Redshifts

Redshift describes the phenomenon in which electromagnetic radiation from distant objects arrives with longer wavelengths than emitted. It is quantified by z = (λ_obs − λ_emit)/λ_emit, or equivalently λ_obs = (1+z) λ_emit. Redshift can arise from several physical effects, including the Doppler effect from relative motion, the expansion of the universe, and gravitational effects near massive bodies.

Doppler redshift occurs when the source recedes, due to relative motion along the line of sight. For non-relativistic speeds, z ≈ v/c; for high velocities, the exact relation is 1+z = sqrt((1+v/c)/(1−v/c)). This form respects special relativity and becomes significant for fast-moving sources.

Cosmological redshift results from the expansion of space itself. As the universe expands, light is stretched and z increases with time. The relation 1+z = a0/ae expresses this, where a is the cosmic scale factor and a0 its present value. Cosmological redshift is integrated with the dynamics of the expanding universe and is central to interpreting distant galaxies and the cosmic microwave background.

Gravitational redshift is due to photons losing energy climbing a gravitational potential, observable near massive bodies and in strong gravitational fields. In weak fields, the fractional shift is approximately Δλ/λ ≈ ΔΦ/c^2, where Φ is the gravitational potential.

Measurements and applications: redshifts are determined by spectroscopy, comparing observed spectral lines to laboratory rest wavelengths. Redshift surveys map large-scale structure, and high-redshift sources probe early epochs, including galaxies, quasars, and the cosmic microwave background (z ≈ 1100). Redshift informs distances, timescales, and cosmological parameters, though peculiar motions and local gravity introduce uncertainties.