*The Simplest Derivation of the Lorentz Transformation*

*By Wolfgang G. Gasser*

Several attempts have been made to demonstrate errors in concrete derivations of the Lorentz transformation. Yet even if all existing derivations turned out to be erroneous, the ideal space-time relations expressed by the Lorentz transformations would remain unaffected. (Whether the Lorentz transformation leads to contradictions in case of accelerations, or whether the Lorentz transformation is somehow "implemented" in our empirical reality, are different questions.)

In order to derive the Lorentz transformation in one spatial dimension, one has to start with the Galilean transformation:

*x**'**
= x - ß c t*

Here the factor *ß *is used to express
the velocity ** v** of coordinate system

*t**'**
= t - ß/c x*

By using concrete values for *x* and *t*,
one can easily recognize that light moving at ** c** in coordinate
system

*x**'**
= (x - ß c t)*

*t**'** = (t - ß/c x)*

and the transformation back to
coordinate system *S*

*x**
= (1 - ß ^{2}) ^{-1 } (x*

*t** = (1 - ß ^{2})
^{-1} (t*

can easily be removed:

*x**'**
= (1 - ß ^{2}) ^{-1/2 } (x -
ß c t)*

*t**'** = (1 - ß ^{2})
^{-1/2 } (t - ß/c x)*

*x**
= (1 - ß ^{2}) ^{-1/2 } (x*

*t**
= (1 - ß ^{2}) ^{-1/2} (t*

This
is an extract from: *Verteidigung der Relativitätstheorie vor
unberechtigter Kritik*