\[\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}\]
Variables
gamma[γ]Lorentz factor
vvelocity (m/s)
cspeed of light (m/s)
Description
What is this formula?
The Lorentz factor calculates relativistic effects that occur when an object moves at speeds close to the speed of light. It is a fundamental quantity in Einstein's theory of special relativity.
When to use it
Use this formula when calculating relativistic time dilation, length contraction, relativistic momentum, and energy for high-speed objects.
Example
Data:
Velocity:
v=2.4×10^8 m/s
Formula:
γ=1/√(1−v²/c²)
Substitution:
γ=1/√(1−(2.4×10^8)²/(3×10^8)²)
Result:
γ=1.67
Applications
- Special relativity
- Particle accelerators
- Astrophysics
- High-energy physics
- Space science
- Relativistic mechanics