Lorentz Transformation/Examples

Examples of Lorentz Transformations

Arbitrary Example

The following equations are examples of those used for a Lorentz transformation:

\(\ds x'\)

\(=\)

\(\ds \beta \paren {x - v t}\)

\(\ds y'\)

\(=\)

\(\ds y\)

\(\ds z'\)

\(=\)

\(\ds z\)

\(\ds t'\)

\(=\)

\(\ds \beta \paren {t - \dfrac {v x} {c^2} }\)

where:

$\beta = \dfrac 1 {\sqrt {1 - \dfrac {v^2} {c^2} } }$

$v$ denotes the magnitude of the relative velocity of the two frames of reference.