` to ``. THE GEODESIC

THE GEODESIC

In general relativity gravity is not a force. A free body coasts along the straightest available path — a geodesic — through curved spacetime, tracing the worldline of extremal proper time. Because the path is geometry, not a pull, all masses fall alike: the equivalence principle. Rendered, not quoted — the universality of free fall, the great-circle geodesic, geodesic deviation as tidal gravity, and the null path of light are all computed live below.

source A. Einstein, “Die Grundlage der allgemeinen Relativitätstheorie”, Annalen der Physik 49 (1916) 769–822 — doi:10.1002/andp.19163540702 amber the §§-numbering of the geodesic derivation differs across the German original and English translations; equations rendered from the standard modern form.

Blue Team · builds & defends
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THE MODEL

A free particle extremizes proper time τ = ∫ dτ. In flat spacetime the extremal timelike path is the straight, constant-velocity worldline (a maximum of τ — the twin paradox). In curved spacetime the same variational law bends the path: this is gravity.

Free fall obeys a = g, independent of mass or composition — the equivalence principle. On a sphere the geodesic is the great circle; two initially-parallel great circles converge, and that convergence is tidal gravity (geodesic deviation).

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THE LINEAGE

Gravity is geometry — Einstein 1916. Free bodies coast on geodesics; the equivalence principle makes all masses fall alike; the curved-space paths are what neighbours render as bends.

→ the-perihelion-precession (Mercury, 43″/century) and the-gravitational-lensing (starlight, 1.75″) are both this one geodesic, seen edge-on.

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THE WITNESS …

Live re-check of the core invariant: two very different masses (1 kg vs 106 kg) must fall on the same trajectory to 1×10-9 (the Eötvös result). The badge confirms green; it flips red the instant the tamper (window 6) makes fall depend on mass.

The Machine
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DATA IN in ↓

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THE PANEL LIT

Free fall of two masses · the great-circle geodesic · light deflection — all from the same pure functions.

↓
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DATA OUT out ↓

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Red Team · attacks & breaks
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THE ADVERSARY WALL

“A geodesic is just a Newtonian orbit dressed up.” No: GR light-bending is 1.75″, exactly twice the Newtonian 0.875″ — Eddington 1919 measured the doubled value. And Mercury's 43″/century is a pure GR surplus Newton cannot produce with any planet.

“Then heavier things fall faster, obviously.” Aristotle's error — falsified to parts in 1013 (Eötvös, then MICROSCOPE 2022). The tamper (6) plants exactly this lie so the witness can catch it.

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THE GRAVEYARD

Gravity is a force pulling masses together. → It is curvature; free bodies feel no force — they follow geodesics.

The bending of starlight is 0.875″ (Newtonian photon). → 1.75″ — twice, because space curves too.

A geodesic always maximises length/time. → It is stationary; timelike geodesics maximise τ, spacelike ones do not, null ones have τ=0.

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THE TAMPER

Disclosed planted void: force free-fall acceleration to depend on mass (heavier falls faster — the Aristotelian error). The equivalence principle breaks and the two masses diverge. Witness (7) catches it live.