Calculateur du Facteur de Lorentz Gratuit
Calculez le facteur de Lorentz gamma pour une vitesse donnée. Déterminez le facteur de dilatation relativiste.
m/s
Lorentz Factor (gamma)
2.29343275
Beta (v/c)0.89993329
1 - beta^20.190120075603
Lorentz Factor (gamma) vs Velocity
Formule
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.
Exemple Résolu
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
Questions Fréquentes
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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