# What is the difference between boost and translation in Galilean Transformation?

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?

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.
• Are $cst$ and $cst2$ constants? Commented May 24, 2020 at 17:57