# Relativity and simultaneity

FossilFew
I read the post entitled "Thought experiment in relativity of simultaneity". It's pretty close to my question but not necessarily needed to answer my questions.

Situation: On observer (A) is "at rest" and another observer (B) is in a reference frame moving with respect to observer (A). Assume that when an observer (B) in the moving reference frame is directly across from the "at rest" observer (A), he sees lightning strike at each end of the car in which he is riding, flash at the same time. What will the observer (A) who is "at rest" see? (assume that the distance between the lightning on the left side of observer (B) and observer (B) is equivalent to the distance between the lightning on the right side of observer (B) and observer (B) )

Based on simultaneity I would say that the observer (A) who is at rest would see one of two scenarios:

1. From the reference frame of observer (A): If observer (B) is moving left of observer (A), observer (A) will see lightning to the right of observer (B) strike first followed by the striking of the lightning to the left of observer (B).

2. From the reference frame of observer (A): If observer (B) is moving right of observer (A), observer (A) will see lightning to the left of observer (B) strike first followed by the striking of the lightning to the right of observer (B).

Does this reasoning seem correct? Both observers will also suspect that the other's clocks are incorrect too.

TIA!

country boy
If I understand your setup, A is coincident with B at the instant that the two flashes reach them. They will therefore each see the two flashes at the same time in their own frames. But A will not agree that the flashes occurred simultaneously.

Yes, you have to be careful about distinguishing what they "see" (in terms of when the light from each flash actually reaches them) and what they measure the time-coordinates of the flashes to be in their own rest frames (often the words 'observe' or 'measure' is often used as a shorthand for this). In terms of their measurements, your reasoning in 1) and 2) is correct.

country boy
Right, the measurements could be peformed anywhere in either moving or rest frames. And when the observers "see" the flashes, those are also measurements (they could have used photodetectors).

Right, the measurements could be peformed anywhere in either moving or rest frames. And when the observers "see" the flashes, those are also measurements (they could have used photodetectors).
Sure, but I meant something more like "the measurement of the time-coordinate of the event in their own rest frames". I think if a physicist says something like "when did this observer measure this event occurring" she'd usually be talking about the retroactively assigned time-coordinate, not the moment the light from the event actually reaches her.

country boy
This goes to the heart of the problem, the difference between remote simultaneity and local simultaneity. When I read that the observer "sees the lightning strike," I assume that light has arrived at her or his eye. That is local, in that the observer and the measurement are at the same place and time. That there is a coincidence does not depend on when the light was emitted. If the measurements take place remotely, a sychronization of clocks would have to be established. When I re-read FossilFew's question, I am pretty sure it means that both observers and the light from both flashes are all at the same location at the same time. Maybe FossilFew will chime in here.

FossilFew
Yes "light from both flashes are all at the same location at the same time". We know that observer (B) will see the two light flashes at the same time (from (B)'s frame of reference).

TIA

Yes "light from both flashes are all at the same location at the same time". We know that observer (B) will see the two light flashes at the same time (from (B)'s frame of reference).

TIA
If you're talking about what they see, then they'll both see the two light signals reach their eyes at the same moment, if I understand your scenario right. But when they subtract out the travel time of the light to figure out when each flash "really" happened in their own rest frame, one will conclude both happened at the same time and one will conclude they both happened at different times.

FossilFew
Weeks later I'm thinking I am incorrect on my assumption. It seems that length contraction is an issue I didn't think about when viewing the lightning flashes

(I search on lightning in this link and read the example which is the same as the one I was attempting to answer:

http://www.upscale.utoronto.ca/GeneralInterest/Logan/Poetry/CHAPTER11-12.html

)

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