Redshift z → velocity (Doppler)

Redshift: z = (λ_obs − λ_emit)/λ_emit

Redshift z measures how much a wavelength stretches between emission and observation: z = (λ_obs − λ_emit)/λ_emit. For low velocities (v ≪ c), the classical Doppler form gives z ≈ v/c; relativistically, 1+z = √((1+β)/(1−β)) with β = v/c. Cosmological redshift reflects expansion of space itself: 1+z = a(t_obs)/a(t_emit), where a(t) is the scale factor. Hubble (1929) found galaxies recede with v = H₀·d, where H₀ ≈ 70 km/s/Mpc. Type Ia supernovae revealed accelerating expansion (Perlmutter, Riess, Schmidt — Nobel 2011, dark energy). Landmarks: z = 1 → the universe was half its current size; z = 11 → the earliest galaxies imaged by JWST; z ≈ 1100 → the cosmic microwave background (CMB), 380,000 years after the Big Bang.

Applications

Cosmology and age-of-the-universe determination (~13.8 Gyr), measuring expansion rate and dark-energy equation of state, exoplanet radial velocities (Doppler tracking of host-star spectra), gravitational-wave source localization (LIGO/Virgo cross-checks), quasar and high-z galaxy surveys, and CMB anisotropy analysis (Planck, COBE, WMAP).

FAQ

Is cosmological redshift a Doppler effect? Not exactly — it comes from the expansion of space between emitter and observer, not motion through space. For nearby galaxies the two pictures agree numerically, but at large z the cosmological interpretation is the correct one.

Can z be greater than 1? Yes. z = 1 means λ doubled, not that v = c. The CMB sits at z ≈ 1100, meaning microwave photons were emitted as visible/UV light 13.8 billion years ago and have been stretched ~1101× since.

What's blueshift? Negative z, when a source approaches. Andromeda (M31) is blueshifted at v ≈ −110 km/s — it will collide with the Milky Way in ~4.5 billion years.