Galilean Transformation

A transformation from one reference frame to another moving with a constant Velocity $v$ with respect to the first for classical motion. However, special relativity shows that the transformation must be modified to the Lorentz Transformation for relativistic motion. The forward Galilean transformation is

$$\left[{\matrix{t'\cr x'\cr y'\cr z'\cr}}\right]=\left[{\matr... ... 0 & 1\cr}}\right]\left[{\matrix{t\cr x\cr y\cr z\cr}}\right],$$

and the inverse transformation is

$$\left[{\matrix{t\cr x\cr y\cr z\cr}}\right] =\left[{\matrix{... ... 1\cr}}\right]\left[{\matrix{t'\cr x'\cr y'\cr z'\cr}}\right].$$

See also Lorentz Transformation