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This is probably a newbie question (but I guess is what I am right now) but I can't understand de difference between Galilean Boost and Galilean Translation.

I thought a boost was something like an S' frame of reference with constant velocity in relation to an S frame of reference. Mathematically:

$$ x' = x - vt; y' = y; z' = z; t' = t$$

so a boost would be an uniform motion between these to frame of reference and a translation would be an S'' frame of reference "fixed" but the origins dislocated in relation with S.

The thing is: I found in pdf files (and wikipedia) that these equations of a galilean transformation is actually a translation. Is that right?

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A boost refers to a coordinate transformation associated with a change in velocity and is mathematically equivalent to a translation of the coordinates by $vt$ where $v$ is the velocity and $t$ is time. This type of translation is not constant in time. On the other hand, a translation is a constant shift in coordinates.

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  • $\begingroup$ So the exemple I made is a boost while something like x' = x - cst; .... t' = t - cst2 is a trasnlation? $\endgroup$
    – evmiz
    May 23, 2020 at 20:21
  • $\begingroup$ Are $cst$ and $cst2$ constants? $\endgroup$ May 24, 2020 at 17:57
  • $\begingroup$ Yes they are!!! $\endgroup$
    – evmiz
    May 25, 2020 at 21:07
  • $\begingroup$ In that case yes, the case in you comment above is a translation. $\endgroup$ May 26, 2020 at 1:22

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