Gravity & the equivalence principle

gravitational redshift

When light climbs upward out of a gravitational well — away from a planet, a star, or a black hole — it loses energy and its color shifts toward the red end of the spectrum. A blue beam sent up from the ground arrives at the top of a tower very slightly redder than it left. Send light the other way, falling deeper into the well, and it gains energy and shifts toward the blue. The deeper the well it must escape, the larger the redshift.

Photons do not slow down — light always travels at c — so the energy loss shows up as a drop in frequency, which for visible light means a shift in color. This is really the same fact as gravitational time dilation, seen through light instead of clocks. A wave's frequency is just a clock counting crests; if the clock at the bottom runs slow, then by the time those crests arrive at the top, fewer of them pass per second there, and the light looks redder. Redshift is the optical face of slowed time.

The effect was first nailed down on Earth in the famous Pound–Rebka experiment of 1959, which measured the tiny color shift of gamma rays falling down a 22-meter tower at Harvard, in beautiful agreement with Einstein. It is seen on a grand scale too: light leaving the surface of a white dwarf or a neutron star arrives noticeably reddened, and it must be accounted for when comparing clocks across the solar system. It is a clean, direct test of how gravity reaches into the flow of time.

Δλ/λ ≈ g h / c² (fractional redshift for light rising a height h in field g)

Light rising a height h in a field g is redshifted by a fraction ≈ gh/c² — tiny on Earth, large near compact stars.

Gravitational redshift is not the cosmological redshift of distant galaxies (that comes from the expanding universe) nor the Doppler redshift of a receding source. All three redden light, but the cause differs; here it is the depth of the gravitational well the light escapes.

Also called
Einstein shiftgravitational frequency shift引力频移