Light climbing out of a gravity well loses energy and reddens. It is not the Doppler shift and the photon never slows — its speed stays c — but a clock deeper in the well ticks slower, so a wave that leaves it arrives stretched. In 1960 Pound and Rebka measured the shift over 22.5 m of a Harvard tower: a fractional change of ~2.5×10-15, caught only by the Mössbauer effect. Down the center the photon goes in, the metric computes, the shift comes out. The blue team builds it; the red team tries to break it.
source Pound & Rebka, Apparent Weight of Photons, Phys. Rev. Lett. 4, 337 (1960) — doi:10.1103/PhysRevLett.4.337. Rendered, not quoted.
Static emitter at re, static observer at ro, in the Schwarzschild field of mass M. The Schwarzschild radius is rs = 2GM/c² (the Sun: ~2.95 km). A clock at r runs at rate √(1 − rs/r) relative to infinity. The exact redshift is the ratio of those rates:
1 + z = √(1 − rs/ro) / √(1 − rs/re)
Weak field (r ≫ rs) it collapses to the tower law z ≈ gH/c² = ΔΦ/c² — linear in height. Live values for the current setup:
| quantity | value |
|---|
Redshift and the-gravitational-time-dilation are the same effect: a stretched wave is a slowed clock read in Hz. The identity 1 + z = dt/dτ holds exactly (window 7 checks it live).
As the emitter falls toward the-schwarzschild-radius, √(1−rs/re)→0 and z→∞ — the horizon is where escaping light is redshifted to nothing. Pound-Rebka 1960 measured the tiny weak-field end of the very same law.
The blue team's live check: recompute the sign, the tower magnitude, the divergence, and the 1+z = dt/dτ identity from the pure functions. If red flips the sign (window 6), this badge catches it.
Feed the engine a well and two heights. A photon of frequency fe is emitted at radius re and received at ro. The only inputs that matter are the two depth ratios rs/r — the mass and the emitted frequency cancel out of z.
Strong field: radii as multiples of rs near a black hole. Tower: the weak-field Pound-Rebka regime, height H in metres at Earth gravity. That is what you hand to the panel below.
Strong field: the exact Schwarzschild metric. Emitter deeper than observer → light climbs out → redshift.
The wave leaves the emitter (bottom) and climbs; its length stretches by exactly 1+z and its colour reddens. Every number is computed from the metric on the spot, never looked up.
What the machine proves: light climbing out is redshifted (z > 0), light falling in is blueshifted (z < 0); the weak field obeys z ≈ gH/c², linear in H; the Pound-Rebka tower gives z ≈ 2.46×10-15; and z diverges at the horizon. Redshift is time dilation: 1+z = dt/dτ.
The blue witness (left) confirms these live; the red team (right) tries to make the sign lie.
r = rs is a coordinate singularity, not a curvature one: an infalling observer crosses it in finite proper time and feels nothing special. The infinite redshift there is what a distant, static observer sees — a statement about clocks and light paths, not a wall in space.
"Gravitational redshift is a Doppler effect / the photon slows down." Cut. The photon's speed is always c; its frequency drops because the emitting clock ran slow. No relative motion is required.
"Pound-Rebka saw a big, obvious shift." Cut. It was ~2.5×10-15 — one part in 1015 — visible only through recoil-free (Mössbauer) γ-rays from 57Fe.
"The photon loses energy 'to gravity' like a thrown ball." Kept, corrected. Energy is frame-dependent; the invariant statement is 1+z = dt/dτ — clocks at different potentials tick at different rates.
The red team's move: flip the sign of the shift so climbing light gains energy (blueshift on the way out). If it slipped past, energy would come free from a gravity well. The blue witness (window 7) is watching.
Flip the sign and light climbing out of the well is reported as gaining energy — the out-is-redshifted check fails, the witness recomputes, disagrees, and turns red. Nothing is faked; the attack is real and it is caught.