I'm confused about what exactly this is, and wikipedia hasn't really helped. It says here the proper length is the length of an object in it's rest frame. Yet it says here that "the proper length between two spacelike-separated events is the distance between the two events, as measured in an inertial frame of reference in which the events are simultaneous". If for example a train goes past a platform at a relativistic speed and an observer on the platform sees two strikes of lightning hit each end of the train simultaneously, and they're 50m apart, then what is the proper length of the train? Is it 50m because the two events are simultaneous in this frame? Or is it 50m multiplied by the lorentz factor, because this would be the value in the trains rest frame? (since for the platform observer the train appears contracted). I do not see how the two definitions are consistent and I'm not sure which one I'm supposed to use.