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Suppose there is an observer sitting in the middle of a moving train, and another obsever outside on a platform. When this train passes the outside observer, so that the ends of the train are equidistant from the outside observer, a flash of light is emitted from both ends. This can be the commonly used lightning strike or just some light pulse.

I reconstructed this scenario in desmos. The outside observer sees both lights at the same time and upon measuring the distances concludes that they flashed simultaneously. The observer inside the train, however, sees the light on the right flash and then the light on the left and concludes that the lights did not flash simultaneously. This makes sense since Einstein postulates that the speed of light must remain constant in all reference frames and the observer in the train is moving towards and away from the flash on the right and the flash on the left, respectively.

I constructed an alternate scenario in desmos as well. This is essentially the same scneraio, just viewed from the inertial reference frame of the observer sitting inside the train cart. In this case, the observer inside sees the 2 lights flash simultaneously and the observer outside sees them flash in a different order.

Are these scenarios equivalent? If no, why not? If yes, how is it possible that the same observer sees the events play out in a different order? Which is the correct order?

And most importantly, what do each of the observers see?

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    $\begingroup$ If I did not misinterpret what you described, The two physical situations are different. In the first one the flashes are simultaneous on the platform, but not on the train, and vice versa. $\endgroup$
    – user65081
    Commented Oct 29, 2021 at 20:47
  • $\begingroup$ The observers see different things in the two situations. $\endgroup$
    – user65081
    Commented Oct 29, 2021 at 20:55
  • $\begingroup$ Well how are the scenarios any different? The hyperlinks might show seemingly different scenarios, but aren't they the same just from a different frame of reference? $\endgroup$
    – Maj Zobrani
    Commented Oct 29, 2021 at 21:00
  • $\begingroup$ Did you read my first comment? the simultaneity happens in different reference systems in the two different cases $\endgroup$
    – user65081
    Commented Oct 29, 2021 at 21:01

2 Answers 2

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Imagine two people, A and B, with faulty spirit levels- one spirit level tips down to the left, the other tips down to the right. Person A uses their spirit level to draw two level marks on a wall. Person B checks them and says one mark is higher than the other. Person B then uses their level to drawn two level marks on the wall- Person A checks them and declares one to be higher than the other. So, two marks can be drawn level according to Person A or they can be drawn level according to Person B- two marks cannot be drawn to appear level to both Person A and Person B.

The example above is directly analogous to your scenario with the lights and the train. Either the two lights can be made to flash at moments that are simultaneous to the person on the train, or they can be made to flash at two moments that are simultaneous to the person on the platform. There are no two moments that are simultaneous to both the person on the train and to the person on the platform. The two options are simply reciprocal arrangements- neither is more right or wrong than the other.

You ask how the same observer can see the events at different times- the answer is because the events occur at different times. In one scenario the flashes happen at the same time on the train, and therefore at two separate times on the platform- in the other they happen at two separate times on the train and the same time on the platform.

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Yes, the scenarios are equivalent. As for "which is the correct order", I don't know what "correct" means. In either scenario, the flashes occur in one order in one frame and a different order in the other.

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  • $\begingroup$ If both are equivalent, then what do each of the observers see? Do they both see the flashes happen at the same time? $\endgroup$
    – Maj Zobrani
    Commented Oct 29, 2021 at 20:17
  • $\begingroup$ They are equivalent up to a swapping of the observers. In one scenario, the flashes are simultaneous in the frame of observer A but not observer B, and in the other they are simultaneous in the frame of observer B, but not of observer A. In other words, one scenario IS the other scenario with the names of the observers reversed. $\endgroup$
    – WillO
    Commented Oct 29, 2021 at 20:49
  • $\begingroup$ So what do observer A and B actually see? Does A see that the flashes are simultaneous or not? What about B? $\endgroup$
    – Maj Zobrani
    Commented Oct 29, 2021 at 20:50
  • $\begingroup$ One of them sees the flashes as simultaneous and one doesn't. Which one sees the flashes as simultaneous depends on which scenario you're talking about. $\endgroup$
    – WillO
    Commented Oct 29, 2021 at 21:08

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