Lorentz Factor Calculator
Compute the Lorentz factor gamma = 1 / sqrt(1 - v^2/c^2), the key quantity in special relativity.
Lorentz Factor (gamma)
2.29343275
Lorentz Factor (gamma) vs Velocity
Formula
## The Lorentz Factor Gamma is the cornerstone of special relativity, appearing in time dilation, length contraction, and relativistic energy. ### Formula **gamma = 1 / sqrt(1 - beta^2)** where beta = v/c. - gamma = 1 at rest - gamma = 1.15 at 0.5c - gamma = 7.09 at 0.99c - gamma approaches infinity as v approaches c
Esempio Risolto
Object at 0.9c.
- 01beta = v/c = 2.698e8 / 2.998e8 = 0.8999
- 02beta^2 = 0.8099
- 031 - beta^2 = 0.1901
- 04gamma = 1 / sqrt(0.1901) = 1 / 0.4360 = 2.294
Domande Frequenti
Why is gamma always at least 1?
Because v can never exceed c, the denominator sqrt(1-v^2/c^2) is always between 0 and 1, making gamma at least 1.
What is the physical meaning of gamma?
It tells you the factor by which time dilates, length contracts, and inertia increases. A gamma of 2 means clocks run half as fast and lengths shrink by half.
What gamma do particle accelerators achieve?
The LHC accelerates protons to gamma of about 7500, meaning they travel at 99.999999% of light speed.
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