space has no effect on local physics. There is no term related to expansion in Maxwell's equations that govern light propagation. The cosmological redshift can be interpreted as an accumulation of infinitesimal Doppler shifts along the trajectory of the light.
There are several websites for calculating various times and distances from redshift, as the precise calculations require numerical integrals for most values of the parameters. For parameter values as of 2018, H0=67.4 and OmegaM=0.315; see the table at .
Distinguishing between cosmological and local effects