Author: A A Andrews (---.dynamic.dsl.as9105.com)
Date: 08-02-06 17:50
The Relativity of Simultaneity
Thank you for your e-mail. The Laws of Physics are independent of the number and location of the Observers so there is no possibility that your amended arrangement would result in either of your suggested consequences occurring.
Since we are considering the situation from the point of view of the observers on the train, it is the embankment that is moving and it is moving at some velocity v towards observer A' on the train.
Let us have the situation, similar to before, that the centre of the embankment is aligned exactly with the centre of the train, the switch controlling the lights is just made, that new observer A' is exactly opposite light A on the embankment and new observer B' is exactly opposite light B. Let each observer possess identical clocks and, at this instant, let all three clocks be set to zero.
Because the embankment has velocity v in the direction of A, light B is moving towards the electricity whilst light A is moving away. Thus light B illuminates before light A. Hence, illumination of the lamps is not simultaneous. The times of the illuminations will not be recorded by A' & B' as being the same.
The additional observers do not affect the sequence of events for either the observer in the centre of the train nor for the observer at the centre of the embankment, who will still see both lights come on together.
No matter what the circumstances. no matter the number or the location of the observers, no matter how complcated a scenario, it is not possible for two observers in relative motion both to agree that two events are simultaneous.
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