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Wikipedia article on Galilean coordinate transformations.
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My challenge is to a Euclidean space version of the Galilean coordinate transformations. That is, while this is a physical based interpretation
at Wikipedia, this challenge is challanging the underlying math. Their equation in Physics is x' = x - vt. The equation is being challenged, as merely x' = x - d. Logically, if using distance does not work mathematically, then substituting vt for distance, will also not work. In that context, this mathematical challenge will not be dealing with observers, wavelengths, light, time, delays...nor anything physical in any sense.
I have paraphrased the Wikipedia article, noted just above, to reflect my math only approach in this challenge. The notation below describes the related values under the Galilean transformation between the coordinates (x,y,z) and (x',y',z') of a single arbitrary POINT, in two Euclidean space coordinate systems S and S', after translation in their common x and x’ directions, with their spatial origins coinciding. x' = x - vt
y' = y
z' = z my own take... x' = x y' = y z' = z |