Relativity of simultaneity

The common example demonstrating relativity of simultaneity is something like this:

Say there is Person #1 and #2, each on their own train, in the middle of the train from both ends. #1 thinks #2 is moving, but #2 thinks #1 is moving. Lightning hits both ends of the trains. In #1's reference frame, let's say that light from the events hits #1 at the same time. But #1 sees #2 moving, so #1 will believe that #2 sees one event before the other. The example thus ends that it is in fact true that #2 sees one event before the other.

But this is just from #1's reference frame! I mean, how do we know what #2 will actually see? We can't just judge from #1's reference what #2 will see?? According to #2, it is #1 that is moving, so #2 will say that #1 did not see the events at the same time, even though #1 says that he did see them at same time. So if we do not know purely from #2's reference what #1 actually saw, then by symmetry we can't say what #2 actually saw from #1's reference...?

ghwellsjr
Gold Member
We know because of what you said: you said in #1's frame the lightning hit both ends of the train at the same time and that's what makes it happen at different times in #2's frame. If you define a different scenario, then the outcome will be different.

mfb
Mentor
But this is just from #1's reference frame! I mean, how do we know what #2 will actually see?
You can simply track the light which is moving around (with detectors or something else), and find out that light from one side hits #2 before the other light is there.

According to #2, it is #1 that is moving, so #2 will say that #1 did not see the events at the same time
#2 will see the light rays reaching #1 at the same time. For a single point, "at the same time" is still well-defined.

It is possible to go through the whole process from the view of #2 to:
Both light rays hit #1 at the same time (this is true for all observers), but #1 is close to the back of the train at this time (because #1 moves towards the back). Therefore, the lightning strike at the front must have been earlier than the strike at the back.

The common example demonstrating relativity of simultaneity is something like this:

Say there is Person #1 and #2, each on their own train, in the middle of the train from both ends. #1 thinks #2 is moving, but #2 thinks #1 is moving. Lightning hits both ends of the trains.

As has been pointed out you supplied the vital parameter when you added the condition of simultaneous reception by #1.
Solely with this initial information above , it is not possible to conclude much other than both can't receive the flashes simultaneously.. Neither observer might receive the flashes simultaneously.

In fact, if you stipulated that the trains had the same rest length this would necessarily be the case.

This can be seen if you look at the event (A) of the lightning strike at the meeting of the front of train #1 with the rear of train #2.
At this time, according to the simultaneity of the clocks on train 1 the front of train 2 has not yet reached the back of train 1. = Event (B)
So (A) is earlier than (B)
According to the clocks on train 2 the back of train 1 has already passed the front of train 2
So event (A) is later than event (B)
Of course the reciprocal is true at the meeting of the front of train 2 and back of train1.

This might be a little hard to grasp at first but it not only relates length contraction to
simultaneity but is necessary to understanding the resolution of the contraction paradox I.e.; train 1 is longer than train 2 AND train2 is longer than train 1

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i would actually like to jump in with a question on same line..for 2 frames moving with uniform relative velocity to each other,can there actually be an event which is simultaneous to both frames?..since rate of time flow will differ for each frame its hard to perceive exactly how simultaneity would be acheived?

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Doc Al
Mentor
i would actually like to jump in with a question on same line..for 2 frames moving with uniform relative velocity to each other,can there actually be an event which is simultaneous to both frames?
To talk about simultaneity you need to have at least two events.

Since clock desynchronization only occurs along the direction of motion, you can have events that are separated along a line perpendicular to the motion occur simultaneously for both observers.