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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 that time can proceed at different rates in frames of reference moving relative to each other. The Lorentz transform regarding length (length contraction) is:

L = L0γ(v)

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 = ——————————

In discussions involving relativistic speeds, a speed is often indicated by its associated Lorentz factor. Some examples:

v γ
0 1
<< c ~1
4/5 c 5/3
40/41 c 41/9 or ~4.556
~0.99995 c 100

Further reading:

Referenced by pages:
conformal field theory (CFT)
relativistic effect
relativistic energy
relativistic invariance
relativistic momentum
relativistic speed