SR - Getting Zero Spatial Displacement

[A_Stone]

Summary:: I have tried for some time to understand my error but can't figure it out. Any help will be much appreciated.

Hi!

I'm trying to figure out why the spatial displacement from two events A and B gives zero when I use one method compared to another which doesn't give zero spatial displacement. I have a picture from the calculations below.

Thanks for any clarification to why the first method is wrong.

 

[Orodruin]

You are assuming that $\Delta x_{AB} = v \Delta t_{AB}$. This is not true. It is only true for events with no spatial separation in $\bar{\mathcal O}$ as those are the events that are separated by $v \Delta t$ in $\mathcal O$.

 

[A_Stone]

You are assuming that $\Delta x_{AB} = v \Delta t_{AB}$. This is not true. It is only true for events with no spatial separation in $\bar{\mathcal O}$ as those are the events that are separated by $v \Delta t$ in $\mathcal O$.

Thank you!