Special Relativity
Time Dilation
Interactive visualization of Einstein's theory: watch how time slows, objects contract, and the universe warps near light speed.
Controls
0.5c (50% light speed)
Lorentz Factor γ
1.15
γ = 1/√(1−β²)
Time Dilation
1.15 ×
Slower on ship
At this speed:
1 year aboard = 0.87 years on Earth
1 year aboard = 0.87 years on Earth
Twin Clock Paradox
Left: Stationary Earth clock. Right: Moving spaceship clock (Δt = proper time × γ). Watch the moving clock tick slower due to time dilation.
Statistics
β (v/c ratio)
0.500
γ (Lorentz factor)
1.15
Coordinate Time Δt
1.15 y
Proper Time Δτ
1.00 y
Length Contraction
86.8 m
Relativistic KE
0.15 mc²
Real-World Examples
GPS Satellites
v ≈ 3.87 km/s → γ ≈ 1.000000082
Clocks run 38 microseconds faster per day
v ≈ 3.87 km/s → γ ≈ 1.000000082
Clocks run 38 microseconds faster per day
Cosmic Ray Muons
v ≈ 0.9994c → γ ≈ 28.9
Lifetime dilates from 2.2 μs → 63 μs
v ≈ 0.9994c → γ ≈ 28.9
Lifetime dilates from 2.2 μs → 63 μs
LHC Protons
v ≈ 0.9999991c → γ ≈ 6927
Rest mass appears 6927× heavier
v ≈ 0.9999991c → γ ≈ 6927
Rest mass appears 6927× heavier
Relativistic Equations
Lorentz Factor
γ = 1/√(1−β²) where β = v/c
Time Dilation
Δt = γ·Δτ
Moving clock runs slower by factor γ
Length Contraction
L = L₀/γ
Only in direction of motion
Relativistic Energy
E = γmc²
KE = (γ−1)mc²
Relativistic Momentum
p = γmv
Increases dramatically near c
Speed of Light
c = 3×10⁸ m/s
≈ 299,792 km/s