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What is the resoning or the motivation for the minus sign in the space-time interval?
It comes from the original attempt by Einstein to discover frame invariants. He was the first to show that , if you define :Thinking about [tex]s^{2}=t^{2}-(x^{2}+y^{2}+z^{2})[/tex]
Let us say we have two spatial dimensions (x and y) defining a plane, then by Pythagoras the length of the diagonal connecting a point at the origin to a point with coordinates (x,y) is the familiar [itex]\sqrt{(x^2+y^2)}[/itex].Ofcourse, but that's not what im asking about. I'm asking why treat time differently? Is there some reasoning other than "we do it because it works". In eucledian geometry one would just add everything, but in Lorentz geometry there is this minus.