Length contraction

Length contraction is the phenomenon of a decrease in length of an object as measured by an observer who is traveling at any non-zero velocity relative to the object. This contraction is usually only noticeable at a substantial fraction of the speed of light.

$$ L = Lo \sqrt{ 1 - \frac {v^2}{c^2}} $$


  • Lo is the proper length (the length of the object in its rest frame),
  • L is the length observed by an observer in relative motion with respect to the object,
  • v is the relative velocity between the observer and the moving object,
  • c is the speed of light,
  • and the Lorentz factor, γ(v), is defined as

    $$ L = \frac {Lo}{\gamma} $$

    In this equation it is assumed that the object is parallel with its line of movement.

    Length contraction
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