Redshift

Redshift is the displacement of electromagnetic radiation toward longer wavelengths and lower frequencies relative to its emitted or reference values. The name refers to the red end of visible light, but the phenomenon applies throughout the electromagnetic spectrum. Its opposite is blueshift. In astronomy, redshift provides information about celestial motion and the expansion of the universe; gravitational redshift also probes how gravity affects radiation and clocks. These effects have different physical origins, although they can contribute to the same observation. (esa.int)

Definition and measurement

Redshift is expressed by the dimensionless quantity $z$:

where $\lambda$ denotes wavelength and $\nu$ frequency. Positive $z$ indicates redshift; negative $z$ indicates blueshift. Thus $z=1$ means that the observed wavelength is twice its emitted value, not that the source travels at the speed of light. Redshift measures a wavelength ratio; interpreting it as a velocity requires a physical model. (ned.ipac.caltech.edu)

Astronomers commonly determine redshift through spectroscopy, identifying spectral lines whose rest wavelengths are known from laboratory measurements. Emission and absorption features associated with an atom or ion provide recognizable patterns. Matching several features helps distinguish a genuine shift from a mistaken line identification. The whole spectrum shifts, while the lines supply convenient reference markers. (esa.int)

Spectroscopic redshifts can be measured from individual lines or by comparing an observed spectrum with a template. Photometric redshifts instead estimate the shift from brightness measurements across several wavelength bands and models of a source’s spectral energy distribution. They are generally less precise than spectroscopic measurements but can be useful when detailed spectra are unavailable. (ned.ipac.caltech.edu)

Doppler redshift

The Doppler effect arises from relative motion between a source and an observer. Recession produces a redshift, while approach produces a blueshift. For light, the quantitative relationship follows special relativity, rather than the classical formula for sound propagating through a medium. For purely radial recession in flat spacetime,

where $v$ is the relative recession speed and $c$ is the speed of light. When $v\ll c$, this reduces to $z\simeq v/c$. The exact expression includes relativistic time dilation as well as the changing separation between emitter and receiver. (einstein-online.info)

Doppler shifts reveal motions of stars and gas. Alternating shifts can trace orbital motion in a binary star, while different shifts across a galaxy reveal its internal motions. Such measurements concern motion through space and must be distinguished from the redshift associated with cosmic expansion. (science.nasa.gov)

Cosmological redshift

In cosmology, radiation traveling through an expanding universe acquires a cosmological redshift. Within the homogeneous, isotropic expanding models used in general relativity, its wavelength grows in proportion to the cosmic scale factor $a(t)$:

If today’s scale factor is normalized to one, radiation observed at cosmological redshift $z=3$ was emitted when the scale factor was one quarter of its present value. This describes the relative scaling of cosmic distances, not expansion from a central point into surrounding space. (ned.ipac.caltech.edu)

For nearby galaxies participating approximately in the expansion, the Hubble–Lemaître law gives $v\simeq H_0d$, so $cz\simeq H_0d$ at small redshift. Here $H_0$ is the Hubble constant. At larger redshifts, neither this linear approximation nor the special-relativistic Doppler formula provides a general conversion to cosmic distance. Different distance measures depend on the universe’s expansion history. (ned.ipac.caltech.edu)

Redshift therefore supplies an observational coordinate for studying cosmic evolution, rather than a model-independent distance or age. Converting it to distance or lookback time requires an expansion model and its parameters. In Big Bang cosmology, the stretching of radiation also explains why an initially hotter radiation field cools as the universe expands, an important property of the cosmic microwave background. (science.nasa.gov)

Gravitational redshift

Gravitational redshift occurs when radiation passes from a lower gravitational potential to a higher one, as measured by appropriately stationary observers. Radiation traveling in the reverse direction is gravitationally blueshifted. The effect is closely related to gravitational time dilation: otherwise identical clocks at different gravitational potentials accumulate time at different rates. It does not require the emitter to recede from the receiver. (science.gsfc.nasa.gov)

Precision comparisons of atomic clocks at different heights test this prediction. Such measurements also connect clock rates with differences in gravitational potential, providing a basis for clock-based geodesy. These experiments distinguish gravitational frequency shifts from shifts caused by relative motion. (arxiv.org)

Interpretation and astronomical uses

An observed galaxy redshift can combine cosmic expansion with the galaxy’s peculiar motion relative to the average expansion. These contributions combine through factors of $1+z$, rather than by simply adding redshifts, although addition can approximate sufficiently small shifts. Consequently, nearby objects can be blueshifted despite the universe’s overall expansion. (ned.ipac.caltech.edu)

Comparing redshifts with independently estimated distances allows astronomers to investigate expansion history. Observations of distant supernovae provided evidence in 1998 that cosmic expansion is accelerating, motivating studies of dark energy. Cosmological redshift also stretches observed time intervals by $1+z$; measurements of supernova spectral evolution test this prediction independently of wavelength shifts. (science.nasa.gov)