Gravitational ebb
Kinematic ram pressure
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 → boundary spends energy resisting flow → less energy to tick
Flow v/c
0.40
Energy budget of mc²
Internal (drives the tick)
Boundary cost (resisting flow)
Clock rate:
ν/ν
0
= √(1 − v²/c²) =
0.917