Definition:Lorentz Transformation

Definition

The Lorentz transformation is a transformation which changes the position and motion in one inertial frame of reference to a different inertial frame of reference.

The equations governing such a transformation must satisfy the postulates of the special theory of relativity.

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Examples

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.

Also see

• Definition:Galilean Transformation

• Results about Lorentz transformations can be found here.

Source of Name

This entry was named for Hendrik Antoon Lorentz.

Historical Note

The Lorentz transformations replace the Galilean transformations when converting between inertial frames of reference in the special theory of relativity.

They show that the idea of the universality of time is invalid.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): relativity
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): relativity