Newtonian Spacetime

Newtonian Spacetime differs from Relativistic spacetime in that time is considered an absolute (i.e. \(t^{\prime} = t\)). Transformations between reference frames can be achieved with Galilean transformations. A particle traveling along the x axis in \(S\) at a constant speed u, has a speed \(u^{\prime}\) found by:

\begin{equation} u^{\prime}_{x} = \frac{dx^{\prime}}{dt^{\prime}} = \frac{dx^{\prime}}{dt} = \frac{dx}{dt} - v = u_{x} - v\tag{1} \end{equation}

remembering that the first derivative of position is velocity, and the second derivative of motion is acceleration

\([1]\) is derived from \(x^{\prime} = x - vt\) of the Galilean transformations.