Is the Relativity of Simultaneity Always True?

[DAC]

I also have a question about the Relativity of Simultaneity ( S&G part 1 sec. 9 ). In Einstein's thought experiment lightning strikes the tracks at each end of a train. The embankment observer who is equidistant from the strikes sees them as simultaneous. The onboard ( moving ) train observer, moving to one strike and 'away' from the other, sees them as separate events. If we alter this so that the flashes strike the tracks at the front left and right of the train, and place an observer on a footbridge who is aligned with the observer in the train, along the trains long axis, then both observers will be equidistant from the flashes and see them as simultaneous, despite being in different frames.
Einstein said events which are simultaneous in the embankment frame are not simultaneous in the train frame. Can you explain.
Thanks.

 

[Nugatory]

Einstein said events which are simultaneous in the embankment frame are not simultaneous in the train frame. Can you explain.

He said such events are not necessarily simultaneous. He did not say that they were never simultaneous. You've identified one of the special cases in which a particular pair of events just happens to be simultaneous for some observers who are not at rest relative to one another.

 

[ghwellsjr]

I also have a question about the Relativity of Simultaneity ( S&G part 1 sec. 9 ). In Einstein's thought experiment lightning strikes the tracks at each end of a train. The embankment observer who is equidistant from the strikes sees them as simultaneous. The onboard ( moving ) train observer, moving to one strike and 'away' from the other, sees them as separate events. If we alter this so that the flashes strike the tracks at the front left and right of the train, and place an observer on a footbridge who is aligned with the observer in the train, along the trains long axis, then both observers will be equidistant from the flashes and see them as simultaneous, despite being in different frames.
Einstein said events which are simultaneous in the embankment frame are not simultaneous in the train frame. Can you explain.
Thanks.

If the train is moving along the x-direction and you use the common Lorentz Transformation, you will see that two events that have the same x and t coordinates in one frame will have the same x and t coordinates in all frames and therefore will be simultaneous in all frames. They can have different y (or z) coordinates but those variables are not in the equation for the t transform.

 

[td21]

Simultaneity is not absolute. One can observe a simultaneous event in one frame, but then not on the other frames.
Try watching this animation,


In general, the order of events is not necessarily preserved. If in one frame event A is observed to happen before event B, the same order (event A happens before event B) can only be preserved in another frame if the two events are time-like.

 

[DAC]

He said such events are not necessarily simultaneous. He did not say that they were never simultaneous. You've identified one of the special cases in which a particular pair of events just happens to be simultaneous for some observers who are not at rest relative to one another.

"We thus arrive at the important result: Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa." SG 1.9

" but that two events which viewed from a system of co-ordinates are simultaneous, can no longer be looked on as simultaneous events when envisaged from a system which is in motion relatively to that system." On The Electrodynamics, Section 2, last para.

Could you explain?

 

[Nugatory]

Could you explain?

You are reading the words and not the math that they go with. As ghwellsjr pointed out in #3 of this thread, there is absolutely no ambiguity in the math, and it is quite clear what Einstein is saying.

 

[Nugatory]

The question in the original post has been answered, so I am closing this thread.