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 $v$.