🚀 Einsteinian Physics & Relativistic Spacetime
Special Relativity & Time Dilation Calculator
Compute the Lorentz factor ($\gamma$), elapsed dilated time ($\Delta t = \gamma \Delta t_0$), relativistic length contraction ($L$), and relativistic kinetic energy as speed approaches $c$.
🚀 0.50 c ($\gamma = 1.155$)
⏱️ 0.866 c ($\gamma = 2.000$)
⚡ 0.99 c ($\gamma = 7.089$)
🌌 0.9999 c (Muons, $\gamma = 70.7$)
🔬 CERN LHC Protons ($\gamma = 7,450$)
Velocity & Proper Dimensions
c
meters (m)
Lorentz Factor (γ) & Dilated Time
γ = 2.000
Contracted Length ($L$)
50.00 m
-50.0% Length
Actual Velocity ($v$)
259,620 km/s
0.866 c
Kinetic Energy Factor
1.000 mc²
E_k = (γ-1)mc²
💡 The Twin Paradox Experience:
While 1.0 year passes on the traveling spacecraft at 0.866c, an observer on Earth ages by exactly 2.00 years.
Einstein's Special Theory of Relativity
Postulating the constancy of light speed in all inertial reference frames:
- Lorentz Factor: $$\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} = \frac{1}{\sqrt{1 - \beta^2}}$$
- Time Dilation: $$\Delta t = \gamma \Delta t_0 \quad (\Delta t > \Delta t_0)$$
- Length Contraction: $$L = \frac{L_0}{\gamma} \quad (L < L_0)$$
- Total Relativistic Energy: $$E = \gamma m c^2 = mc^2 + KE_{\text{rel}}$$