I'm trying to re-ask the Q based on the feedback I got on this forum. Here is the premise for the Q.
Consider an IRF, S. Assume only 2-D i.e (x,t). And the observer, O, is as assumed typically "fixed" at the origin of S.
Let an event, E, happen in the 'space' which we are trying to 'measure' using S and O (which I understand is a mathematical abstraction to study the laws of physics)
The observer O assigns (and thus records in his notebook) coordinate (x0,t0) to the event E.
My questions is how does he do that? (What is the precise physical procedure, even if idealistic, followed to measure x0 and t0?)
Some challenges I'm dealing with to understanding this (and to give a background why I'm asking this Q)
Observer O (origin of reference frame S) and E are separated by 'space' - How does information about E reach O? Does this non-locality has greater implications?
What is the significance of 'clock' present at every 'x'? And t0 is the time shown by local clock present at E? Are all the clocks in S synchronized? Why can't observer O, use his local clock at the origin (say when information about the event E has happened reaches O)?
- Similarly how does O measure x0? How does the reading on his 'meter sticks' reach him? etc.
I have been struggling to properly define the act of 'measurement' - and I'm unable to do so. Most books also do not cover this in adequate detail and for me it is quite important to understand this Q - to understand SRT