Galilean Transformations

In Newton’s formulation of spacetime, time is an absolute; meaning that every observer experiences the same flow of time. Assuming an inertial frame with only translation across the x axis, an event \(P\), can be translated between \(S\) and \(S^{\prime}\) by the following linear transformations:

\begin{equation} t^{\prime} = t\tag{1} \end{equation}

\begin{equation} x^{\prime} = x - vt\tag{2} \end{equation}

\begin{equation} y^{\prime} = y\tag{3} \end{equation}

\begin{equation} z^{\prime} = z\tag{4} \end{equation}

Switching between coordinates (\(S\) v. \(S^{\prime}\)) requires only switching the sign on \(v\).