Atomic WatchCs-133 · 9.19 GHz

Relativistic Time Dilation & Cesium Hyperfine Frequency Simulator

Cs-133 at 9,192,631,770 HzRELATIVISTIC REFERENCE CLOCK
Local Ground Time
--:--:--.---
Cs-133 cycles counted by ground clock
0
Cycles counted by your clock at speed & altitude
0
Speed (Velocity relative to Earth)3.89 km/s
0 m/s (Ground)7.66 km/s (ISS)150,000 km/s (0.5c)
Altitude above Sea Level20,200 km
0 km (Sea Level)408 km (ISS)20,200 km (GPS)35,786 km (GEO)

Exact Relativistic Drift Telemetry

Speed effect (Special Relativity)Moving clocks tick slower (Δt > Δt')
−7.275 µs
Altitude effect (Gravitational Potential)Clocks in weaker gravity tick faster
+45.724 µs
Net drift per 24 hoursSum of Special & General Relativity
+38.449 µs
Accumulated drift since page openedReal-time discrepancy with sea-level clock
0 s
GPS position error caused by driftdrift × speed of light c
0.000 cm
Lorentz factor (γ − 1)1 / √(1 − v²/c²) − 1
8.420e-11
One Cs-133 oscillation duration
108.78 ps
Distance light travels in 1 cycle
3.261 cm

Compared with a stationary reference clock at Earth sea level. Earth's rotation is ignored. Drift uses exact relativistic formulas with Earth's mass (M ≈ 5.972×1024 kg) and mean radius (R = 6,371 km).

The Physics of Cesium-133 & Relativistic Spacetime

How atomic vibrations and Einstein's field equations define modern timekeeping and global satellite navigation.

• 9,192,631,770 Hz SI Standard• Special Relativity (γ − 1)• Gravitational Time Dilation

1. The Atomic Second Definition

Since 1967, the International System of Units (SI) defines one second as exactly 9,192,631,770 cycles of the microwave radiation corresponding to the transition between the two hyperfine ground state levels of the Cesium-133 atom at absolute zero.

2. Velocity vs. Gravity Balance

Special relativity predicts moving clocks tick slower by Δt' = Δt √(1 − v²/c²). General relativity predicts clocks in weaker gravity tick faster. In low Earth orbit (ISS at 408 km), speed dominates and clocks run slow (−25 µs/day). In high orbit (GPS at 20,200 km), gravity dominates and clocks run fast (+38.6 µs/day)!

3. Speed of Light & Position Error

Light and radio waves travel at 299,792,458 meters per second (~30 cm per nanosecond). An uncorrected clock drift of just 1 microsecond translates into a 300-meter positioning error on Earth. Atomic accuracy is essential to make modern civilization, aviation, and internet synchronization work.