← Theory of RelativityPart 2 — General Relativity · 16

Why Light Changes Color

▶ DRILL

Light is a wave, and its colour depends on how stretched that wave is. To reach Liza high above, light from a star has to climb out of the star's gravity — and climbing costs energy, so the wave stretches and slides toward red. The deep reason is the clock drills all over again: clocks run slow deep in gravity, so light born down there comes out stretched and slow. It's real (measured on Earth, corrected for by GPS) and becomes extreme near a black hole. Use the Explain it for a kid / a grown-up switch to set the depth.

EXPLAIN IT FORsimple words & pictures
STAR'S GRAVITYheavy star
SLOW-MOnormal
made:seen:
✨ light climbs out of the star — and stretches toward red🔭 Liza sees: red!🕐 clock here: normalthe starmade here: blue-white🕐 clock here: SLOWwavelength (the wiggle spacing):at the starup at Liza↳ stretched 3.3× → redder

The big idea — when light climbs out of gravity, its wave stretches and turns redder — that's gravitational redshift. The deeper reason is the same as the clock drills: clocks run slow deep in gravity, so light born down there comes out stretched and slow (= red) to anyone higher up. It's tiny near the Earth or Sun but absolutely real — measured in a lab, and corrected for by every GPS satellite. Light falling IN does the reverse (it blueshifts). Near a black hole it becomes extreme — the next drill.

# formula1 + z = 1/√(1 − 2GM/rc²) ≈ 1 + GM/rc² — light loses frequency climbing out of a gravity well
# same asgravitational time dilation — a deeper clock ticks slower, so its light arrives lower in frequency (redder)
# realPound–Rebka (1959) measured it over 22.5 m on Earth; the Sun's surface gives z ≈ 2×10⁻⁶; light falling in blueshifts
# scalethe stretch and colour shift are hugely exaggerated; near a black-hole horizon the redshift grows without bound (next drill)