Simultaneity in Einstein's train-lightning thought experiment: An operational method.

Einstein's train-lightning thought experiment is used to illustrate the relativity of simultaneity. A train rider observes lightning flashes arrive at different times and concludes that the strikes must have occurred non-simultaneously at their source locations. However, this conclusion follows from Einstein's consideration that the train is at rest in its own frame, with the light traveling equal distances from each end of the train to the rider at the midpoint. This paper presents a complementary operational method that avoids such rest-frame assumptions. Instead of adopting the perspective that the train frame considers itself to be stationary, the method recognizes the rider's motion relative to fixed emission points--whether lightning or bulbs--in the ground frame. Yet the train rider is not merely performing calculations as if situated in the ground frame. Rather, the train rider uses quantities entirely from her own frame: the train's length in the train frame, a single midpoint clock on the train, the relative velocity between frames, and the constant speed of light. The question is then whether this motion fully explains the observed asymmetry in light arrival times. If it does, as it does here, then simultaneity is determined from the physical configuration alone. This approach requires no synchronized clocks and still respects the constancy of light speed in all directions. While it uses the frame of the light sources to define the emission, and the train rider now considers their own frame to be moving, this does not violate special relativity. Rather, it reflects the physical structure of the situation: The frame in which the source emissions occur provides the natural basis for evaluating whether those emissions were simultaneous. [ABSTRACT FROM AUTHOR]