I read that the form of a galilean transformation on the point (t,x) is the following:(adsbygoogle = window.adsbygoogle || []).push({});

constant velocity transform by velocity v: (t,x) ---> (t,x+vt)

translation transform by (t_{0},x_{0}): (t,x)--->(t+t_{0},x+x_{0})

rotation transformation by rotation matrix R: (t,x)--->(t,Rx)

and that it is based on the following postulates: two observers observe the same time between events, and two observers measure the same distance for simultaneous events.

My question is, based on those two postulates, couldn't you modify the first transform to

(t,x)--->(t,x+vf(t))

This transformation preserves the time between events (it doesn't change time at all). It also preserves simultaneous distance:

|(x_{1}+vf(t))-(x_{2}+vf(t))|=|x_{1}-x_{2}|

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# Galilean group

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