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Gravitational Redshift

Photons lose energy escaping a gravitational well — clocks run slower closer to mass

General Relativity Astrophysics Schwarzschild Time Dilation

Mass 1.0 M☉ Emit radius 3 Rs Photon freq. 500 nm

Rs = 2.95 km z = — νobs/νem = — λobs = — nm Clock ratio = —

🔭 Gravitational Redshift

General relativity predicts that photons emitted near a massive body lose energy as they climb out of the gravitational potential. The frequency observed far away is lower (redshifted):

νobs/νem = √(1 − Rs/r) z = νem/νobs − 1 = 1/√(1 − Rs/r) − 1

where Rs = 2GM/c² is the Schwarzschild radius (event horizon for a black hole). As r → Rs, z → ∞ — photons emitted at the event horizon never escape.

Gravitational time dilation: clocks at radius r tick slower by the same factor: dτ/dt = √(1 − Rs/r). A clock on Earth's surface runs about 45 µs/day slower than in deep space — a correction required by GPS satellites.

The Pound-Rebka experiment (1959) measured gravitational redshift over just 22.5 m in Jefferson Laboratory at Harvard, confirming Einstein's prediction to 10%.