Page:The Meaning of Relativity - Albert Einstein (1922).djvu/40

28 another, and regulated alike, could be distributed over the systems $$K$$ and $$K'$$ at rest relatively to them, and their indications would be independent of the state of motion of the systems; the time of an event would then be given by the clock in its immediate neighbourhood.

2. Length is absolute; if an interval, at rest relatively to $$K$$, has a length $$s$$, then it has the same length $$s$$, relatively to a system $$K'$$ which is in motion relatively to $$K$$.

If the axes of $$K$$ and $$K'$$ are parallel to each other, a simple calculation based on these two assumptions, gives the equations of transformation {{MathForm2|(21)| $$ \left. \begin{align} x_\nu' & = x_\nu - a_\nu - b_\nu t \\ t' & = t - b \end{align} \right\} $$}}

This transformation is known as the "Galilean Transformation." Differentiating twice by the time, we get

Further, it follows that for two simultaneous events,

The invariance of the distance between the two points results from squaring and adding. From this easily follows the co-variance of Newton's equations of motion with respect to the Galilean transformation (21). Hence it follows that classical mechanics is in accord with the principle of special relativity if the two hypotheses respecting scales and clocks are made.

But this attempt to found relativity of translation upon the Galilean transformation fails when applied to