Time Dilation Visualizer
Time Dilation Visualizer shows how time slows in a moving frame, with a plot and animated clock for relativistic effects.
Formulas Used in Time Dilation Visualizer
The visualizer computes time dilation for a moving frame:
Lorentz Factor:
\\[ \gamma = \frac{1}{\sqrt{1 – \frac{v^2}{c^2}}} \\]Time Dilation:
\\[ \Delta t’ = \gamma \Delta t \\]Where:
- \\(\Delta t\\): Proper time in rest frame (s)
- \\(\Delta t’\\): Dilated time in moving frame (s)
- \\(v\\): Relative velocity (m/s)
- \\(c\\): Speed of light (\\(2.99792458 \times 10^8 \, \text{m/s}\\))
- \\(\gamma\\): Lorentz factor (dimensionless)
Example Calculation
Example: \\(\Delta t = 1 \, \text{s}, v = 1.5 \times 10^8 \, \text{m/s}\\)
\\[
\gamma = \frac{1}{\sqrt{1 – \frac{(1.5 \times 10^8)^2}{(2.99792458 \times 10^8)^2}}} \approx 1.1547
\\]
\\[
\Delta t’ = 1.1547 \times 1 \approx 1.1547 \, \text{s}
\\]