Lorentz Transformation Calculator
Lorentz Transformation Calculator computes transformed position and time in special relativity for given velocity.
Formulas Used in Lorentz Transformation Calculator
The calculator applies the Lorentz transformation for a frame moving at velocity \\(v\\):
Lorentz Factor:
\\[ \gamma = \frac{1}{\sqrt{1 – \frac{v^2}{c^2}}} \\]Position Transformation:
\\[ x’ = \gamma (x – v t) \\]Time Transformation:
\\[ t’ = \gamma \left(t – \frac{v x}{c^2}\right) \\]Where:
- \\(x, t\\): Position and time in original frame (m, s)
- \\(x’, t’\\): Position and time in transformed frame (m, 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: \\(x = 0 \, \text{m}, t = 0 \, \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
\\]
\\[
x’ = 1.1547 (0 – 1.5 \times 10^8 \times 0) \approx 0 \, \text{m}
\\]
\\[
t’ = 1.1547 \left(0 – \frac{1.5 \times 10^8 \times 0}{(2.99792458 \times 10^8)^2}\right) \approx 0 \, \text{s}
\\]