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.

  • gamma = 1 at rest
  • gamma = 1.15 at 0.5c
  • gamma = 7.09 at 0.99c
  • gamma approaches infinity as v approaches c
  • Exemple Résolu

    Object at 0.9c.

    1. 01beta = v/c = 2.698e8 / 2.998e8 = 0.8999
    2. 02beta^2 = 0.8099
    3. 031 - beta^2 = 0.1901
    4. 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.

    Apprendre

    Understanding Newton's Laws of Motion

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