iSoul In the beginning is reality

Galilei for space and time

Consider the now-classic scenario in which observer K is at rest and observer K′ is moving in the positive direction of the x axis with constant velocity v. The basic problem is that if they both observe a point event E, how should one convert the coordinates of E from one reference frame to the other?

First assume time is absolute and space is relative with no characteristic speed. Only the spatial coordinates in the positive direction of the x axis are affected. The other coordinates do not change. The transformation equation for the positive direction of the x axis is

rx′ = rx − vtx

where rx is the spatial coordinate and tx is the temporal coordinate in the positive direction of the x axis. The inverse transformation is

rx = rx′ + vtx.

This is called the Galilei (or Galilean) transformation.

Now consider the case in which space is absolute and time is relative with no characteristic speed. Only the temporal coordinates in the positive direction of the x axis are affected. The other coordinates do not change. The transformation equation for the positive direction of the x axis is

tx′ = tx − rx/v

and the inverse transformation is

tx = tx′ + rx′/v.

This could be called the temporal Galilei transformation since only temporal coordinates change. The transformation above would then be called the spatial Galilei transformation.

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