The formula to calculate the speed (v) from the gamma factor (γ) is:
\[ v = c \sqrt{1 - \frac{1}{\gamma^2}} \]
Where:
Gamma (γ), also known as the Lorentz factor, is a factor that appears in several equations in special relativity. It describes how much time, length, and relativistic mass change for an object while that object is moving. The Lorentz factor is defined as:
\[ \gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} \]
where \( v \) is the velocity of the object and \( c \) is the speed of light. As the object's speed approaches the speed of light, the Lorentz factor increases dramatically.
Let's assume the following value for Gamma (γ):
Using the formula to calculate the speed (v):
\[ v = 299792458 \sqrt{1 - \frac{1}{2^2}} = 299792458 \sqrt{1 - \frac{1}{4}} = 299792458 \sqrt{\frac{3}{4}} \approx 299792458 \times 0.866 \approx 259627884 \text{ meters per second} \]
The speed (v) is approximately 259,627,884 meters per second.