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I am trying to understand relativity and Lorentz Transformation more clearly but I have some problems. Assume that we have frame F' which is moving at velocityvwith respect to F. Now assume we have an object, O, moving at velocity,w,with respect to F. Frame F has its own time,t, and the position of O isx=wt. Now, if I want to find the position of O in frame F', I need to apply the Lorentz Transformation to findx' andt'. The equation fort' is,

t' =γ(t-vx/c^{2})

My confusion is the term "x" in the above equation. This suggests that time experienced in F' depends on O, sincexis the position of O. So if I were to introduce another object, P, moving at a velocity,u ≠ wwith respect to F, thent' would be different for O and P. Intuitively, I would think thatt' only depends onv. Please let me know where I have made my mistake.

thanks,

Aaron

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# Confusion in Lorentz Transformation and Relativity

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