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Lorentz Transformation

(Lorentz Transform)
(equations describing the effect of relative motion on length and velocity)

The Lorentz Transformation (or Lorentz Transform) is a series of equations describing the effect of relative motion of multiple objects on the position of objects at given times. According to the transformation (unlike the Galilean Transformation), it affects relative length (Length Contraction) and time as well as position.

Henrick Lorentz produced a version in an effort to explain why Light appeared to move at the same speed no matter how fast one was traveling in relation to it, and Albert Einstein derived it from his theory of Special Relativity, his method assuming time is not invariant between frames of reference moving relative to each other.

The Lorentz Transform regarding length (Length Contraction) is:

L = L0γ(v)
  • L0 - the length at rest.
  • L - the transformed length.
  • v - (relative) velocity.
  • γ(v) - Lorentz Factor.

The Lorentz Factor (γ or Γ) is used in probably all the Lorentz transformations as well as other related formulae, and is defined as:

γ = ——————————
  • γ - Lorentz factor.
  • v - velocity.
  • c - speed of light in a vacuum.

In some discussions involving Relativistic Speeds, a speed is indicated by its associated Lorentz factor. Some examples;

v γ
<<c ~1
4/5 c 5/3
40/41 c 41/9 or ~4.556
~0.99995 c 100
c infinity


Referenced by: