Consider the following experimental setup:
- 2 parallel lines close to each other. The direction of +ve x-axis is same for both the lines.
- There is a standard 1-meter rod on each of these lines. Let they be called S and S'. The end-point towards the +ve x-axis for S is P and S' is P'. The other end-point is O and O' respectively.
- O and O' are origins of reference frame S and S'. And O' moves +V with respect to O
- Event E1 is when O and O' coincide (i.e. are right next to each other. Assume please: the lines are very close to each other) - By convention, this is also considered as the origin for both the reference frame S and S'
- Event E2 is when P and P' coincide.
Now a few questions:
- What is the velocity of P' with respect to P?
- In each (or any) of the reference frames S and S' - Are events E1 and E2 simultaneous? If not which precedes the other?
This is not a homework question - I have been thinking about this to better get an intuitive grasp of special relativity. I think I know the answers (I have used Lorentz Transformation to get the answers above) - but I lack a good physical understanding, intuition or argument (I don't exactly know what I lack here :)) to arrive at those conclusions.
So for e.g. even an answer like E1 precedes E2 in the reference frame S because <some physical argument> will be very helpful.
(I don't really want to use math to answer the above)