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In Revolutions in Twentieth Century Physics, David Griffith's introduces the relativity of simultaneity with a thought experiment akin to the "Train and platform" problem wherein the outcome is that two observers (one on a moving train car and the other on a stationary platform) differ in their observation of whether a flash of light (initiated at the moment both observers pass one another) hits the rear and front of the train car simultaneously or at different points in time.

I follow the thought experiment and the logic of the explanation, however when modifying the experiment as follows I loose myself and cannot reconcile what the outcome would be and why:

  • If we add a condition that if light strikes the rear and front ends simultaneously, the observer on the train car (A) lives and if it strikes each end at a different time, observer A dies, would observer A live or die?

  • From the perspective of the observer A, light would strike both ends simultaneously and he should continue to riding the train, however from the perspective of the observer on the platform he should die.

What would the "real" outcome be and how would we reconcile it theoretically?

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    $\begingroup$ Alice is facing north. Bob is facing south. A light beam is fired in a random direction. If the light beam hits a target to their left, they die. The beam hits a target. Alice says "Oh, no! That target is on our left! We're doomed!". Bob says "Wrong! That target is on our right! We get to live!". What would be the real outcome and how would we reconcile it theoretically? $\endgroup$ – WillO Apr 2 '18 at 14:28
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What would happen depends on how you went about implementing the mechanism that kills observer A if the light strikes the two ends of the train car at different times. The mechanism would require some kind of sensors to detect when a flash of light strikes an end of the car, and a comparator device that receives signals from the sensors, and determines whether the two signals occurred simultaneously. The ambiguity as to what happens is due to it being impossible for a sensor to send a signal to the comparator faster than the speed of light.

Suppose the sensors are attached to the ends of the train car, and connected by fiber optic cables to a comparator attached to the center of the car. In that case, the comparator would receive the signals from the sensors at the same time, and conclude that the light flashes struck the ends of the car simultaneously, letting observer A live. But the station observer would say that observer A got let off easy. The station observer would say that the flash of light struck the read end of the car before it struck the front end, but the signal from the rear sensor took longer to reach the comparator than the signal from the front sensor, due to the comparator moving away from the location where the flash hit the rear end, and toward the location where the flash hit the front end.

In contrast, if the mechanism was implemented via sensors and a comparator that are attached to the train station, that mechanism would decide that the flash struck the two ends of the train car at different times, and would trigger the bomb or whatever that kills observer A.

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  • $\begingroup$ Thank you so much, this clears up my confusion! I did not consider the feedback mechanism (i.e. the kill process) and had implicitly and erroneously assumed it to be faster than light! $\endgroup$ – ZYH Apr 2 '18 at 15:49

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