The Relativity Of Simultaneity.

[siddharth5129]

Say there are two observer S and S'. Let's assume that their frames coincide at the instant t=0 and that observer S' is moving to the right at a speed 'v' with respect to the observer S along the X axis. Two lightning strikes occurs at the points A and B in the S frame at t=0. The corresponding points in the S' frame are A' and B', which coincide with A and B at t=0. My textbook says that the two events are simultaneous for the observer S, but not for the observer S'. This is what I don't get. The events are simultaneous for the observer S because the light pulses from the two events hit the midpoint O at the same time. Now, in determining whether or not the event is simultaneous in the S' frame, shouldn't we analyze the scenario form the S' frame, in which case, the light pulses would arrive simultaneously at O', and the two lightning strikes would be simultaneous in the S' frame as well. Isn't it erroneous to analyze the scenario from the S frame and then claim that the two events are not simultaneous in the S' frame. Shouldn't simultaneity of events in a frame be determined by clocks in that frame. In this case, the events would be simultaneous for both observers.

 

[Doc Al]

Now, in determining whether or not the event is simultaneous in the S' frame, shouldn't we analyze the scenario form the S' frame, in which case, the light pulses would arrive simultaneously at O', and the two lightning strikes would be simultaneous in the S' frame as well.

You are assuming that the lightning strikes at A' and B' occur simultaneously according to the S' frame. But they don't.

 

[Dale]

Now, in determining whether or not the event is simultaneous in the S' frame, shouldn't we analyze the scenario form the S' frame, in which case, the light pulses would arrive simultaneously at O', and the two lightning strikes would be simultaneous in the S' frame as well.

Except that in the primed frame O' is not midway between the light pulses when they arrive at O'. Since the light arrives simultaneously at a location that is not midway between them then you know that they did not occur simultaneously.

 

[harrylin]

Say there are two observer S and S'. Let's assume that their frames coincide at the instant t=0 and that observer S' is moving to the right at a speed 'v' with respect to the observer S along the X axis. Two lightning strikes occurs at the points A and B in the S frame at t=0. The corresponding points in the S' frame are A' and B', which coincide with A and B at t=0. My textbook says that the two events are simultaneous for the observer S, but not for the observer S'. This is what I don't get. The events are simultaneous for the observer S because the light pulses from the two events hit the midpoint O at the same time. Now, in determining whether or not the event is simultaneous in the S' frame, shouldn't we analyze the scenario form the S' frame, in which case, the light pulses would arrive simultaneously at O', and the two lightning strikes would be simultaneous in the S' frame as well. Isn't it erroneous to analyze the scenario from the S frame and then claim that the two events are not simultaneous in the S' frame. Shouldn't simultaneity of events in a frame be determined by clocks in that frame. In this case, the events would be simultaneous for both observers.

It could be good to start with http://www.fourmilab.ch/etexts/einstein/specrel/www/ section 1, "Definition of simultaneity".

Assuming that you understand that part, I continue:
You know that in S the flashes arrive at the same point O (and not O') at the same time; this cannot be otherwise in S' (if this is not immediately clear, try to find a way how it can be any different!). From the fact that the flashes don't arrive at the same time at midpoint O', it is immediately clear that the strikes "were not simultaneous in S' " - according to the definition of simultaneity in S'. The clocks of S' are set accordingly.