Final answer:
The question mixes the operation of train lighting with relativistic physics concepts. Although lighting regulations for trains depend on visibility and safety regulations, the student seems to be asking about the Lorentz Transformation and how it affects the perception of simultaneous events from different reference frames.
Step-by-step explanation:
The question at hand deals with the concept of the Lorentz Transformation and the phenomenon of simultaneity in the context of special relativity. When discussing the illumination of running lamps and tail lamps on trains, one might refer to railways regulations which typically require these lamps to be illuminated during low visibility conditions and nighttime. However, the student's question seems to inadvertently mix this subject with a different concept related to physics: how the speed of light affects our perception of simultaneous events, like the flashing of light bulbs on a moving train, from different reference frames.
In the context of the Lorentz Transformation, an observer on the ground would perceive events happening at the same time differently than an observer on a train moving at a significant fraction of the speed of light. According to the principles of special relativity, and assuming the train is moving at a speed of c/2, the time at which the flashes are observed would indeed differ due to the relative motion between the observers. For an observer seated on a moving train, events that appear simultaneous to an observer at rest may not appear so to them.
It is essential to separate the technical aspects of railway operation from the theoretical implications of high-speed physics to prevent confusion. The question seems to have conflated operational safety procedures with relativistic physics problems involving trains as examples.