Understand Relativity & Lorentz Transformation - Aaron

[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

 

[ShayanJ]

This suggests that time experienced in F' depends on O, since x is the position of O.

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.

 

[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

 

[Matterwave]

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

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.