# Confusion in Lorentz Transformation and Relativity

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1. Jan 4, 2015

### doaaron

Hi all,

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 velocity v with 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 is x = wt. Now, if I want to find the position of O in frame F', I need to apply the Lorentz Transformation to find x' and t'. The equation for t' is,

t' = γ(t - vx/c2)

My confusion is the term "x" in the above equation. This suggests that time experienced in F' depends on O, since x is the position of O. So if I were to introduce another object, P, moving at a velocity, u ≠ w with respect to F, then t' would be different for O and P. Intuitively, I would think that t' only depends on v. Please let me know where I have made my mistake.

thanks,
Aaron

2. Jan 4, 2015

### ShayanJ

It doesn't depend on O, but on O's position.

Excluding the above sentence, your only mistake is leaning towards your intuition which you acquired by living in a non-relativistic world and studying non-relativistic physics.

3. Jan 4, 2015

### doaaron

Thanks for the reply. Actually I think I understand my mistake. x', t' simply describes a coordinate in frame F', so it is possible to calculate x', t' for each object, O, P etc.

thanks,
Aaron

4. Jan 4, 2015

### Matterwave

Yes, the t' is the coordinate label for an event O in the primed frame. Or a different event K, it will have a similarly different set of coordinate labels.