Redshift

Redshift is a cool idea in physics and astronomy. It is when the wavelength of light or other electromagnetic radiation gets longer, and its frequency gets lower. This happens when the light source is moving away from us, or because of the universe expanding, or even because of strong gravity. The opposite effect, where the wavelength gets shorter and the frequency higher, is called blueshift.

In astronomy, scientists use redshift to study faraway objects and the shape of the universe. For example, the light from the Big Bang, which started as very high-energy radiation, has shifted over time to become the cold cosmic microwave background we see today. Redshift helps us learn how fast objects are moving and how far away they are.

Redshift is also useful in everyday tools like Doppler radar and radar guns. These tools measure the speed of cars or weather systems. Even gravitational waves, which are ripples in space-time, experience redshift just like light does when they travel through the universe.

History

The idea of redshift started in the 1800s when scientists studied waves and motion. Austrian mathematician Christian Doppler explained in 1842 that waves, like sound or light, change when their source moves. Dutch scientist Christophorus Buys Ballot tested this with sound waves in 1845.

Later, scientists used this idea for light from stars. In 1929, astronomer Edwin Hubble discovered that the farther away a galaxy is, the faster it seems to move away from us. This became known as Hubble's law. This helped scientists understand that the universe is expanding.

Physical origins

Redshifts happen when the wavelength of light gets longer, which means the light’s frequency gets lower. This can occur in three main ways: because of movement, the expansion of the universe, and gravity.

When a light source moves away from us, we see a redshift. This is called the Doppler effect. When the universe expands, light from faraway galaxies also appears redshifted. This is called cosmological redshift. Finally, gravity can cause redshift too. When light escapes from a strong gravitational field, it loses energy and its wavelength stretches. This is known as gravitational redshift.

Redshift summary

Redshift type	Geometry	Formulae
Relativistic Doppler	Minkowski space (flat spacetime)	For motion completely in the radial or line-of-sight direction: 1 + z = γ ( 1 + v ∥ c ) = 1 + v ∥ c 1 − v ∥ c {\displaystyle 1+z=\gamma \left(1+{\frac {v_{\parallel }}{c}}\right)={\sqrt {\frac {1+{\frac {v_{\parallel }}{c}}}{1-{\frac {v_{\parallel }}{c}}}}}} z ≈ v ∥ c {\displaystyle z\approx {\frac {v_{\parallel }}{c}}} for small v ∥ {\displaystyle v_{\parallel }} For motion completely in the transverse direction: 1 + z = 1 1 − v ⊥ 2 c 2 {\displaystyle 1+z={\frac {1}{\sqrt {1-{\frac {v_{\perp }^{2}}{c^{2}}}}}}} z ≈ 1 2 ( v ⊥ c ) 2 {\displaystyle z\approx {\frac {1}{2}}\left({\frac {v_{\perp }}{c}}\right)^{2}} for small v ⊥ {\displaystyle v_{\perp }}
Cosmological redshift	FLRW spacetime (expanding Big Bang universe)	1 + z = a n o w a t h e n {\displaystyle 1+z={\frac {a_{\mathrm {now} }}{a_{\mathrm {then} }}}} Hubble's law: z ≈ H 0 D c {\displaystyle z\approx {\frac {H_{0}D}{c}}} for D ≪ c H 0 {\displaystyle D\ll {\frac {c}{H_{0}}}}
Gravitational redshift	Any stationary spacetime	1 + z = g t t ( receiver ) g t t ( source ) {\displaystyle 1+z={\sqrt {\frac {g_{tt}({\text{receiver}})}{g_{tt}({\text{source}})}}}} For the Schwarzschild geometry: 1 + z = 1 − r S r receiver 1 − r S r source = 1 − 2 G M c 2 r receiver 1 − 2 G M c 2 r source {\displaystyle 1+z={\sqrt {\frac {1-{\frac {r_{S}}{r_{\text{receiver}}}}}{1-{\frac {r_{S}}{r_{\text{source}}}}}}}={\sqrt {\frac {1-{\frac {2GM}{c^{2}r_{\text{receiver}}}}}{1-{\frac {2GM}{c^{2}r_{\text{source}}}}}}}} z ≈ 1 2 ( r S r source − r S r receiver ) {\displaystyle z\approx {\frac {1}{2}}\left({\frac {r_{S}}{r_{\text{source}}}}-{\frac {r_{S}}{r_{\text{receiver}}}}\right)} for r ≫ r S {\displaystyle r\gg r_{S}} In terms of escape velocity: z ≈ 1 2 ( v e c ) source 2 − 1 2 ( v e c ) receiver 2 {\displaystyle z\approx {\frac {1}{2}}\left({\frac {v_{\text{e}}}{c}}\right)_{\text{source}}^{2}-{\frac {1}{2}}\left({\frac {v_{\text{e}}}{c}}\right)_{\text{receiver}}^{2}} for v e ≪ c {\displaystyle v_{\text{e}}\ll c}

Measurement

Using a telescope and a spectrometer, scientists can measure how the light from stars changes. They compare this to the light we know from gases like hydrogen studied in labs on Earth. By looking at features like absorption lines or emission lines in the starlight, they can see if the light has shifted.

Redshift and blueshift are described using a number called z. This number shows how much the wavelength of light has changed. The Doppler effect causes blueshifts when objects move away from us. Gravitational redshifts happen when light escapes from strong gravitational fields.

Calculation of redshift, z {\displaystyle z}

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

Observations in astronomy

Astronomers measure redshift by looking at special patterns of light, called spectra, from stars and galaxies. These patterns are like fingerprints. When they shift toward red light, it tells us about how the object is moving. This shift can happen for three reasons: the object moving away from us, gravity pulling on the light, or the expansion of the universe itself.

Studying these redshifts helps scientists learn how stars move, how fast galaxies spin, and how the universe is expanding. By measuring how much the light has shifted, astronomers can find distances to faraway objects and learn about the universe's history.

Effects from physical optics or radiative transfer

When light hits matter or other light, its wavelength and frequency can change. This happens through things like scattering from tiny particles or changes in how light moves through different materials. These changes are often called "reddening" instead of "redshift" because the light's color changes but its spectral lines stay in the same place.

Scattering can make light look redder, especially when there are many low-energy photons. This is why the sky looks blue during the day and the Sun looks red at sunrise or sunset. Unlike true redshift, reddening also makes the light dimmer and can change how it looks.

Blueshift

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

The opposite of a redshift is a blueshift. A blueshift is when the wavelength of light gets shorter and its energy gets stronger. This makes the light appear more blue.

Doppler blueshift happens when something with light moves toward us. We see this in places like the Andromeda Galaxy, which is moving closer to our Milky Way galaxy. Some stars and galaxies can also show blueshifts when they spin in certain ways.

Gravitational blueshift happens when light gets pulled into a strong gravity area, which makes the light more energetic. This was shown in experiments and helps explain patterns in the cosmic microwave background. Some far-away active galaxies sometimes show blueshifts in their light.