« Last post by Dimensional on Today at 23:15:26 »
Hi.Yeah this makes sense to me. Thank a lot.Is your origin (0,0) at the very back of the back fin of the ship like in the video?Yes. The origin is intended to be exactly where they placed it in the original video (although I only sketched it, I didn't get a ruler and compass).
The planet based observer says the back of the fin is at x= 0 when t =0. Spaceman says the back of the fin is at x'=0 when t' =0.
- - - - - - - - - -
Just to emphasize one issue, although in my diagrams it looks like the x and x' co-ordinates of the rock collision event are both +5, they aren't actually exactly the same. That's just that the diagram is only a sketch and I haven't placed all the gridlines exactly the same space apart etc. I just want to dispel the notion that there was any reason why they had to agree on the spatial location of the event... there isn't.
I've run the precise calculation with these figures (they are roughly what was used in the video).
Set the velocity of the rocket = half the speed of light.
Use units for measuring time and distance so that the speed of light, c = 1 in those units (Just to be clear that's not going to be seconds and metres. It's just conventional to set c = 1).
Set the rock collision event to co-ordinates (x, t) = ( +5.00 , +1.00 ) as was shown in my diagram for the planetary observer.
This becomes (x', t') = ( +5.20 , -1.73) in the spacemans co-ordinate system.
So, with these figures, the spaceman and planet based observer disagree on the both the location and time of the collision event.