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## Main Question or Discussion Point

So I've been doing some review on special relativity and I realized that I never fully understood how simultaneity is relative in special relativity. Taking the thought experiment about a lightbulb being turned on in a train, I get that the observer in the middle of the train will see light hitting both sides of the train simultaneously and that the observer at rest will not.

What I'm wondering about is whether this is because there is a lag between when the events happen and between when the observer on the train observes them which is different for the two events. Let's say the train is moving east. Will the light moving west actually impact the wall before the light moving east but simply take longer to reach the observer since on the return trip, it would take longer due to the light now facing east?

Essentially, on the return trip, since the direction of the train now works against the light moving west, it seems that you could have the light impact the west side of the train before the east side and still observe them to be simultaneous, hence actual simultaneity would be preserved between the moving frame of reference and the stationary one despite the observations being different.

My intuition is that this isn't the case and that it's just the example used which isn't entirely illustrative, otherwise this thought experiment doesn't seem to be as significant as it should be. I guess what I want to ask is in the train example above, if you had two people at each end of the train (moving with the train) observe when the light hits them, would they record the events as simultaneous (assuming they could instantly communicate the result to each other as such). Or alternatively, if two lightbulbs at different ends of the train were turned on at the same time, would the observer in the middle see the light from both lightbulbs hit them simultaneously?

Sorry for the long winded question I'm having some difficulty wrapping my head around this and any help/confirmation is appreciated!

What I'm wondering about is whether this is because there is a lag between when the events happen and between when the observer on the train observes them which is different for the two events. Let's say the train is moving east. Will the light moving west actually impact the wall before the light moving east but simply take longer to reach the observer since on the return trip, it would take longer due to the light now facing east?

Essentially, on the return trip, since the direction of the train now works against the light moving west, it seems that you could have the light impact the west side of the train before the east side and still observe them to be simultaneous, hence actual simultaneity would be preserved between the moving frame of reference and the stationary one despite the observations being different.

My intuition is that this isn't the case and that it's just the example used which isn't entirely illustrative, otherwise this thought experiment doesn't seem to be as significant as it should be. I guess what I want to ask is in the train example above, if you had two people at each end of the train (moving with the train) observe when the light hits them, would they record the events as simultaneous (assuming they could instantly communicate the result to each other as such). Or alternatively, if two lightbulbs at different ends of the train were turned on at the same time, would the observer in the middle see the light from both lightbulbs hit them simultaneously?

Sorry for the long winded question I'm having some difficulty wrapping my head around this and any help/confirmation is appreciated!

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