### 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 (relativistically invariant).

The Lorentz transform regarding length (*length contraction*) is:

L = L_{0}γ(v)

- L
_{0} - 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:

1
γ = ——————————
√(1-v²/c²)

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 | ∞ |

(*physics,relativity*)
**Further reading:**

http://en.wikipedia.org/wiki/Lorentz_transformation

**Referenced by pages:**

metric

relativistic energy

relativistic invariance

relativistic momentum

relativity

spacetime

Index