免费洛伦兹因子计算器

根据速度计算狭义相对论中的洛伦兹因子γ。

m/s

Lorentz Factor (gamma)

2.29343275

Beta (v/c)0.89993329
1 - beta^20.190120075603

Lorentz Factor (gamma) vs Velocity

公式

## 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

计算示例

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

常见问题

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.

学习

Understanding Newton's Laws of Motion

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