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The theory of relativity shows us that the relationships of positions and times as measured in one coordinate system and another are not what we would have expected on the basis of our intuitive ideas. It is very important that we thoroughly understand the relations of space and time implied by the Lorentz transformation, and therefore we shall consider this matter more deeply in this chapter.

The Lorentz transformation between the positions and times (x,y,z,t) as measured by an observer “standing still,” and the corresponding coordinates and time (x′,y′,z′,t′) measured inside a “moving” space ship, moving with velocity u are