Gravitational ebb
Kinematic motion
M Substrate flows inward vₑₕₕ = √(2GM/r) velocity v Clock flies through substrate Oncoming flow = v
The clock's experience is identical
Substrate flows past at speed v → the clock's signal is pinned at c to the medium → it must cross a diagonal → the tick stretches by γ
Flow v/c 0.40
Energy ledger: total γmc² = 1.091 mc²
The clock, mc²/γ — a beat on a longer path The dressing, γmv² = p·v — energy the pusher supplied
Clock rate: ν/ν0 = √(1 − v²/c²) = 0.917
Gravitational: v = vebb = √(2GM/r), the clock at rest in the river. In orbit the two add as one vector, |vrel|² = vebb² + v². Open the river view →