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Chapter 9 on the theory of relativity discusses a thought experiment (http://www.bartleby.com/173/9.html) about a passenger on a train that claims that
it is impossible to say in an absolute sense whether two events occur at the same time if those events are separated in space.
I have devised a modification to this thought experiment to disprove this.
Assume you have two long ropes laying side-by-side with the tracks, both going from point A to point B. You have a watchman standing at point A, and a watchman standing at point B. They will pull their rope when they see lightning strike their point. The passenger can see the grooves of the rope shift when it is pulled. If the passenger sees both ropes get pulled simultaneously at the midpoint, he will see them get pulled simultaneously anywhere.
...
This is because all points of the rope get pulled instantaneously. There is no waiting time like with the traveling of light. For example, consider a rope that is one lightyear long. When the rope gets pulled from one endpoint, a person at the other endpoint a lightyear away will see the rope's end move with no delay, due to the laws of matter. Even though no actual material is traveling faster than the speed of light, the knowledge that the rope was pulled is traveling faster than the speed of light.
So if you consider when the rope gets pulled to correspond to when the event of lightning occurs, there seems to be an absolute sense of simultaneity no matter where the train is or how it is moving.
it is impossible to say in an absolute sense whether two events occur at the same time if those events are separated in space.
I have devised a modification to this thought experiment to disprove this.
Assume you have two long ropes laying side-by-side with the tracks, both going from point A to point B. You have a watchman standing at point A, and a watchman standing at point B. They will pull their rope when they see lightning strike their point. The passenger can see the grooves of the rope shift when it is pulled. If the passenger sees both ropes get pulled simultaneously at the midpoint, he will see them get pulled simultaneously anywhere.
...
This is because all points of the rope get pulled instantaneously. There is no waiting time like with the traveling of light. For example, consider a rope that is one lightyear long. When the rope gets pulled from one endpoint, a person at the other endpoint a lightyear away will see the rope's end move with no delay, due to the laws of matter. Even though no actual material is traveling faster than the speed of light, the knowledge that the rope was pulled is traveling faster than the speed of light.
So if you consider when the rope gets pulled to correspond to when the event of lightning occurs, there seems to be an absolute sense of simultaneity no matter where the train is or how it is moving.